DIFFERENCE OF TWO SQUARES or NOT?

“On this night, we share a roof protecting us from fleets of inequity. Our unification promises a better tomorrow. Those larger than myself, sitting on their marble thrones, sipping blood from cups composed of human skin and singing songs of so-called virtue, grow weaker each moment. Their caravans are revolting. There is hope yet. There is progress! Though tonight may mark a countdown, it is still a celebration. Look at all we have done, not just for Trials but for Palatium Infra as a whole. In four years, when I’m no longer Sovereignty, the Spoiled Purity and his people will continue to strive. So drink! Smoke! Crush up those exotic plants and snort them! We will not falter, weaken, or wane. Our influence is expanding, and somebody new opens their eyes every day. Even the Silbys of Aculeus have reached alarming potentials despite their embittered minds. So long as you relish in tonight, dance, and pray to your “dead” Gods, our revolution shall rise beyond the bounds of class, and when I’m only a commoner, we shall rise again beyond our brainwashed adversaries! Cheers, my people. Cheers!” Followers raised their cups. Some clinked theirs together. Others stood still and screamed breathlessly in agreement. I smiled with courtesy, then stepped off my platform. My voice still rang across the cellar. Speeches before were grander. Those displays were supposed to be emptying, and yet this one left me bloated, swollen tight. I watched as they popped the corks of their bottles and chanted in the name of Purity. Maybe the quality of my words wasn’t what mattered to them anyway, so long as I screamed loud enough. There’s no merit in attacking your people, a voice corrected me. “That’s right,” I said aloud. “Knox, my-my Sovereign!” squealed a nearby devotee, jittering as he stuffed his face with catered pastries. He was one I’d never seen before or had failed to remember. “Look what I’ve found! It’s wine, and not the shoddy Infran kind, either. Earth-made with good fruit! I don’t know how anyone managed to get their hands on this. Maybe some space travel mischief.” He giggled and held up a small glass bottle. “How neat.” “I want you to have it, Sir.” I nodded my head. “Yes, of course. Thank you.” Backing off into the midst of rowdy disciples, I clutched the bottle. What a waste of grapes. It could have been jam instead. Earthly food had a superior taste, ripe with delicate intricacies and nostalgia, but Palatium Infra had mastered the art of alcohol. Why waste your time with a drunkenness so sad and sickening? The booze of trash. Not many more followers approached me. The barren peroration must have upset them. My hands itched to submerge into my suit pockets, and my legs stood suddenly numb, wobbling. Four more years until I’m nothing. But tonight, you are nothing. “Shut up,” I told myself. Tightly packed together in the corner of the dwelling sat the Sibyls. A mound of writhing fabric and tones of skin made up their unified silhouette. I snapped the strap of the nearest gown, balancing on my hands and knees, waving the bottle before them. In their almost rodent nature, narrow noses prodded my way. Their dresses wrinkled and fell to their ankles. Knees dropped, and eyes widened. Many grumbled at me like hungry she-beasts. Those newer ones with faded curtains for hair, sunken eyes, and dirtied nails looked, hid their face, then sobbed. I imagined them in a pack together, fighting wildly against the Spoiled Purity in their rat decorum–biting down with square teeth laced with rabies. “I’ve got you all something,” I said. “Go back off to your pedestal and yap some more. We don’t want it.” A woman rose from the pile and spat. “You don’t even know what it is yet. It's Earth hooch, or more likely a near-flawless replica. I figured you girls would also like a chance to enjoy yourselves tonight.” “Your playmates have been harassing us since the moment you hung the banners and opened the cellar door.” The youngest, with a striking cyan mop upon her head, uncoiled from the mass. What was she now? 20, 21? We celebrated a birthday recently, I thought as she spun around me. “I remember something about a promise. Multiple promises, actually. Are you trying to bribe us into just shutting up and taking it? Because if another sticky, 40-year-old, Earth-born virgin gropes my shoulder, I’m going to have an aneurysm!” the girl continued. “Why not an Infran follower? Do you like it when they touch you?” I returned her accusing tone. “I’m sorry, sweet prophets, that you feel I’ve neglected my duties. I’ll keep a better eye out. Remember, you can always just holler if somebody is bothering you. And Anwen, friend, if I’ve ever tried to bribe you with anything, it was certainly the hair dye. I mean, look at you! Such handsomeness!” I exclaimed. The other Siblys began to encircle her, uttering compliments or even announcements of their envy. Anwen disappeared in a wink with flushed cheeks back into the mound. “I’ll just leave this here.” Smiling, I set down the bottle. ** “141, 143. . .” I counted each step as I trekked the staircase. There was no doubt I lost track somewhere. The ledges kept spawning under my feet, infinitely multiplying until I wasn’t moving at all–swallowing me up in a whirlpool of stone. My tie still hung around my neck, and my blazer remained tied around my hips as a skirt. Streaks of red dribbled off from the cavity in my chest. It was a gorgeous marking, sensual to my fingertips as I traced its edges. Purity, oh, Purity. Purity and his wings of burnt skin. Purity and his many faces. Purity the spoiled. Purity the mutilated. The Silbys did not bother waiting for me. On bare feet, they stormed up the stairs to their room. A trail of red, though in paint unlike mine, streamed after them. None looked remotely near me as they squeaked and gossiped intangibly. I saved them, those Infran broads, enlightened them. As much as they liked to deny it, spit at me, and bask in the thought of their victimhood, in this home, they stood empowered. You’ve done well, my thoughts affirmed, though in the manner of an insincere commentator rather than a hype man. Teeth grace in tile violin goes laundry paper when. It dissolved into an intruding drivel. I rubbed my head and sniveled. “Do you need help, Knox?” called a Silby. Fattened by my coddling, her shadow fell upon me from the doorway steps ahead. I attempted counting again. There must’ve been at least another hundred between me and her. “I’m hallucinating some,” I said, breathing deeply to suppress a burp as I struggled to recall her name. Two syllables. Typically Latin, though sometimes English. Drops of slobber leaked from my mouth. “I’m hallucinating some, Tybal. Do you like your name, Tybal? I would have named you something better. Ty-Tyballinia. No, we’d have to eliminate the ‘ball’ aspect. It sounds too crude.” “One foot in front of the other,” she said. So I walked. Mess greeted me at the doorway. Dirtied culinary obscured the dark wooden countertops, and the sink lay running. I approached the kitchen table, sat, and set my face down upon its cool wooden surface. Assaulting my nose was the smell of neglected flowers, like soil mixed with the kind of sweet cough medicine that would have left me gagging as a child. Open windows whispered songs of the twilight hour through the vessels of busy trolleys and shooting guns. My mouth strained to vomit, but there was nothing in my stomach to regurgitate except the petals of Stulto’s bloom, which came out effortlessly in little sputters. Teetering, I stood up and brushed disgorged plant parts off the tabletop. “Love,” I said as I slogged up yet another staircase. “Are you awake?” She said she’d wait. Somebody’s gotten her. No, she always misses movie night. That sleepyhead, I assured myself. There was a stirring amidst the manor’s cloak of dusk. Portraits of myself, my wife, and my daughter turned to face me as the hallway lights flickered, escaping their quartz frames to penetrate my ears with nonsense. The taxidermied heads of Infran creatures bared their teeth. I stopped to stare at my favorite, an adabactor with daunting spiked tusks poking out from its forehead. Its nose remained black and sharp, and its eyes wide with malice. “Where is my Spes, Adaba-boy? Is she sleepy?” There’s someone in the house. The sounds of the stirring rose along with my blood pressure. Footsteps orbited around me, drawing near and far and then near again, little dancers in the dark. The carpet immersed me in its mass of purples and blues, leaving my skin stained indigo and my vision abstracted. I toiled to reach the master bedroom across the aisle as it stretched out to me with bright lights and celestial howling, like a dove struggling in a pool of oil. Never again with Stulto’s bloom. Never again on what was already a bad night. My hand brushed the doorknob, and the high abruptly faded into only a persistent hum-buzz twirling around my brain. The portraits returned to their typical depression–Spes posing with her ax, Ari’s school photo, and myself in the cap I wore when addressing the military with the Verbis emblem embroidered in its center. All lifeless shots. Who were they for when they captured not the subject’s essence but only some fragment of their identity? They used to feel personal, not advertisements of some supposed characters. Servants, babysitters, and likewise civilian guests, I reminded myself, mustn’t forget whose home they’re in. Yet my body moved independently, taking Ari’s from its hook and laying it backward against the wall to hide her distant grin and tamed posture. It was time for new pictures. Sweet ones, real ones; time was ticking. I approached my own when the stirring began again. Groans and squeals erupted from the vents as if someone had set a pen of pigs loose in my crawlspace. No, not the crawlspace, my bedroom door. I turned the ruby knob. Underneath a blanket wrestled my two squealing piglets, their skins melting together beneath the layer of duvet. Fishnet leggings and manicured nails outstretched and scraped at the sheet beneath them. One raised its head, a salmon-colored man with sweat running down his forehead. Through the crack in the door, we met eyes, his Infran Dr. Sesuss nose flaring its narrow nostrils. No mark of the Spoiled Purity existed carved onto his naked body. My chest felt tight. I stepped back. I was suffocating. Spes emerged from the linens, her hair flowing down her back and her dark skin glistening in front of the bedroom window. She giggled and held the man, the blanket falling and revealing inches of her body I had not seen in months. “Darling,” whispered the rosy-faced man, “look.” He was unfathomably ugly and grotesquely young, with beady, lifeless pupils that dilated when he faced me. The excess flesh on his face sagged while he bit down on his thin lips. My wife faced me, gasped, and strained to cover herself. Suddenly, I was a stranger. A small child who had walked into his parents having sex. I unfurled the door completely. “Get out of my house,” I said. The man stayed in place. “Get out of my house,” I repeated. “Knox,” Spes began. Tears ran down her round cheeks. “Shut up!” I turned to the man, picking up a marble trophy from on top of my dresser. “Get out of my house! I’ll kill you!” “Knox!” Spes sobbed. “God damn it! I hate you! You barely look at me. Every day, there’s less passion. God, God, God, I don’t want to fuck a dead man!” she screamed, “You get out! Get! Get!” My hands wrapped tighter around the statue. That pig of a man was attached to her at the side, his face equipped with a scowl that challenged mine. He thought I was weak; frail like a decaying dementia-ridden senior. I imagined his skull bashed in, his scowl gone, and the feist and confidence in his face beaten into numbness. A new portrait was in order of such brutality, him as a splintered slab of wood, rashed and beaten, a carcass licking my boot. The churning in my brain had come back. Every wall shook. Clock faces came to life and rang in alarm. Indescribable noises caressed my eardrum before breaking into sorrowful weeps. Was it my own? I stared at Spes in motionless frenzy, clenched my teeth, and screamed like a siren. Passionless. What a lie! An excuse, more like. One that erased all my ventures, reducing me to a nobody. But I was not a nobody. I thought of my sect, my campaigns, my endurance through the political brutality of my empty hive-mind world–even my collection of literature, maps, and artifacts. I thought of daring nights alone with Spes when we were young, ravaging each other, two sardonic eggheads suddenly overcome with desire. The veins in my neck throbbed as I gasped for air. It was all I had. I threw the figurine at the man’s head. Eye shut, I heard the thud. A million singing voices of victory flooded out of the cracks in the floorboard. Proving myself a man to the woman I loved in a display of fervent violence was passion. I strained my ears for his cries, though I did not look yet. There had to be a pause, a moment of relief, where I stood tall as a skyscraper and seemingly fought to stay contained in front of my wife and her wounded, quivering paramour. Frantic footsteps rushed off the bed and past my side. I turned and grappled against myself to seize my wife’s shoulder. “Spes!” My eyelids lifted. Escaping was the man with that same numb expression in which I had imagined him. “You’re insane,” he said. I swiveled back towards the bed. With her curly locks flowing over her breasts and her limbs bent at her sides, Spes sat limp pressed against the headboard, her forehead bludgeoned and the statue resting on her stomach. Lips pursed and sweet, my Renaissance beauty reclined there in the guise of a squashed bug. But she was not dead. The desk ornament I flung was only the size of my shoe. Spes, that dramatist, may have been slightly hurt but was far from dead. She only wanted me to think she was to observe me at my most distraught, like a leech feeding on misery. “Get up.” Staggering toward the bed, I said. “You wanted passion? I showed you passion. ‘Shoved it right into your head. Of course, we both know who that gesture was meant for. . .” I fumbled to find my wit. Cold skin met my hands as I stroked her face, unable to resist checking her pulse, even though she was not dead. “I love you, Spes,” I said. Rain pelted against a nearby window. “Spes, please. Please.” No vibration answered my plea. I lifted my hand, sitting next to her now. Tears did not come. There was not any blood on the trophy, but when I picked it up, it felt to be now only a cruel instrument. It depicted a younger me in white marble, with my glasses and collared shirt being the only things painted. Both were in pink. It was a favorable color. I scrambled from the bed to vomit pure digestive bile on the rug. My stomach heaved. I ran my nails along every piece of myself I saw, a dog chasing my tail. As I slammed myself against walls and convulsed, my own heart grew ever louder in my chest. “Dad? I heard–” Ari’s slippered feet hammered across the floor. “Mom? Mom?” I kept my eyes on the storm. Silence fell. “She-She isn’t—your—.” Gasps interrupted every syllable she spoke. “You’re a murderer. Bad. Like they said,” she breathed, “ You beat her!” The words became mush, alphabet soup. Ari ran back down the hall. “My-My mom is dead. . . .Yes. . . Manor of the Trials Sovereignty. . .Ari Sorkin. . . I’m afraid he’s going to hurt me,” she said, presumably over the phone. It was all too fast. I crawled onto the windowsill, opened the glass, and let myself plummet into the alley below. Gusts of wind howled. The lack of motion or sensation informed me I had passed and again lived. Another Palatium Infra, another strange planet in which the celestial endowed rotting men with the opportunity to inhabit. Was this it? Was it all just an impossible limbo of galactic traveling? My surroundings were overwhelmingly gray, an abyss of clouds. Perhaps I had now met the real coming world, and my family and old friends lived here, ready to rush to my sides, lift me up, and jump for joy. Spes would be there. She would be enraged, but at least she’d be there. You are a bad man. You are a bad man. My eyelashes fluttered. There was a tugging sensation in my leg. The fog was wavering along with my ascendance. “No,” I yearned, trying to grip the clouds and stick them in place. “Stay with me.” But the peace was fleeting. I felt the cement under me and the moist garments clinging to my figure. My leg burned. Carefully, I craned my neck, only to observe the promenade as my surroundings. The most underwhelming of filth and danger, individually Infran. Forever my coming world. What a fool I was, having forgotten my blessing. Those idiot Gods could not tell the difference between assassination and self-infliction; a faulty insurance plan. The urge to cry at last set over me, and so I sat and wailed hot salvia into my palm, shielding my mouth to muffle the noise. Thunder echoed my hushed howling. Raindrops turned to pebbles. Under the ambiance of the stormy night, I could have sworn I heard troops stomping, guns cocking, and the chanting of my name. They had all been waiting for this. Billboards came to life, and I could only sit and spectate as the scenery flashed red. I inhaled fear and sobriety through runny nostrils. “Trials Sovereign Vsevolod “Knox” Sorkin is currently at large for the suspected homicide of Spes Sorkin, breaking the first term of the Sovereignty Charter. We now instruct you to report any sightings of the Earth-born, caucasian, roughly 195 centimeters tall, brown-haired, and brown-eyed man to your local Guard post. One can identify the suspected convict specifically by an occult tattoo of Purity’s Coronet on his lower back. No attempted execution or elongated punishment will take place until our Guards conduct an autopsy proving his guilt, per Life’s 1238 commandment. We cannot be sure when or if the Gods will revoke his blessing. Remember, when Gods frown upon strife, opt for a peaceful life. We permit all grieving festivities until Cagidus 4th. Good year!” towering buildings sang out in broadcast, repeating that same convoluted message quicker the instant it ended. Sometimes, the announcer spoke in Latin for the Infran children, other times in Chinese, Hindi, or Spanish to cater to those of irrelevant tongues. You aren’t a bad man. You are a stupid boy. Puddles sloshed. Somebody was approaching. I didn’t dare waste any remaining energy avoiding the Guards and their prodding blades. How did that phrase go? You dug your grave. Now lie in it. And so I embraced the cement. “Knox?” said the Guard. No, her tone was too sincere, and no authority would proceed in such a manner. There wasn’t confirmation on whether or not I was armed, and it wasn’t as if she could shoot me first. She was a partygoer, having just left from the cellar’s backdoor. I shooed her away with my hand. She hovered, and I discerned her shadow hesitating over my body. A man could not rot in peace. “Come on, get up! They’re after you!” Hands reached around my torso, struggling to handle my weight as they urged me onto my feet. That leg, the burning one, my right, trembled and bent unnaturally upon impact with the ground. The partygoer slung my arm over her shoulder, balancing me. My eyes caught a glimpse of a cyan mop. “Anwen?” I rasped, “hu-who let you out?” Keys jangled in her hands–my keys. “I escaped,” she said casually, coercing me to walk beside her. “Quicken your pace. I just heard somebody on your front porch. ‘You see that compost bin down the alley? We’re gonna burrow right down into the depth of that. If they open it and uncover us, I’ll be on top, and I can hide you and act like I’m just a homeless amica trying to take a nap.” With a tightening grip, she led me like livestock to the stinking crate. “I don’t understand, Anwen,” I said. “They’re going to torture and kill you, stupid. You know they’ve been wanting to, and you just handed the opportunity to them!” “I understand that.” It was becoming increasingly challenging to hide the fragility emerging in my voice. “You said you were escaping. Why stop and help your captor?” “What else could I do? Leave you there?” Attempts to shove my wounded body inside its mass of discarded fruits and vegetables began. She yanked down upon my head and submerged me in the fertilizer sea. The evidence grows indisputable, I thought as I stared at the abruptly humane Infran girl, diving in after me, that I belong here. “Damn me to hell! I’ve killed her! My love is dead!” an uncontrollable cry leaped from my mouth. “Shut up! Soon you’ll be, too, if you don’t quiet down.” The actual noise of the Guards darted past us: disorientated marching, guns clanking against each other, cluttered belts rattling, the Latin squawking. One paused to open the bin’s lid, though only rummaged through the surface layer of peat before carrying on. “What are they talking about? I struggle with my Latin,” I whispered. “The search, mainly.” Aggression remained firey in Anwen’s clenched jaw. Though she sat on top of me, there was a monumental distance between our rain-soaked forms. I curled up into a ball, ducked my head between my knees, and dreamt of Spes, ignoring the stench of spoiled food rising from every crevice of my dwelling. The next coming world was due to adopt me again as I forced sleep. I prayed for a canyon of fluffy haze, where I waltzed with pale memories but found nothing but the petrifying stillness of my mind. Killed and ran. Violent as a Guard just to prove a point and watch it backfire. Why would any heaven want to welcome me? I clung to the picture of Spes in my head like it was the last ember of an extinguished flame. “Did you mean to kill her?” Anwen interrogated. “Someone like you would immutably believe yes.” “And who is someone like me? You can’t even treat me like a person for a moment, can you?” grating drama decorated her words. “You know my opinions. I have not seen much of your or your breed’s faces besides that of cruelty and ignorance.” I retorted. “I just saved you! Does that make me cruel and ignorant?” “It makes you an idiot, which is another word for somebody ignorant.” “And why am I an idiot?” She asked. “Because you helping me does no good. Thank you anyhow. Now, do yourself a favor and scram.” As she bent her leg in anticipation, preparing to strike me on the forehead, I sensed an invisible withdrawal widening the gap between us. “You never answered my question,” Anwen took me by the end of my tattered tie suddenly and started her game of shepherd and sheep over again, pulling me back up to the crate’s exit. It appeared as a shining light at the end of a maze of rubbish and mold. “No. Of course not. Spes was my everything,” I sniffled. “I knew it. You couldn’t even bring yourself to hit us, let alone murder your wife. The girls and I always figured you were sensitive.” My heart rate quickened. Today was one of humbling and misery–one to pray a hail spike would fall from the sky as sharp as a needle, pierce into my eyelid, and lobotomize me. I wished I could have merely died or hit my head hard enough not to have to deal with it all. No, I wished I was Anwen with her snarky, careless glow and lack of depth in her eyes. As we emerged from the compost bin together, I fantasized about strangling her until her face turned purple, her weakening spirit no longer categorizing me as “sensitive”, but the thought could only remind me of wielding that trophy and the microscopic traces of my wife’s tender skin tainting it, which turned my guts inside out. “That’s why I think you could use a little help,” Anwen said, “It seems like you can’t walk, either. Your leg is all twisted up.” She undid one of her trim pigtails and handed me the band. “Take off your tie and put up your hair. ‘Will make you less recognizable. Then swallow your pride and stick with me.”

If and , then the difference between the largest and smallest possible values of is The integer 2019 can be formed by placing two consecutive two-digit positive integers, 19 and 20, in decreasing order. What is the sum of all four-digit positive integers greater than 2019 that can be formed in this way? We call the pair of positive integers a if the greatest common divisor of and is a perfect square. For example, is a happy pair because the greatest common divisor of 20 and 24 is 4. Suppose that is a positive integer such that is a happy pair. The number of possible values of with is 3628243027 Starting with a positive integer , Alicia creates a sequence by applying the following algorithm: Step 1: Alicia writes down the number as the first term of the sequence. Step 2: If is even, Alicia sets . If is odd, Alicia sets . Step 3: Alicia writes down the number as the next term of the sequence. Step 4: Alicia sets equal to the value of the term that she just wrote down in Step 3. Step 5: Alicia repeats Steps 2, 3, 4 until she has five terms, at which point she stops. For example, starting with , Alicia’s sequence would be 1, 4, 7, 16, 25. Alicia starts a sequence with . What is the fifth term of her sequence? A lock code is made up of four digits that satisfy the following rules: At least one digit is a , but neither the second digit nor the fourth digit is a . Exactly one digit is a , but the first digit is not . Exactly one digit is a . The code includes a , or the code includes a , or the code includes two s. How many codes are possible?

THE FIDE LAWS OF CHESS. Introduction FIDE Laws of Chess cover over-the-board play. The Laws of Chess have two parts: 1. Basic Rules of Play and 2. Competitive Rules of Play. The English text is the authentic version of the Laws of Chess (which were adopted at the 93rd FIDE Congress at Chennai, India) coming into force on 1 January 2023. Preface. The Laws of Chess cannot cover all possible situations that may arise during a game, nor can they regulate all administrative questions. Where cases are not precisely regulated by an Article of the Laws, it should be possible to reach a correct decision by studying analogous situations which are regulated in the Laws. The Laws assume that arbiters have the necessary competence, sound judgement and absolute objectivity. Too detailed a rule might deprive the arbiter of his/her freedom of judgement and thus prevent him/her from finding a solution to a problem dictated by fairness, logic and special factors. FIDE appeals to all chess players and federations to accept this view. A necessary condition for a game to be rated by FIDE is that it shall be played according to the FIDE Laws of Chess. It is recommended that competitive games not rated by FIDE be played according to the FIDE Laws of Chess. Member federations may ask FIDE to give a ruling on matters relating to the Laws of Chess. BASIC RULES OF PLAY. Article 1: The Nature and Objectives of the Game of Chess 1.1 1.2 1.3 1.4 The game of chess is played between two opponents who move their pieces on a square board called a ‘chessboard’. The player with the light-coloured pieces (White) makes the first move, then the players move alternately, with the player with the dark-coloured pieces (Black) making the next move. A player is said to ‘have the move’ when his/her opponent’s move has been ‘made’. The objective of each player is to place the opponent’s king ‘under attack’ in such a way that the opponent has no legal move. 1.4.1 The player who achieves this goal is said to have ‘checkmated’ the opponent’s king and to have won the game. Leaving one’s own king under attack, exposing one’s own king to attack and also ’capturing’ the opponent’s king is not allowed. 1.4.2 The opponent whose king has been checkmated has lost the game. 1.5 If the position is such that neither player can possibly checkmate the opponent’s king, the game is drawn (see Article 5.2.2). Article 2: The Initial Position of the Pieces on the Chessboard 2.1 2.2 The chessboard is composed of an 8 x 8 grid of 64 equal squares alternately light (the ‘white’ squares) and dark (the ‘black’ squares). The chessboard is placed between the players in such a way that the near corner square to the right of the player is white. At the beginning of the game White has 16 light-coloured pieces (the ‘white’ pieces); Black has 16 dark-coloured pieces (the ‘black’ pieces). These pieces are as follows: A white king usually indicated by the symbol K A white queen Two white rooks Two white bishops Two white knights Eight white pawns A black king A black queen Two black rooks Two black bishops Two black knights Eight black pawns usually indicated by the symbol Q usually indicated by the symbol R usually indicated by the symbol B usually indicated by the symbol N usually indicated by the symbol usually indicated by the symbol K usually indicated by the symbol Q usually indicated by the symbol R usually indicated by the symbol B usually indicated by the symbol N usually indicated by the symbol Staunton Pieces p Q K B N R 9 2.3 The initial position of the pieces on the chessboard is as follows: 2.4 The eight vertical columns of squares are called ‘files’. The eight horizontal rows of squares are called ‘ranks’. A straight line of squares of the same colour, running from one edge of the board to an adjacent edge, is called a ‘diagonal’. Article 3: The Moves of the Pieces 3.1 It is not permitted to move a piece to a square occupied by a piece of the same colour. 3.1.1 If a piece moves to a square occupied by an opponent’s piece the latter is captured and removed from the chessboard as part of the same move. 3.1.2 A piece is said to attack an opponent’s piece if the piece could make a capture on that square according to Articles 3.2 to 3.8. 3.1.3 A piece is considered to attack a square even if this piece is constrained from moving to that square because it would then leave or place the king of its own colour under attack. 3.2 The bishop may move to any square along a diagonal on which it stands. 3.3 The rook may move to any square along the file or the rank on which it stands. 3.4 The queen may move to any square along the file, the rank or a diagonal on which it stands. 3.5 3.6 3.7 When making these moves, the bishop, rook or queen may not move over any intervening pieces. The knight may move to one of the squares nearest to that on which it stands but not on the same rank, file or diagonal. 3.7 When making these moves, the bishop, rook or queen may not move over any intervening pieces. The knight may move to one of the squares nearest to that on which it stands but not on the same rank, file or diagonal. The pawn: 3.7.1 The pawn may move forward to the square immediately in front of it on the same file, provided that this square is unoccupied, or 3.7.2 on its first move the pawn may move as in 3.7.1 or alternatively it may advance two squares along the same file, provided that both squares are unoccupied, or 3.7.3 the pawn may move to a square occupied by an opponent’s piece diagonally in front of it on an adjacent file, capturing that piece. 3.7.3.1 A pawn occupying a square on the same rank as and on an adjacent file to an opponent’s pawn which has just advanced two squares in one move from its original square may capture this opponent’s pawn as though the latter had been moved only one square. 3.7.3.2 This capture is only legal on the move following this advance and is called an ‘en passant’ capture. 3.7.3.3 When a player, having the move, plays a pawn to the rank furthest from its starting position, he/she must exchange that pawn as part of the same move for a new queen, rook, bishop or knight of the same colour on the intended square of arrival. This is called the square of ‘promotion’. 3.7.3.4 The player's choice is not restricted to pieces that have been captured previously. 3.7.3.5 This exchange of a pawn for another piece is called promotion, and the effect of the new piece is immediate. 3.8 There are two different ways of moving the king: 3.8.1 by moving to an adjoining square. 3.8.2 by ‘castling’. This is a move of the king and either rook of the same colour along the player’s first rank, counting as a single move of the king and executed as follows: the king is transferred from its original square two squares towards the rook on its original square, then that rook is transferred to the square the king has just crossed. 3.8.2.1 The right to castle has been lost: 3.8.2.1.1 If the king has already moved, or 3.8.2.1.2 With a rook that has already moved. 3.8.2.2 Castling is prevented temporarily: 3.8.2.2.1 if the square on which the king stands, or the square which it must cross, or the square which it is to occupy, is attacked by one or more of the opponent's pieces, or 3.8.2.2.2 if there is any piece between the king and the rook with which castling is to be effected. 3.9 The king in check: 3.9.1 The king is said to be 'in check' if it is attacked by one or more of the opponent's pieces, even if such pieces are constrained from moving to the square occupied by the king because they would then leave or place their own king in check. 3.9.2 No piece can be moved that will either expose the king of the same colour to check or leave that king in check. 3.10 Legal and illegal moves; illegal positions: 3.10.1 A move is legal when all the relevant requirements of Articles 3.1 – 3.9 have been fulfilled. 3.10.2 A move is illegal when it fails to meet the relevant requirements of Articles 3.1 –3.9. 3.10.3 A position is illegal when it cannot have been reached by any series of legal moves. Article 4: The Act of Moving the Pieces 4.1 4.2 Each move must be played with one hand only. Adjusting the pieces or other physical contact with a piece: 4.2.1 Only the player having the move may adjust one or more pieces on their squares, provided that he/she first expresses his/her intention (for example by saying “j’adoube” or “I adjust”). 4.2.2 Any other physical contact with a piece, except for clearly accidental contact, shall be considered to be intent. 4.3 Except as provided in Article 4.2.1, if the player having the move touches on the chessboard, with the intention of moving or capturing: 4.3.1 one or more of his/her own pieces, he/she must move the first piece touched that can be moved. 4.3.2 one or more of his/her opponent’s pieces, he/she must capture the first piece touched that can be captured. 4.3.3 one or more pieces of each colour, he/she must capture the first touched opponent’s piece with his/her first touched piece or, if this is illegal, move or capture the first piece touched that can be moved or captured. If it is unclear whether the player’s own piece or his/her opponent’s was touched first, the player’s own piece shall be considered to have been touched before his/her opponent’s. 4.4 If a player having the move: 4.4.1 touches his/her king and a rook he/she must castle on that side if it is legal to do so 4.4.2 deliberately touches a rook and then his/her king he/she is not allowed to castle on that side on that move and the situation shall be governed by Article 4.3.1. 4.4.3 intending to castle, touches the king and then a rook, but castling with this rook is illegal, the player must make another legal move with his/her king (which may include castling with the other rook). If the king has no legal move, the player is free to make any legal move. 4.4.4 promotes a pawn, the choice of the piece is finalised when the piece has touched the square of promotion. 4.5 4.6 If none of the pieces touched in accordance with Article 4.3 or Article 4.4 can be moved or captured, the player may make any legal move. The act of promotion may be performed in various ways: 4.6.1 the pawn does not have to be placed on the square of arrival. 4.6.2 removing the pawn and putting the new piece on the square of promotion may occur in any order. 4.6.3 If an opponent’s piece stands on the square of promotion, it must be captured. 4.7 When, as a legal move or part of a legal move, a piece has been released on a square, it cannot be moved to another square on this move. The move is considered to have been made in the case of: 4.7.1 A capture, when the captured piece has been removed from the chessboard and the player, having placed his/her own piece on its new square, has released this capturing piece from his/her hand. 4.7.2 Castling, when the player's hand has released the rook on the square previously crossed by the king. When the player has released the king from his/her hand, the move is not yet made, but the player no longer has the right to make any move other than castling on that side, if this is legal. If castling on this side is illegal, the player must make another legal move with his/her king (which may include castling with the other rook). If the king has no legal move, the player is free to make any legal move. 4.7.3 Promotion, when the player's hand has released the new piece on the square of promotion and the pawn has been removed from the board. 4.8 4.9 A player forfeits his/her right to claim against his/her opponent’s violation of Articles 4.1 – 4.7 once the player touches a piece with the intention of moving or capturing it. 4.8. A player forfeits his/her right to claim against his/her opponent’s violation of Articles 4.1 – 4.7 .4.9. If a player is unable to move the pieces, an assistant, who shall be acceptable to the arbiter, may be provided by the player to perform this operation. Article 5: The Completion of the Game 5.1.1 The game is won by the player who has checkmated his/her opponent’s king. This immediately ends the game, provided that the move producing the checkmate position was in accordance with Article 3 and Articles 4.2 – 4.7. 5.1.2 The game is lost by the player who declares he/she resigns (this immediately ends the game), unless the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves. In this case the result of the game is a draw. 5.2.1 The game is drawn when the player to move has no legal move and his/her king is not in check. The game is said to end in ‘stalemate’. This immediately ends the game, provided that the move producing the stalemate position was in accordance with Article 3 and Articles 4.2 – 4.7. 5.2.2 The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7. 5.2.3 The game is drawn upon agreement between the two players during the game, provided both players have made at least one move. This immediately ends the game. COMPETITIVE RULES OF PLAY Article 6: The Chessclock 6.1 ‘Chessclock’ means a clock with two time displays, connected to each other in such a way that only one of them can run at a time. ‘Clock’ in the Laws of Chess means one of the two time displays. Each time display has a ‘flag’. ‘Flag-fall’ means the expiration of the allotted time for a player. 6.2 Handling the chessclock: 6.2.1 During the game each player, having made his/her move on the chessboard, shall pause his/her own clock and start his/her opponent’s clock (that is to say, he/she shall press his/her clock). This “completes” the move. A move is also completed if: 6.2.1.1 6.2.1.2 the move ends the game (see Articles 5.1.1, 5.2.1, 5.2.2, 9.2.1, 9.6.1 and 9.6.2), or the player has made his/her next move, when his/her previous move was not completed. 6.2.2 A player must be allowed to pause his/her clock after making his/her move, even after the opponent has made his/her next move. The time between making the move on the chessboard and pressing the clock is regarded as part of the time allotted to the player. 6.2.3 A player must press his/her clock with the same hand with which he/she made his/her move. It is forbidden for a player to keep his/her finger on the clock or to ‘hover’ over it. 6.2.4 The players must handle the chessclock properly. It is forbidden to press it forcibly, to pick it up, to press the clock before moving or to knock it over. Improper clock handling shall be penalised in accordance with Article 12.9. 6.2.5 6.2.6 Only the player whose clock is running is allowed to adjust the pieces. If a player is unable to use the clock, an assistant, who must be acceptable to the arbiter, may be provided by the player to perform this operation. His/Her clock shall be adjusted by the arbiter in an equitable way. This adjustment of the clock shall not apply to the clock of a player with a disability. 6.3 Allotted time: 6.3.1 When using a chessclock, each player must complete a minimum number of moves or all moves in an allotted period of time including any additional amount of time added with each move. All these must be specified in advance. 6.3.2 The time saved by a player during one period is added to his/her time available for the next period, where applicable. In the time-delay mode both players receive an allotted ‘main thinking time’. Each player also receives a ‘fixed extra time’ with every move. The countdown of the main thinking time only commences after the fixed extra time has expired. Provided the player presses his/her clock before the expiration of the fixed extra time, the main thinking time does not change, irrespective of the proportion of the fixed extra time used. 6.4 Immediately after a flag falls, the requirements of Article 6.3.1 must be checked. 6.5 Before the start of the game the arbiter shall decide where the chessclock is placed. 6.6 At the time determined for the start of the game White’s clock is started.6.7. Default time: 6.7.1 The regulations of an event shall specify a default time in advance. If the default time is not specified, then it is zero. Any player who arrives at the chessboard after the default time shall lose the game unless the arbiter decides otherwise. 6.7.2 If the regulations of an event specify that the default time is not zero and if neither player is present initially, White shall lose all the time that elapses until he/she arrives, unless the regulations of an event specify, or the arbiter decides otherwise. 6.8 A flag is considered to have fallen when the arbiter observes the fact or when either player has made a valid claim to that effect. 6.9 Except where one of Articles 5.1.1, 5.1.2, 5.2.1, 5.2.2, 5.2.3 applies, if a player does not complete the prescribed number of moves in the allotted time, the game is lost by that player. However, the game is drawn if the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves. 6.10 Chessclock setting: 6.10.1 Every indication given by the chessclock is considered to be conclusive in the absence of any evident defect. A chessclock with an evident defect shall be replaced by the arbiter, who shall use his/her best judgement when determining the times to be shown on the replacement chessclock. 6.10.2 If during a game it is found that the setting of either or both clocks is incorrect, either player or the arbiter shall pause the chessclock immediately. The arbiter shall install the correct setting and adjust the times and move-counter, if necessary he/she shall use his/her best judgement when determining the clock settings. 6.11.1 If the game needs to be interrupted, the arbiter shall pause the chessclock. 6.11.2 A player may pause the chessclock only in order to seek the arbiter’s assistance, for example when promotion has taken place and the piece required is not available. 6.11.3 The arbiter shall decide when the game restarts. 6.11.4 If a player pauses the chessclock in order to seek the arbiter’s assistance, the arbiter shall determine whether the player had any valid reason for doing so. If the player has no valid reason for pausing the chessclock, the player shall be penalised in accordance with Article 12.9. 6.12.1 Screens, monitors, or demonstration boards showing the current position on the chessboard, the moves and the number of moves made/completed, and clocks which also show the number of moves, are allowed in the playing hall. 6.12.2 The player may not make a claim relying only on information shown in this manner.

Allele variation of a specific gene Artificial Insemination (AI) collecting and preserving semen from sires and using artificial means to introduce it to the dam’s reproductive tract Body Cells make up the organs and tissue of an animal and have chromosomes in pairs, called diploids Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR) gene editing technology Codominance heterozygous individual expresses the phenotype of both alleles simultaneously Complete Dominance heterozygous gene pair is expressed the same as a homozygous dominant gene pair Crossbreeding sire from one breed and a dam from another, with each breed excelling in a certain characteristic to benefit the producer and the offspring Deoxyribonucleic Acid (DNA) stores genetic information and acts as a blueprint for all genetic material in the organism in two strands arranged in a double helix Dominant Alleles represent a dominant phenotype and are expressed as uppercase letters Embryo Transfer eggs are collected from a desirable female, fertilized and then implanted in several other females Expected Progeny Differences (EPDs) measure of the heritability of breeding values and traits Gametes fulfill the purpose of sexual reproduction, passing on half of the genetic code in the form of sperm and ovum and are also called haploids or sex cells Genotype organism's genetic composition, which determines its heredity potential and limitations Grading Up using a purebred sire to breed grade (unregistered or commercial) females Heritability degree to which offspring resemble their parent for a particular trait Heterosis (Hybrid Vigor) ability of crossbred animals to have the best traits from each parent Heterozygosity phenomenon of inheriting a different version of an allele from each biological parent Homozygosity phenomenon of inheriting the same version of an allele from each biological parent Inbreeding breeding of closely related animals with the goal of concentrating traits from a superior individual Incomplete Dominance dominant allele does not completely overcome the recessive Law of Dominance states genes will express themselves with the dominant gene appearing in the phenotype Law of Independent Assortment states unlinked or distantly linked gene pairs separate independently of other genes Law of Segregation states paired genes must segregate equally into gametes in a way so offspring have an equal likelihood of inheriting either factor Locus place on a chromosome where a gene is found Meiosis process of cellular reproduction of gametes and results in four genetically different daughter cells Mitosis process of cellular reproduction of body cells which creates two genetically identical daughter cells Outcrossing breeding highly unrelated individuals within a breed Phenotype all the observable characteristics of an organism resulting from the interaction of its genotype with its environment Polygenic Traits controlled by many gene pairs Punnett Square graphical representation of the possible genotypes of an offspring arising from a particular breeding, using letters to represent the genes Recessive Alleles non-dominant phenotypes which can still affect the appearance of an animal, but not as commonly, and are expressed as lowercase letters Ribonucleic Acid (RNA) replicates genetic information found in DNA to build proteins in processes known as transcription and translation Simply Inherited Traits typically controlled by one gene pair

A BAD CASE OF THE STRIPES By David Shannon Parts(18): Camilla Narrator 1 Narrator 2 Narrator 3 Narrator 4 Mr. Harms Mother Father Dr. Bumble Old Woman Environmental Therapist Dr. Grop Dr. Gourd Dr. Sponge Mr. Mellon Dr. Cricket Dr. Young <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> Narrator 1: A BAD CASE OF THE STRIPES By David Shannon Narrator 2: Camilla Cream loved lima beans. But she never ate them. Narrator 3: All of her friends hated lima beans, and she wanted to fit in. Camilla always worried about what other people thought of her. Narrator 4: Today she was fretting even more than usual. It was the very first day of school, and she couldn't decide what to wear. There were so many people to impress! Narrator 1: She tried on forty-two outfits, but none seemed quite right. She put on a pretty red dress and looked in the mirror. Then she screamed. Narrator 2: Her mother ran into the room, and she screamed, too. Mother: "Oh my heavens! You're completely covered with stripes!" Narrator 3: she cried. This was certainly true. Camilla was striped from head to toe. She looked like a rainbow. Narrator 4: Mrs. Cream felt Camilla's forehead. Mother: "Do you feel all right?" Narrator 1: she asked. Camilla: "I feel fine, but just look at me!" Narrator 2: Camilla answered. Mother: "You get back in bed this instant. You're not going to school today." Narrator 3: her mother ordered. Camilla was relieved. She didn't want to miss the first day of school, but she was afraid of what the other kids would say. And she had no idea what to wear with those crazy stripes. Narrator 4: That afternoon, Dr. Bumble came to examine Camilla. Dr. Bumble: "Most extraordinary! I've never seen anything like it! Are you having any coughing, sneezing, runny nose, aches, pains, chills, hot flashes, dizziness, drowsiness, shortness of breath, or uncontrollable twitching?" Narrator 1: he asked. Camilla: "No, I feel fine." Narrator 2: Camilla told him. Dr. Bumble: "Well then, I don't see any reason why she shouldn't go to school tomorrow. Here's some ointment that should help clear up those stripes in a few days. If it doesn't, you know where to reach me." Narrator 3: Dr. Bumble said, turning to Mrs. Cream. And off he went. Narrator 4: The next day was a disaster. Everyone at school laughed at Camilla. They called her "Camilla Crayon" and "Night of the Living Lollipop." Narrator 1: She tried her best to act as if everything were normal, but when the class said the Pledge of Allegiance, her stripes turned red, white, and blue, and she broke out in stars! Narrator 2: The other kids thought this was great. One yelled out, Narrator 3: "Let's see some purple polka dots!" Narrator 4: Sure enough, Camilla turned all purple polka-dotty. Someone else shouted, Narrator 1: "Checkerboard!" Narrator 4: and a pattern of squares covered her skin. Soon everyone was calling out different shapes and colors, and poor Camilla was changing faster than you can change channels on a T.V. Narrator 2: That night, Mr. Harms, the school principal, called. Mr. Harms: "I'm sorry, Mrs. Cream, I'm going to have to ask you to keep Camilla home from school. She's just too much of a distraction, and I've been getting phone calls from the other parents. They're afraid those stripes may be contagious." Narrator 3: he said. Camilla was so embarrassed. She couldn't believe that two days ago everyone liked her. Now, nobody wanted to be in the same room with her. Narrator 1: Her father tried to make her feel better. Father: "Is there anything I can get you, sweetheart?" Narrator 2: he asked. Camilla: "No, thank you," Narrator 3: sighed Camilla. What she really wanted was a nice plate of lima beans, but she had been laughed at enough for one day. Dr. Bumble: "Hmm, well, yes, I see. I think I'd better bring in the Specialists. We'll be right over.” Narrator 4: said Dr. Bumble to Mr. Cream on the phone. About an hour later, Dr. Bumble arrived with four people in long white coats. He introduced them to the Creams. Dr. Bumble: "This is Dr. Grop, Dr. Sponge, Dr. Cricket, and Dr. Young." Narrator 1: Then the Specialists went to work on Camilla. They squeezed and jabbed, tapped and tested. It was very uncomfortable. Dr. Grop: "Well, it's not the mumps." Dr. Sponge: "Or the measles." Dr. Cricket:"Definitely not chicken pox." Dr. Young: "Or sunburn." Narrator 2: replied the Specialists. Specialists:"Try these. Take one of each before bed." Narrator 4: said the specialists. They each handed her a bottle filled with different colored pills. Then they filed out the front door followed by Dr. Bumble. Narrator 1: That night, Camilla took her medicine. It was awful. Narrator 2: When she woke up the next morning, she did feel different, but when she got dressed, her clothes didn't fit right. She looked in the mirror, and there, staring back at her, was a giant, multi-colored pill with a face on it. Narrator 3: Dr. Bumble rushed over as soon as Mrs. Cream called. But this time, instead of the Specialists, he brought the Experts. Narrator 4: Dr. Gourd and Mr. Mellon were the finest scientific minds in the land. Once again, Camilla was poked and prodded, looked at and listened to. Narrator 1: The Experts wrote down lots of numbers. Then they huddled together and whispered. Dr. Gourd finally spoke. Dr. Gourd: "It might be a virus," Narrator 2: he announced with authority. Suddenly, fuzzy little virus balls appeared all over Camilla. Mr. Mellon: "Or possibly some form of bacteria," Narrator 3: said Mr. Mellon. Out popped squiggly little bacteria tails. Dr. Gourd: "Or it could be a fungus," Narrator 4: added Dr. Gourd. Instantly, Camilla was covered with different colored fungus blotches. The experts looked at Camilla, then each other. Experts: "We need to go over these numbers again back at the lab. We’ll call you when we know something," Narrator 1: said the Experts. But the Experts didn't have a clue, much less a cure. Narrator 2: By now, the T.V. news had found out about Camilla. Reporters from every channel were outside her house, telling the story of "The Bizarre Case of the Incredible Changing Kid." Narrator 3: Soon a huge crowd was camped out on the front lawn. Narrator 4: The Creams were swamped with all kinds of remedies from psychologists, allergists, herbalists, nutritionists, psychics, an old medicine man, a guru, and even a veterinarian. Narrator 1: Each so-called cure only added to poor Camilla's strange appearance until it was hard to even recognize her. She sprouted roots and berries and crystals and feathers and a long furry tail. But nothing worked. Narrator 2: One day, a woman who called herself an Environmental Therapist claimed she could cure Camilla. She said, Environmental Therapist: "Close your eyes, breathe deeply, and become one with your room." Camilla: "I wish you hadn't said that," Narrator 3: Camilla groaned. Slowly, she started to melt into the walls of her room. Her bed became her mouth, her nose was a dresser, and two paintings were her eyes. The therapist screamed and ran from the house. Mother: "What are we going to do? It just keeps getting worse and worse!" Narrator 4: cried Mrs. Cream. She began to sob. Narrator 1: At that moment, Mr. Cream heard a quiet little knock at the front door. He opened it, and there stood an old woman who was just as plump and sweet as a strawberry. Old Woman: "Excuse me, but I think I can help." Narrator 2: she said brightly. Narrator 3: She went into Camilla's room and looked around. Old Woman: "My goodness, what we have here is a bad case of the stripes. One of the worst I've ever seen!" Narrator 4: she said with a shake of her head. She pulled a container of small green beans from her bag. She said, Old Woman: "Here. These might do the trick." Mother: "Are those magic beans?" Narrator 1: asked Mrs. Cream. The old woman replied, Old Woman: "Oh my, no, there's no such thing. These are just plain old lima beans. I'll bet you'd like some, wouldn't you?" Narrator 2: she asked Camilla. Camilla wanted a big, heaping plateful of lima beans more than just about anything, but she was still afraid to admit it. She said, Camilla: "Yuck! No one likes lima beans, especially me!" Old Woman: "Oh, dear, I guess I was wrong about you." Narrator 3: said the old woman sadly. She put the beans back in her bag and started toward the door. Narrator 4: Camilla watched the old woman walk away. Those beans would taste so good. And being laughed at for eating them was nothing, compared to what she'd been going through. She finally couldn't stand it. Camilla: "Wait! The truth is...I really love lima beans." Narrator 1: she cried. The old woman smiled, popping a handful of beans into Camilla's mouth, and said, Old Woman: "I thought so." Camilla: "Mmmmmmm," Narrator 2: said Camilla. Suddenly the branches, feathers, and squiggly tails began to disappear.Then the whole room swirled around. When it stopped, there stood Camilla, and everything was back to normal. Camilla: "I'm cured!" Narrator 3: she shouted. The old woman said, Old Woman: "Yes, I knew the real you was in there somewhere." Narrator 4: She patted Camilla on the head and went outside and vanished into the crowd. Narrator 1: Afterward, Camilla wasn't quite the same. Narrator 2: Some of the kids at school said she was weird, but she didn't care a bit. Narrator 3: She ate all the lima beans she wanted, and she never had even a touch of stripes again.

Electrostatics The section of CBSE Class 12 Physics electrostatic potential and capacitance notes mainly deals with the in-depth analysis of electromagnetic phenomena when they are not performing any movements. Additionally, it is divided into ten further sub-topics to study the companion processes of reaching the state. These are - 1. Electric charge In this section of Physics ch 2 Class 12 notes, you get to learn about the basic features of electric charge and its expression in Physics. Along with its basics, the sections help to understand the full potential of charge. Different aspects of Charge included in Class 12 Physics Chapter 2 notes are - Definition Type: Positive and Negative Charge Unit and dimensional formula Point Charge Properties of Charge Comparison of Charge and Mass Methods of Charging Electroscope 2. Coulomb's Law Force is created when charges of opposite signs attract each other, and they repulse if the signs are the same. Coulomb's law tries to define this phenomenon through a mathematical formula, explicitly mentioned in Physics Class 12 notes Chapter 2. Moreover, there is key information about the variation of the constant k and its effect on a medium. Coulomb's law's vector form and the principle of superimposition are also explained in ch 2 Physics Class 12 notes. (Image will be uploaded soon) 3. Electric Field As stated in Class 12 Physics Chapter 2 notes, every positively or negatively charged particle has their respective electric fields. It feels a force at the time of interaction which might be attraction or repulsion. As it arises from electric charge, it is crucial to know about its different parts like - Electric field intensity Relation between electric force and electric field Super imposition of electric field Point charge Continuous charge distributions Properties of Electric Field Lines Motion of Charged Particles in an Electric field Learning more about the electric field from electric potential and capacitance notes Class 12 helps a student to get a grasp of upcoming chapters. 4. Electric Potential Energy When energy helps a charge to move from an electric field, it is known as the Electric Potential Energy. This section of electrostatic chapter Class 12 notes requires a student to study the Electron volt (eV), and the potential energy that an n number of charges can hold. 5. Electric Potential This section of Class 12 Physics Chapter 2 notes focuses on in-depth learning of Electric Potential or Voltage. Basically, it defines the potential movement of energy. 6. Relation between Electric Field and Potential Apart from knowing more about the relationship between the two values, Physics Class 12 Chapter 2 notes also discuss equipotential surfaces. 7. Electric Dipole Essentially, 'Dipoles' are two opposite points of charge represented with q and –q, with their distance between each other being 2a. Electric Dipoles are crucial in your study of Physics Class 12 Chapter 2 notes to learn more about electric fields and their potential. Additionally, Class 12 Physics Chapter 2 notes focus on the influence of electric dipoles on a uniform electric field mainly through Force and Torque, Work, and Potential Energy. In the last part of Electrostatics, further focus is on using the formulas to their fullest potential. It includes subsections of Electric Field, Electric Potential Energy, Electric Potential, and Electric Dipole. In the notes for electrostatic potential and capacitance, you will find proper solutions accompanied by clear and crisp diagrams for better understanding. 8. Gauss's Law Apart from just discussing the Gauss's Law, in Physics Class 12 ch 2 notes there is a thorough explanation of its properties and applications. The Gauss' Law states that net electric flux passing through a hypothetical closed surface is equal to the net electric charge present within the same closed surface. Being a broad part of the whole chapter, you may need to spend a little more time on it. Moving forward, it starts discussing the properties of conductors in relation to Gauss's Law. The Class 12 Physics notes Chapter 2 perfectly defines the journey to Gauss' Law from Coulomb's Law. Here is the Gauss's Law present in the Class 12 Physics ch 2 notes, (image will be uploaded soon) 9. Capacitors There is a dedicated section about Capacitors in the Class 12 Physics Chapter 2 notes elucidating its functions and importance as storage of potential electric energy. After explaining the structure of a capacitor, it points out the different types, parallel plate, spherical and cylindrical. The section of Chapter 2 notes of Physics Class 12 is further divided into subheads like: Properties of an ideal battery Grouping of capacitors Simple circuits (Series and Parallel) Dielectric Van de Graaff generator Combination of drops Charge distribution method Wheatstone Bridge-based circuit Extended Wheatstone Bridge Infinite network of capacitors Redistribution of charge between two capacitors Vedantu prepares the Class 12 Physics Chapter 2 notes with help from subject matter experts. In the PDF, you get a comprehensive idea of the topic along with potential answers to the most asked questions. Furthermore, the detailed explanation on each section and subsections are written in a simple language allows a student to ace their exams with wholesome knowledge. These Physics Chapter 2 Class 12 notes are going to be one of the best supplementary study materials besides a student’s textbooks. Visit the Vedantu website or download the app to get your hands on all important notes! Important Questions A charge of 4 × 10–8C is uniformly distributed on the surface of a spherical conductor, having a radius of 15 cm. Determine the electric field just outside this sphere at a point that is 15 cm from the centre of this sphere. Determine the capacitance given that the distance between the two plates has been reduced by half and the parallel plate capacitor holds a capacitance of 20 pF (where 1pF = 10-12 F) having air between the two plates. What will be the total capacitance of a combination where three capacitors, each having a capacitance of 20 pF, are connected in series. A square having a side of 10 cm has a 500 µC charge at its centre. Determine the work done to move a charge of 10 µC between two points that are diagonally opposite each other on the square. At an equatorial point, what will be the electrostatic potential because of an electric dipole? Calculate the work done to move a test charge, q, through a length of 1 cm along the equatorial axis of an electric dipole? Polarisation A capacitor has its plates enclosed in a medium that can be filled by insulating substances. A net dipole moment is then induced by an electric field in the dielectric. This event causes the field in an opposite direction. Equipotential Surface An equipotential surface is a type of surface where the potential always has a constant value. If considered as a point charge, the concentric spheres that are centred at a particular area of this charge are basically equipotential surfaces. Advantages of Vedantu's Revision Notes: A Comprehensive Resource for Effective Learning There are several reasons why one may refer to Vedantu's revision notes for studying a subject like Electrostatic Potential and Capacitance. Here are some key points: Comprehensive Coverage: Vedantu's revision notes provide a comprehensive coverage of the entire topic, ensuring that all important concepts and subtopics are included. Concise and Organized: The notes are designed to be concise, focusing on the key points and core ideas. They are organized in a structured manner, making it easy for students to navigate and revise the content. Simplified Explanation: The revision notes offer simplified explanations of complex concepts, making them more accessible and easier to understand. This helps students grasp the material more effectively. 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