Positive & Negative Square Roots

Square roots of positive and negative numbers

Given an equation in the form of 𝒙²=𝒑, where 𝑝 is a perfect square between 𝟎 and 𝟐25, determine: ➢ a positive solution (L2) ➢ positive and negative solutions (L4)

8.AR.2.3 Given an equation in the form of 𝒙²=𝒑, where 𝑝 is a perfect square between 𝟎 and 𝟐25, determine: ➢ a positive solution (L2) ➢ positive and negative solutions (L4)

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. Key Formulas and Equations: The notes highlight the key formulas and equations relevant to the topic, ensuring that students have a clear understanding of the mathematical aspects of Electrostatic Potential and Capacitance. Examples and Illustrations: Vedantu's revision notes often include examples and illustrations that help clarify concepts and provide practical applications, enabling students to better relate theory to real-world scenarios. Quick Recap: The revision notes serve as a quick recap of the important points, allowing students to review the material efficiently before exams or assessments. Exam-Oriented Approach: Vedantu's revision notes are designed with an exam-oriented approach, focusing on the topics and concepts that are frequently asked in examinations. This helps students prepare effectively and increase their chances of scoring well. 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What is Electric Force? Electric force is just one of many types of forces in the world of physics. Forces are how and why things move, and can be explained by Newton's Laws of Motion. On the smallest scale, electric force is the resulting interaction between two charged particles. These charges can be either positive or negative. Larger objects can be charged by having an abundance of either of these particles, and therefore can create an electric force on a larger scale. Electric force is the reason why hair will sometimes stand up on its own and is also why we have electricity, allowing us to live in the modern world with lights and technology. Even out in nature electric force is present, as electric force causes lightning to strike. Electric force is fundamental to our everyday way of living. Reviewing Newton's Laws of Motion Newton's Laws of motion are the basic principles or ground rules that are applied all across physics. They describe how objects move and can be used to describe the interaction of charges. They are the following: An object in motion will stay in motion unless an external force is applied The force exerted on an object is equal to the mass times the acceleration of the object. ( ) Every force has an equal and opposite force Newton's laws explain how and why charged particles move. Since there is a force involved (e.g. electric force), particles will move around, which is explained by the first law. The second law describes how acceleration of charges can be calculated once the electric force is known. The third law explains how attractive and repulsive forces between charged objects are equal and opposite. Electric Force Examples and Types of Charge As previously mentioned, there are only two types of charges; positive and negative. Two like charges will repel (or move away from) each other, and two opposite charges will attract (or move towards) each other. In other words, two positive or two negative charges will repel, while a positive and a negative charge will attract. Opposite charges will attract while like charges will repel. Attraction versus Repelling Forces Notice how the forces acting upon each other are equal and opposite, as Newton's third law states. Both charges are exerting forces onto each other. Charges in Atoms An atom is made up of three types of particles; protons, neutrons, and electrons. Protons have a positive charge, neutrons have no charge, and electrons have a negative charge. There are no positive or negative charges smaller than protons and electrons. Objects on a larger scale result in an overall positive or negative charged due to an uneven distribution of protons to electrons. An atom consisting of more protons than electrons would be considered positive, and an atom with more electrons than protons would be considered negative. Protons are held close to the nucleus and are tightly bound to an atom, so it's difficult for protons to escape an atom. Electrons, on the other hand, are much further away from the nucleus of an atom. This makes it much easier for them to be removed from an atom. Electrons can leave or join atoms, making them positive or negative depending on the amount of protons. Similarly, for the bigger picture, overall materials and objects with more electrons than protons would be considered negative, and vice versa. Electric Force Examples Hair standing up: When hair is brushed, the hairbrush can strip electrons from hair strands, resulting in the hair being positively charged. This addition of electrons to the hairbrush in turn makes the hairbrush negatively charged. Since the hair is now positively charged, and like forces repel, hair strands will move away from each other, resulting in the hair standing up. Current electricity: All of our everyday technology is powered through current electricity, which is the consistent flow of electrons through conductive materials. This flow is caused by the electric force, as the electrons flow from a negative source to a positive source. Lightning: During a storm, it is common for an abundance of electrons to build up on the bottom of a cloud, making that part of the cloud negatively charged. Positive charges in the ground start to gather on the surface or even on tall objects such as trees as they are attracted towards the negatively charged undersides of clouds. Lightning strikes as a result of these charges becoming extremely built up. Lightning is caused by electric force Lightning Electric Force Equation: Coulomb's Law The magnitude of the electric force, or the amount of force in which objects repel or attract, depends on the distance between the two charged objects and the amount of charge each object carries. The electric force is stronger the closer together the two charges are, and weaker as the two charges move apart. Electric force is also stronger with more charge, and weaker with less charge. This effect on electric force is predictable, and is known as Coulomb's Law. It can be calculated using a mathematical equation, and the resulting magnitude of electric force is measured in Newtons. Coulomb's Law Electric force can be calculated using the following equation known as Coulomb's Law: In this equation, F is the electric force measured in newtons, K is a constant known as the electrostatic constant, and are charges one and two measured in coulombs, and is the radial distance in meters between the two charges. Since the distance is squared and on the denominator, the electric force drops off exponentially as charges move away from each other. This means that the Electric force is inversely proportional to distance. As charges move away from each other, the electric force between them gets smaller and smaller, until the force is negligible. The amount of charges are in the numerator of this equation, making the magnitude of the force larger with more charge. This means that the force is directly proportional to the amount of charge. When the charges are smaller, the amount of force will be smaller. When there is a lot of charge, the force will be much greater. When calculating the electric force using Coulomb's law, the resulting answer only gives the magnitude of the force and not the direction. In order to know the direction, you must know the types of charges. Once again, like forces repel, and unlike forces attract. It helps to draw a visual representation, or a free-body diagram, of the charges and forces acting upon them in order to understand the resulting force direction. Electric Field versus Electric Force An electric field is a direct result of an electric force. Its pure definition is electric force per unit charge, and can be thought of as a mapping of the force vectors. An electric field is present anytime there is an electric force. Therefore, when there are two or more charged particles, there is a surrounding electric field. The direction of the electric field is the direction a positive charge would flow if it were placed within the field. The electric field moves out from a positive charge and goes into a negative charge. Particles with unlike charges move towards each other, and their corresponding electric field lines move out from the positive charge and into the negative charge. The strength of the force at any given point can be seen through the spacing of the electric field lines. The electric force is strongest where the electric field lines are closest together, and weaker as these lines move apart. Like Coulomb's law expresses, electric field lines show how the electric force is strongest with a minimum distance between the two charges. Unlike charges will result in a repelling force, and the resulting electric field is a visual representation of this effect. Electric fields of two positive charges have the electric field moving out away from both of them. As with two negative charges, the field lines move in towards each negative. Lesson Summary An electric force is created when there are two or more charged particles or objects. These charges can be either positive or negative. Like charges will attract (move towards each other) while unlike charges will repel (move away from each other). As Newton's third law suggests, the forces acting upon each other are both equal and opposite. Electrons and protons within an atom are the two smallest types of charges there are. Electrons carry a negative charge while protons carry a positive charge. Electrons can be easily removed or added to atoms, making the overall charge positive or negative. Objects with more electrons than protons are negatively charged. Electric force is strengthened with increased charge and a shorter distance between the charges. This effect is known as Coulomb's law and can be calculated with the Coulomb's law equation. The magnitude of the force is measured in Newtons, and the direction can be determined by knowing whether the charges are attracting or repelling each other. An electric field is present wherever there is an electric force. The direction of this electric field is the direction a positive charge would flow if it where to be dropped in the field, which is from the positive to the negative.

Positive/Negative/Neutral Objects - How are they different? Positive: has fewer electrons than protons Negative: Has more electrons than protons Neutral: has equal numbers of protons and electrons Laws of Electric Charges - What are they? How are they applied? Like charges repel, opposites charges attract, charged AND neutral objects attract Induced Charge Separation - Explain this process. A shift of the position of electrons when a charged object is brought near it. If the charged object is positive, the electrons will move toward it. If the charged object is negative, the electrons will move away from it. Charging by Friction (What is happening with the charges? - Know electrostatic series examples) Process in which objects made from different materials rub against each other, producing a net static charge on each object. When charged by friction, one material will have a stronger attraction to electrons and will pull the electrons off the other material Charging by Conduction (Be able to explain what the electrons are doing) Charging by contact with a charged object. An object that becomes charged by contact always gets the same type of charge that is on the object that charges it. Grounding (Be able to explain how it happens) A method of removing static charges from an object. Electrons from the ground move up to the charged object. If the object is negative, electrons leave the object. If the object is positive, electrons enter the object. The ground always remains neutral Conductors/Insulators/Semiconductors (Know examples for each and characteristics) Conductor: A material that allows electrons to flow through it easily. GOOD CONDUCTORS: Silver, copper, gold, aluminium, magnesium, iron, usually metals Insulator: A material that prevents electrons from flowing through it. Plastic, wood and glass are examples. To prevent electric shocks, conductive wires are wrapped in insulators. Semiconductors: Have special properties that make them fair conductors, they are the foundation of modern electronics, including radios, computers and telephones. Charging by Induction (How do we induce a PERMANENT charge?) You can permanently charge an object using induction by attaching a conducting wire to the neutral object that goes to the ground Electric Discharge - What causes it? Know everyday examples. How is lightning formed? When two objects that have a charge imbalance are brought close together or come in contact with each other, electrons are transferred rapidly. Electrons move from the object with a more negative charge to the object with the less negative charge. Lightning occurs through an imbalance of charge between clouds and the ground. Negative charge at the bottom of a cloud repels the electrons at the earth's surface which move away, causing the ground to become positively charged Current Electricity: Refers to the electrons that flow in a controlled way through a conductor Forms of Current Electricity - Alternating Current (AC) vs Direct Current (DC) - How do they differ? AC: Electrons move back and forth, alternating their direction. produced in generating stations and is then distributed over long distances ex. Something plugged into a wall outlet

Positive & Negative tú Commands - Cap. 3

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