The magnetic field at the the center of circular arc of radius R and central angle $\phi$ (measured in radians) is

$B=\frac{\mu_o i \phi}{4\pi R}$

$B=\frac{\mu_o i \phi}{4\pi R^2}$

$B=\frac{\mu_o i \phi}{2\pi R}$

$B=\frac{\mu_o i \phi}{8\pi R}$

The magnetic field at point C has magnitude and direction

$\frac{\mu_o i}{4R}$ into the plane of the page

$\frac{\mu_o i}{4R} +\frac{\mu_o i}{4\pi R}$ into the plane of the page

$\frac{\mu_o i}{4R}$ out of the plane of the page

$\frac{\mu_o i}{4R} +\frac{\mu_o i}{4\pi R}$ out of the plane of the page

The magnetic field due to a long a solenoid depends only

the current and the number of turns per unit length

the current and the number of turns

the current and the radius of the solenoid

The magnetic field due to an ideal solenoid is all except

uniform and directed radially outward from the the central axis of the solenoid

uniform and directed along the central axis of the solenoid

proportional to the current in the solenoid

proportional to the number of turns $N$ and inversely proportional to the total length $L$

The magnetic field due to a Toroid with N number of turns, and current $i$, a distance $r$ from the center of the toroid. (r is between the inner and outer radius of the toroid)

$B=\frac{\mu_o i N }{2\pi r^2}$

$B=\frac{\mu_o i^2 N }{2\pi r}$

$B=\frac{\mu_o i N^2 }{4\pi r}$

Because magnetic monopoles do not exist (at least not that we know of Gauss' Law for Magnetism says

the closed surface integral of B dA must always be 0.

you can break a magnet into only a north pole

you can break a magnet into only a south pole

The force per unit length $\frac{F}{L}$ between two long current carrying wires that are a distance $d$ apart and carry currents $i_a$ and $i_b$

$=\frac{\mu_o i_a i_b}{2 \pi d}$

$=\frac{\mu_o i_a i_b}{4 \pi d}$

$=\frac{\mu_o i_a i_b}{2 \pi d^2}$

The magnetic field due to a circular current carrying wire with radius R a distance z above the center of the circle of wire is

$B=\frac{\mu_o i R^2}{2(R^2+z^2)^{3/2}}$

$B=\frac{\mu_o i R}{2(R^2+z^2)^{3/2}}$

$B=\frac{\mu_o i}{2(R^2+z^2)^{3/2}}$

$B=\frac{\mu_o i R^2}{2(R^2+z^2)^{1/2}}$

Magnetic Fields due to Currents

Continental Drift Theory. From the discussion of the rock cycle, it has been pointed out that through Earth's external and internal processes. Earth's surface is constantly changing. However, this idea of a changing environment did not conform with the belief of earlier scientists. Rather, they thought that the geographic positions of ocean basins and continents have been static since the beginning of time. It was around the 1500s when Leonardo da Vinci, upon his discovery of fossil seashells found at the high mountains of Italy, first thought of the idea that the areas where mountains are located may have been oceans in the past. Through time, other fossils of marine organisms found far above the current sea level further supported the idea that mountains were uplifted and weathering wore them down. At around the 1800s, most scientists have accepted the idea that Earth's crust is undergoing large vertical movements or uplifting. There was also evidence of possible horizontal movements, but the scientists then were not convinced about it. Alfred Wegener showed evidence of horizontal or lateral movement of the continents in his continental drift theory. According to him, the continents have drifted around the world and have once formed a giant landmass or supercontinent called Pangaea. To support his theory, Alfred Wegener presented a set of geographical, biological, and climatic evidence.Wegener's geographical evidence included the jigsaw puzzle fit of the current continents. He pointed out that the coastlines of South America and Africa seem to fit together. He also pointed the presence of mountain ranges having similar rock types and age but separated by vast oceans, like that of the folded rocks of the Caledonian mountains. The same folded rocks run through West Africa, North America, Newfoundland, Ireland, Wales, Scotland, Greenland, and Norway, all of which are now separated by the Atlantic Ocean. A geographical evidence on the similar rock types in West Africa, North America, Greenland, and Europe is found. The biological evidence came in the discovery of similar plant and animal fossils in different continents separated by oceans. The animal fossils of Mesosaurus and Lystrosaurus indicate that they were not capable of crossing the oceans to reach the other continents. If they were, the fossils should have been more widely distributed Africa, Australia, India, and South America were too large to be carried by wind. This indicates that the areas where the fossils were found were closely linked. It has also been found out that the plant only grew in areas with subpolar climate, which would indicate that the landmasses were located near the South Pole.Lastly, for his climatic evidence, Wegener discovered that a glacial period occurred during the late Paleozoic era in Southern Africa, South America, Australia, and India. The initial explanation for this event was global cooling, but it was rejected because large tropical swamps with so much vegetation were found at the same time in the Northern Hemisphere. This further supported the idea that the supercontinent was indeed near the South Pole, and the continents in Northern Hemisphere were once near the equator. The glacial period also left glacial striations, or the scratches glaciers make as they move across on the underlying bedrock, on the aforementioned continents. For such an event to happen, the continents would have to be connected. SCIENCE PIONEER. Alfred Wegener (1880-1930). Alfred Wegener was a German polar researcher, geophysicist, and meteorologist. He was known for his work on the continental drift theory. In his effort to defend his work, he went to the Greenland ice sheet where he died.Even with all the compelling evidence, the continental drift theory hardly convinced the scientific community at that time because Wegener was unable to identify a credible mechanism that drives the continental drift. He was unable to clearly explain how the continents moved and how the larger continents broke through the ocean floor. Eventually, critics of the continental drift began to accept the theory when new evidence supporting the theory was discovered. The new evidence led to a more encompassing theory the theory of plate tectonics. This theory provided a more convincing explanation as to how the continents moved. The evidence that paved the way for the theory of plate tectonics was the idea of wandering poles. Scientists began studying volcanic rocks to determine the location of the magnetic poles. When volcanic rocks crystallize, the minerals with magnetic properties align themselves parallel to Earth's magnetic field at the time the minerals were formed. This finding allowed scientists to determine the polarity of Earth's magnetic field and the magnetic inclination that showed the location of the poles. Upon studying the paleomagnetism of the rocks, geophysicists found out that rocks from various locations point to different magnetic north poles, suggesting that the poles have wandered. Since movement of magnetic poles is very unlikely, scientists have accepted the idea that the continents are indeed moving. And if the continents are moving, scientists thought that maybe the ocean basins are moving too. They also discovered that some rocks showed magnetic reversals, which led them to believe that the magnetic north pole now was not always the magnetic north pole. Seafloor Spreading. After World War II, exploration on the ocean floor became the focus of many geologic studies. It was only then that the ocean ridge system was discovered. A geologist in Princeton University named Harry Hess, along with other scientists, studied this ocean ridge system and hypothesized that the oceanic crust was moving away from the ridge. His hypothesis, known as seafloor spreading, showed that the ocean floor is split along the ridge where the magma rises to form the new ocean floor.Because of this, rocks located near the ridge are younger than those that are located magnetic polarity of Earth is also preserved in those rocks. Withe ridge scientists were able to see the magnetic reversals in the ocean floor, and they were able to make use of information to determine that the ocean floor is moving at a rate of about 10 cm per year. Plate Tectonics. Confirmation of the seafloor spreading hypothesis proved that continents are not moving above the ocean floor. Rather, it is the fragments of the lithosphere. The lithosphere is the rigid layer that is composed of the uppermost mantle and the crust that carry the continents and the ocean basins along. These fragments of the lithosphere are called plates. Underneath the lithosphere is a weaker region in the mantle known as asthenosphere that behaves like a fluid. Thus, the lithosphere floats above the asthenosphere, making it detached and free to move. This became the basis of the theory of plate tectonics. Now that it has been made clear that it is the plates which are moving, the question as to how they move remained. Sir Arthur Holmes proposed the driving force for this plate movement in 1919. He suggested that the movement in the mantle carries the plates along. It was previously discussed that Earth's interior is very hot due to the heat produced by radioactive decay. Convection takes place in the mantle, keeping the asthenosphere hot and weak. The convection currents produced in the asthenosphere are the ones carrying the lithospheric plates and making them move. However, convection currents are not enough. Mechanisms such as ridge push and slab pull aid the convection currents to slowly move the lithospheric plates. Ridge push occurs at mid ocean ridges which are higher in elevation than the surrounding trenches and abyssal plains. The new ocean floor from the ridge is hot and relatively thin. As it moves away from the ridge, it cools down and gets denser, heavier, and thicker. Below this cooling ocean floor is the asthenosphere, which is less dense. This area becomes a massive shear zone and the new ocean floor will effectively slide down the slope of the asthenosphere. When the plate collides with another plate with lesser density, the denser plate sinks and a subduction zone is formed. When the subducting plate sinks, it pulls on the rest of the plate behind it. These mechanisms explain the movement of the plates.Earth has seven major lithospheric plates that account for 94% of Earth's surface. These are the North American Plate, South American Plate, Pacific Plate, African Plate, Eurasian Plate, Indo-Australian Plate, and Antarctic Plate. These plates are constantly moving relative to the other plates. Thus, the interaction of plates occurs mostly along the boundaries. These movements are plotted using information from earthquakes and volcanic activities. There are three main types of plate boundaries: convergent, divergent, and transform boundaries Convergent boundaries are boundaries where two plates move towards each other A convergent boundary is also known as destructive margin since this is where the collision between two plates occhins. There are three types of convergence-oceanic oceanic, oceanic-continental, and continental-continental. Trenches are features of the ocean floor that are present in both oceanic-oceanic boundary and oceanic-continental boundary. Subduction occurs at the trenches, therefore, these are characterized as the deepest parts of Earth. A divergent boundary is the opposite of convergent boundary: two plates move away from each other. Divergent boundaries create new crust; thus, they are also known as constructive margins. The ocean ridge system is a divergent boundary where new ocean floor is produced as magma rises, pushing the older rocks aside.Transform boundary is also known as conservative plate margin since two plates just move past one another, neither creating nor destroying land. Earthquake epicenters are usually detected at transform boundaries because the rocks tend to break and not fold or sink, like in convergent boundaries. Evolution of the Ocean Basins. Both the movement of the plates and seafloor are responsible for the evolution of ocean basins. Along the divergent boundary where ocean ridge systems are found, magma is released and new ocean floor is created. Along convergent boundaries, the ocean floor is being destroyed. The evolution of the ocean basins started during the time when Pangaea was still present and was surrounded by the vast ocean or superocean known as Panthalassa, also called Paleo-Pacific or "old Pacific." Upon the initial break up of Pangaea into Laurasia and Gondwanaland, the Tethys Sea began to form. Then, the Eurasian and North about, forming the North Atlantic. The South Atlantic only started to form when the African Plate and South American Plate separated. The continued movement of the plates created the Himalayas at one side and separated the Pacific Ocean and Atlantic Ocean at the other side, which consequently formed the current ocean basins. Both the movement of the plates and seafloor are responsible for the evolution of ocean basins. Along the divergent boundary where ocean ridge systems are found, magma is released and new ocean floor is created. Along convergent boundaries, the ocean floor is being destroyed. The evolution of the ocean basins started during the time when Pangaea was still present and was surrounded by the vast ocean or superocean known as Panthalassa, also called Paleo-Pacific or "old Pacific." Upon the initial break up of Pangaea into Laurasia and Gondwanaland, the Tethys Sea began to form. Then, the Eurasian and North about, forming the North Atlantic. The South Atlantic only started to form when the African Plate and South American Plate separated. The continued movement of the plates created the Himalayas at one side and separated the Pacific Ocean and Atlantic Ocean at the other side, which consequently formed the current ocean basins.Continents do not immediately end at the point where the ocean meets the land. They may extend slightly into the oceans. The portion of the continent that is submerged is called continental margin. There are two types of continental margin: passive margin and active margin. A passive continental margin consists of a continental shelf, continental slope, and continental rise. It is not associated with plate boundaries; thus, there are very little tectonic activities. An active continental margin only has a continental shelf and a continental slope. It is associated with plate boundaries; thus, a main feature of this boundary is a trench. The different features of a continental margin are the following: 1. The continental shelf is the gently-sloping submerged portion of the continent. 2. The continental slope is the steep slope after the continental shelf. It is still part of the continent. 3. The continental rise is the gently-sloping area after the continental slope and before the ocean floor. 4. The trenches are the deepest parts of the ocean. These are narrow depressions caused by the subduction of the ocean floor along the convergent boundaries. 5. The mid-oceanic ridge is the mountain range system in the ocean. It is responsible for the production of new ocean floor. This is the region where new magma constantly emerges from. SCIENCE CAREER. A scientific illustrator uses art to inform and communicate complex details and concepts of science. He/She makes use of scientifically informed observations and research along with his/her technical art and aesthetic skills to make accurate representations. In Natural History, the scientific illustrators recreate how the extinct species look like by working with scientists and fossil records. Moreover, with the advances in technology, illustrators are now into 3D modelling, animation, and video making. Earth's History. All the processes that have been discussed require long periods of time to create a noticeable change on Earth's surface. You can just imagine how long it would take to create an oceanas vast as the Pacific Ocean if the ocean floor moves only at about 10 cm/year. It is then important to know the history of Earth to learn the complexities of its past and be able to use it to understand the present. Just like learning the history of a country that requires one to read a lot of books, learning the history of Earth involves studying a lot of rocks. Rocks, especially sedimentary rocks, contain a lot of information about Earth's past. It holds the key to most of the geologic processes that happened on Earth and the key to uncovering how life on Earth evolved. But these discoveries are worthless if there is no time perspective. Thus, one of the most important contributions of geologists to mankind is the geologic time scale, which holds a history that is exceedingly long.

THE SOAR SYSTEM A solar system is a group of planets and other celestial bodies that revolve around a star. A solar nebula- a vast cloud of gas and dust, mostly hydrogen and helium. How the Solar System Form • COLLAPSE AND SPINNING DISK FORMATION - Gravity pulls material inward. The cloud flattens into a spinning disk due to conservation of angular momentum. • PROTOSTAR FORMATION- (BIRTH OF THE SUN). Material collects at the center, and begun to heat up. When it reaches to 10 million KELVIN, nuclear fusion begins. thus, SUN is born. • PLANETESIMALS AND PROTOPLANETS. Dust and gas in the disk stick together via static and gravitational forces. These form planetesimals, which grow into protoplanets collision and accretion. • PLANET FORMATION. Inner disk: too hot for gas rocky planets form Mercury, Venus, Earth, Mars. • PLANET FORMATION. Outer disk: gas and ice giants. Jupiter, Saturn, Uranus, Neptune • LEFTOVER DEBRIS. Remaining materials forms moon, asteroids, comets and dwarf planets. DIFFERENT HYPOTHESIS IN THE FORMATION OF SOLAR SYSTEM. 1. NEBULAR HYPOTHESIS- The Solar system formed from a rotating cloud of Gas and Dust (solar nebula). As it rotates conservation of angular momentum caused the cloud to flatten into a disk. the Sun formed at the center (DISK) while planets formed from the surrounding materials through acceleration. thus, it explains the coplanar and nearly circular orbit of the planets all planets orbits around the sun on the same flat, disk shaped plane. Proposed by Immanuel Kant in 1755 and Modified by Pierre Simon Laplace in 1756. PROTOPLANET HYPOTHESIS. The Solar system formed from a rotating cloud of Gas and Dust (solar nebula). As it rotates conservation of angular momentum caused the cloud to flatten into a disk. 2. Protoplanet hypothesis. Builds on the nebular model but focuses more on the role of planetesimals which then form into full planets. PROCESS: - Small solid particles stick together through collisions. As collisions takes place, it grows into kilometer-sized planetesimals. Gravitational interactions lead to the formation of planets. Lead to formation of steroids belts and varying planet sizes 3. Encounter hypothesis. States that the sun encountered a rogue star. The encounter led to the removal of hot gas from both stars due to their gravitational interaction. The hot gas then accumulated and formed the planets. The materials from the less dense rogue star formed the other planets, while that from the sun formed the inner planets. 4. TIDAL HYPOTHESIS. (also called the Tidal Theory) is an early scientific idea about how the solar system might have formed. Proposed by James Jeans and Harold Jeffreys. A massive star passed very close to the early Sun. The hot gas then accumulated and formed the planets. The materials from the less dense rogue star formed the other planets, while that from the sun formed the inner planets. Streams of hot gas were drawn out from the Sun in elongated shape. These streams eventually condensed and cooled, forming planets, moons, and other bodies in the solar system. 5. Not accepted theory. Later studies showed the streams of hot gas would disperse too quickly into space instead of condensing into planets. The theory also couldn’t explain the specific orbital patterns and compositions we see today. Modern science favors the Nebular Hypothesis, which explains solar system formation through the collapse of a rotating gas cloud. Earth as the only habitable planet 1. Right Distance from the Sun (The Goldilocks Zone). Not too hot, not too cold — just right for liquid water to exist. 2. Atmosphere with Oxygen. Earth has a mix of gases, especially oxygen, which most living things need to survive. 3. Liquid Water. Earth has oceans, rivers, and rain — water is essential for all life. 4. Magnetic Field. Earth’s magnetic field protects us from harmful solar radiation. 5. Stable Climate. The atmosphere and natural cycles keep temperatures and weather mostly stable over time. 6. Rich Resources. Earth has soil for growing food, minerals, and energy sources that support life and technology. Solar explorations 1. AUGUST 6, 2014. First space craft to orbit a comet (ROSETTA PROBE). Captures the comet photograph. -Comets have coma and tail as it approaches to the sun. 2. JULY 14, 2015. NASA’s New Horizons spacecraft made history by becoming the first spacecraft to fly by Pluto, giving us our first close-up look at the dwarf planet. First time visiting Pluto. Before this, Pluto was just a blurry dot in telescope images. Revealed a surprising world New Horizons showed mountains of ice, smooth plains, and a heart-shaped region called Tombaugh Regio. Changed what we knew. Scientists thought Pluto would be dull and frozen — instead, it turned out to be geologically active and incredibly complex. 3. SEPTEMBER 8, 2016. NASA launched OSIRIS-REx, the first U.S. mission to collect a sample from an asteroid and return it to Earth. Changed what we knew. Scientists thought Pluto would be dull and frozen — instead, it turned out to be geologically active and incredibly complex. OSIRIS-REx stands for: Origins, Spectral Interpretation, Resource Identification, Security–Regolith Explorer It was sent to study the asteroid Bennu, a near-Earth asteroid about 500 meters wide. Mission Goals: Collect a sample of surface material from Bennu Study the asteroid’s omposition, structure, and history. Mission Goals: Help scientists understand the origins of the solar system. Learn more about asteroids that could impact Earth. 4. August 12, 2018: Launch of NASA’s Parker Solar Probe, the first spacecraft to "touch" the Sun by flying through its outer atmosphere, called the corona. Mission Goal: To study the Sun up close and help scientists understand: How the solar wind (a stream of charged particles) is formed. Why the Sun’s corona is hotter than its surface. What causes solar storms that can affect Earth’s satellites and power grids. 5. November 26, 2018: NASA’s Insight Lander Touches Down on Mars. Its mission was focused on studying the interior of the Red Planet (crust, mantle, and core of the planet). Why the Sun’s corona is hotter than its surface. What causes solar storms that can affect Earth’s satellites and power grids 6. November 26, 2018: NASA’s Insight Lander Touches Down on Mars. Its mission was focused on studying the interior of the Red Planet (crust, mantle, and core of the planet) 7. JULY 30, 2020 PERSEVERANCE PROBE. Perseverance rover as part of the Mars 2020 mission aboard an Atlas V-541 rocket This marked a major step in Mars exploration. 8. DECEMBER 25, 2021-JAMES WEBB SPACE TELESCOPE. Investigate exoplanets’ atmospheres for signs of habitability. Observe the first galaxies formed after the Big Bang. Study the formation of stars and planetary systems. Look deeper into the infrared universe than ever before. RESULTS OF EXPLORATION • Evidence of Ancient Life-friendly Environment. • Sedimentary rocks formed in water-rich environments. • Signs of clay and carbonate minerals, which can preserve biosignatures (traces of past life). • Evidence of Ancient Life-friendly Environment. • Sedimentary rocks formed in water-rich environments. • Signs of clay and carbonate minerals, which can preserve biosignatures (traces of past life). • Evidence of Ancient Life-friendly Environment. • Sedimentary rocks formed in water-rich environments. • Signs of clay and carbonate minerals, which can preserve biosignatures (traces of past life).

Magnetic Fields

Magnetic Fields and Forces

Plotting magnetic fields

110.31.b.17.C

Topic: Reading/Vocabulary Development

STAAR English II High School 2014 - Past Paper

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