UC Merced Electricity Magnetism Transverse Gradient Drift Worksheet A proton (+q) is initially moving with speed V0 in the direction shown in the picture b

UC Merced Electricity Magnetism Transverse Gradient Drift Worksheet A proton (+q) is initially moving with speed V0 in the direction shown in the picture below in a non–uniform magnetic field that is everywhere into the picture. However, the magnetic field is stronger closer to the top of the picture and weaker closer to the bottom. What is the direction of the magnetic force acting on the proton at the location shown? As the proton continues to move, guided by the magnetic force acting on it, what happens to its speed? Show that as the proton continues to move, it always stays in the plane of this picture. Then, use what you know about the deflection of electrically charged particles by magnetic forces to sketch the proton’s subsequent path through the magnetic field region. Assume that the proton always remains within the vertical boundaries of the region. In which direction does the proton systematically “drift” in the magnetic field as it executes many cycles of its motion? This drift motion is called “transverse gradient drift”. Finally, Consider protons and electrons in the Earth’s Van Allen radiation belts moving in the plane of the Earth’s magnetic equator under the influence of the Earth’s magnetic field. These particles undergo the kind of motion analyzed above— each experiences transverse gradient drift because the Earth’s magnetic field gets weaker with distance away from the Earth. In which direction, East or West, does each kind of particle drift? Please be sure your reasoning is clear, including any illustrative diagrams. Do their drift motions contribute electric currents around the Earth’s equator in the same or opposite directions? The resulting electric current is known as the “equatorial ring current.” In which direction (East or West) is this ring current? ♡
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