In a certain region of space near Earth's surface, a uniform horizontal magnetic field of magnitude B exists above a level defined to be y=0. Below y=0, the field abruptly becomes zero. A vertical square wire loop has resistivity ρ, mass density ρ(m), diameter d, and side length l. It is initially at rest with its lower horizontal side at y=0 and is then allowed to fall under gravity, with its plane perpendicular to the direction of the magnetic field.
(a) While the loop is perfectly immersed in the magnetic field (as it falls into the zero-field region), determine the magnetic "drag" force that acts on it at the moment when its speed is v.
(b) Assume that the loop achieves a terminal velocity vT before its upper horizontal side exits the field. Determine a formula for vT.
(c) If the loop is made of copper and B=0.80 T, find vT.
