The Rotating Ring - Magnetic Needle Deviation · RMPH 2018 #1
Physics · electromagnetism
Problem
A metal ring of radius R is made out of a wire of cross section area s; the resistivity of the wire's material is given by ρ. The ring is place in a vertical plane. A small magnetic needle is placed in the center of the ring. The magnetic needle can rotate freely around the vertical axis which passes through the center of the ring. Due to mechanical inertia, the needle points in the direction of the average horizontal magnetic field at the center of the ring. When the ring is motionless in the reference frame of the Earth, the magnetic needle indicates the direction of the horizontal component of Earth's magnetic field. When the ring is rotating around its vertical axis with a constant angular velocity ω, the magnetic needle deviates, in horizontal plane, from this direction by an angle α.
1.a. Find the expression of angle of deviation α of the magnetic needle. Write your expression for α as a function of s, ρ, ω and of the magnetic permeability μ₀.