A light conducting rod of length moves with constant speed along two perfectly…
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Magnetism and Electromagnetism · Magnetism and Electromagnetism
Problem
A light conducting rod of length ℓ moves with constant speed v along two perfectly conducting rails that are oriented perpendicular to a magnetic field. The rails and rod together form a closed rectangular circuit with a fixed resistor R completing the circuit.
Unlike the usual situation of a uniform field, the magnetic field in this region varies with horizontal position x (measured along the rails) according to B(x)=B0(1+ax), where B0 and a are positive constants and x=0 corresponds to the point where the rod begins its motion.
(1) Part 1: Derive an expression for the magnitude of the emf induced in the circuit as a function of the rod’s horizontal position x.
(2) Part 2: Express the emf as an explicit function of time, assuming the rod’s speed remains the constant value v.
(3) Part 3: Given B0=0.50T, a=1.2m−1, ℓ=0.40m, and v=1.5m s−1, calculate the emf after the rod has traveled 0.10m.
(4) Part 4: State whether the magnitude of the current in the circuit increases, decreases, or remains constant as the rod moves, and justify your answer based on your expression for the emf.