All Problems

Electromagnetic Induction. Maxwells Equations

Problem 3.314

In the middle of a long solenoid there is a coaxial ring of square cross-section, made of conducting material with resistivity ρ\rho. The thickness of the ring is equal to hh, its inside and outside radii are equal to aa and bb respectively. Find the current induced in the ring if the magnetic induction produced by the solenoid varies with time as B=βt,B=\beta t, where β\beta is a constant. The inductance of the ring is to be neglected.

Reveal Answer
Iˉ=1/4(b2a2)βh/ρ\bar{I}=1 / 4\left(b^{2}-a^{2}\right) \beta h / \rho