All Problems

Electromagnetic Induction. Maxwells Equations

Problem 3.293

A long straight wire carrying a current II and a II-shaped conductor with sliding connector are located in the same plane as shown in Fig. 3.81. The connector of length ll and resistance RR slides to the right with a constant velocity vv. Find the current induced in the loop as a function of separation rr between the connector and the straight wire. The resistance of the \PiI-shaped conductor and the selfind uctance of the loop are assumed to be negligible.

Reveal Answer
I1nd=α/r, where α=1/2μ0lvI/πRI_{1 \mathrm{nd}}=\alpha / r, \quad \text { where } \quad \alpha=1 / 2 \mu_{0} l v I / \pi R