Chapter 29 Problem 78

Problem

A circular-shaped circuit of radius $r$, containing a resistance $R$ and capacitance $C$, is situated with its plane perpendicular to a spatially uniform magnetic field ${\vec {B}}$ directed into the page. Starting at time $t=0$, the voltage difference $V_{ba}=V_{b}-V_{a}$ across the capacitor plates is observed to increase with time $t$ according to $V_{ba}=V_{0}(1-e^{t/\tau }$, where $V_{0}$ and $\tau$ are positive constants. Determine $dB/dt$ , the rate at which the magnetic field magnitude changes with time. Is $B$ becoming larger or smaller as time increases?