Question

A long thin solenoid has $900$ turns/metre and radius $2.50cm$. The current in the solenoid is increasing at a uniform rate of $60A/s$. What is the magnitude of the induced electric field at a point $1.0cm$ from the axis of the solenoid?

Answer 1

$B={\mu }_{0}ni$
$\therefore \frac{dB}{dt}={\mu }_{0}n\frac{di}{dt}=(4\pi \times {10}^{-7})\left(900\right)\left(60\right)=0.068T/s$
$E=\frac{r}{2}\left(\frac{dB}{dt}\right)$
$E=\frac{(1\times {10}^{-2})}{2}\left(0.068\right)=3.4\times {10}^{-4}V/m$