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 $0.5cm$ from the axis of the solenoid.

• A. $1.7\times {10}^{-4}V/m$
• B. $2.7\times {10}^{-4}V/m$
• C. $1.7\times {10}^{-7}V/m$
• D. $2.7\times {10}^{-7}V/m$

Answer 1

The correct option is A $1.7\times {10}^{-4}V/m$

$B={\mu }_{0}ni$
$\therefore \frac{dB}{dt}={\mu }_{0}n\frac{di}{dt}=(4\pi \times {10}^{-7})\left(900\right)\left(60\right)=0.068T/s$
$E=\frac{r}{2}\left(\frac{dB}{dt}\right)$
$E=\left(\frac{0.5\times {10}^{-2}}{2}\right)\left(0.068\right)=1.7\times {10}^{-4}V/m$