Question

In a long straight solenoid with number of turns per unit length $n$, current varies as $I\text{A/s}$. Find the magnitude of induced electric field strength inside the solenoid as a function of distance $r$ from the axis of the solenoid.

• A. ${\mu }_{0}nIr$
• B. $\frac{{\mu }_{0}nIr}{2}$
• C. $\frac{{\mu }_{0}nIr}{3}$
• D. $2{\mu }_{0}nIr$

Answer 1

The correct option is B $\frac{{\mu }_{0}nIr}{2}$

We know that magnetic field inside a solenoid is given by,

$B={\mu }_{0}ni$

Where $i$ is the current flowing through the solenoid.

Also, the electric field induced at a distance $r$ inside the solenoid is given by,

$E=\frac{r}{2}\frac{dB}{dt}$

$\Rightarrow E=\frac{r}{2}\times \frac{d}{dt}\left({\mu }_{0}ni\right)$

$\Rightarrow E=\frac{r}{2}\times {\mu }_{0}n\frac{di}{dt}$

As, $\frac{di}{dt}=I$

$\therefore E=\frac{{\mu }_{0}nrI}{2}$

Hence, option $\left(\text{B}\right)$ is correct.