Question

A solenoid of radius R and length L has a current $I=I_{0}cosWt$. The value of induced electric field at a distance of r outside the solenoid,is

• A. $\frac{{\mu }_{0}n{I}_0\omega R^2}{2r}sin\omega t$
• B. $\frac{{\mu }_{0}n{I}_0\omega R^2}{r}sin\omega t$
• C. $\frac{{\mu }_{0}n{I}_0{R}^2}{2r}sin\omega t$
• D. zero

Answer 1

The correct option is A $\frac{{\mu }_{0}n{I}_0\omega R^2}{2r}sin\omega t$

Explanation:

The changing magnetic flux inside the solenoid induces electric field.

At a distance r>R,

$\int E.dl=-\frac{d\Phi }{dt}$

$\Rightarrow E\int dl=-\frac{d\left(BACos0\right)}{dt}$

$\Rightarrow E\left(2\Pi R\right)=-\frac{d\left(U_{0}nI\right(\Pi R^2\times 1)}{dt}$

$\Rightarrow E\left(2\Pi R\right)=-\frac{U_{0}n\Pi R^{2}d\left(I_{0}Coswt\right)}{dt}$

$\Rightarrow E\left(2\Pi R\right)=-U_{0}n\Pi R^2{I}_0(-wSinwt)$

Therefore, E = $\frac{U_{0}n{I}_{0}w{R}^{2}Sinwt}{2R}$

Hence, correct option is A.