Question

A magnetic field $B=1.5t\text{T}$ exists in a cylindrical region of radius $R=25\text{cm}$ as shown in the figure. What will be the magnitude of the induced electric field at a distance of $0.2\text{m}$ from the axis of the cylinder ?

• A. $0.5\text{N/m}$
• B. $2.5\text{N/m}$
• C. $0.3\text{N/m}$
• D. $0.15\text{N/m}$

Answer 1

The correct option is D $0.15\text{N/m}$

Given:
$B=1.5t\text{T};R=25\text{cm};r=0.2\text{m}$

Let the induced electric field at a distance $r$ from the axis of the cylinder is $E$.

Using the Faraday's law,

$E=\left|\oint \overrightarrow{E}.\overrightarrow{dl}\right|=|-\frac{d\varphi }{dt}|$

we have,

$E\times 2\pi r=|-\frac{d\left[B\right(\pi r^2\left)\right]}{dt}|$

$E\times 2\pi r=\pi r^2\times \frac{d}{dt}\left(1.5t\right)$

$E=\frac{r}{2}\times 1.5=\frac{1.5r}{2}$

At $r=0.2\text{m}$

$E=\frac{1.5\times 0.2}{2}=0.15\text{N}$

Hence, $\left(\text{D}\right)$ is the correct answer.

Why this question ? This question gives a basic understanding of the calculation of the induced electric field when the magnetic field is varying.