Question

A square coil $AECD$ of side $0.1\text{m}$ is placed in a magnetic field $B=2t^2$. Here, $t$ is in seconds and $B$ is in Tesla. The magnetic field is into the paper. At time $t=2\text{s}$, induced electric field in $DC$ is

• A. $0.05\text{V/m}$
• B. $0.1\text{V/m}$
• C. $\text{along CD}$
• D. $0.2\text{V/m}$

Answer 1

The correct option is D $0.2\text{V/m}$

Magnetic field in $⨂$ direction passing through the coil is increasing, therefore, from Len'z law the induced current will produce $⨀$ magnetic field. Thus, the induced current will be anticlockwise or the induced electric field is along $DC$.
$\oint \overrightarrow{E}.\overrightarrow{dl}=\left|\frac{d\varphi }{dt}\right|$
or $E\left(4l\right)=l^2.\left(\frac{dB}{dt}\right)$
or $E=\frac{l}{4}\left(4t\right)=\left(l\right)\left(t\right)$
$=\left(0.1\right)\left(2\right)=0.2\text{V/m}$