Question

A metallic square loop $ABCD$ is moving in its own plane with velocity $\overrightarrow{V}$ in a uniform magnetic field perpendicular to its plane as shown in fig. Then, an electric field induced

• A. in $AD$, but not in $BC$
• B. in $AB$ and $CD$ both.
• C. neither in $AD$ nor in $BC$
• D. in $AD$ and $BC$ both.

Answer 1

The correct option is D in $AD$ and $BC$ both.

$\Rightarrow$The motional emf induced across the ends of moving rod is :
$\epsilon =VB{l}_{\perp }$
$l_{\perp }=$length of rod perpendicular to its velocity.
In this case the length of rods $AB$ and $DC$ is parallel to direction of velocity,
$\therefore l_{\perp }=0$ for $AB$ and $DC$.
$\Rightarrow \epsilon =0$ for $AB$ and $DC$
However for rod $AD$ and $BC$ the $l_{\perp }$ exists, hence emf $\left(\epsilon \right)$ is induced in these segments.

$\therefore$ Induced Electric field will be present in $AD$ and $BC$ ,since electric field is associated with potential difference (emf).