Question

A simple pendulum with bob of mass m and conducting wire of length L swings under gravity through an angle $2\theta$. The earth's magnetic field component in the direction perpendicular to swing is B. The maximum potential difference induced across the pendulum is?

Answer 1

As shown on the figure ,the emf induced across the pendulum is maximum when velocity of bob is maximum.

Now velocity of pendulum at mean position $p$ is $\left(v\right)$

Applying energy conservation

$\frac{1}{2}m{v}^2$=$mgh$

$v=\sqrt{2gh}$

Now velocity of center of mass of bob and wire system is $v^{\prime }$

$v^{\prime }=\frac{v}{2}=\sqrt{\frac{gh}{2}}$

now emf induced $\epsilon =v^{\prime }BL$

$\epsilon$ =$BL\sqrt{\frac{gh}{2}}$