Question

A rectangular conductor LMNO is placed in a uniform magnetic field of $0.5T$. The field is directed perpendicular to the plane of the conductor. When the arm $MN$ of length of $20cm$ is moved towards left with a velocity of $10m{s}^{-1}$, calculate the emf induced in the arm. Given the resistance of the arm to be $5\Omega$, (assuming that other arms are of negligible resistance) find the value of the current in the arm.

Answer 1

Let $ON$ be $x$ at some instant.
The emf induced in the loop $=e$.
$e=\frac{d\varphi }{dt}=\frac{-d\left(Blx\right)}{dt}$
$e=Bl\left(\frac{-dx}{dt}\right)$
$=Blv=$ $0.5\times 0.2\times 10$
$=1V$
Current in the arm,
$1=\frac{e}{R}=\frac{1}{5}=0.2A$