Question

A plane loop, shaped as two squares of sides $a=1m$ and $b=0.4m$ is introduced into a uniform magnetic field $\perp$ to the plane of loop (figure). The magnetic field varies as $B={10}^{-3}\sin \left(100t\right)T$. The amplitude of the current induced in the loop if its resistance per unit length is $r=5\Omega$ $m^{-1}$ is:

• A. $2A$
• B. $3A$
• C. $4A$
• D. 5A5A
• E. 6A5A

Answer 1

The correct option is B $3A$

As the direction of flow of current in the 2 square loops is opposite , the areas must be subtracted.

$e=\frac{d\varphi }{dt}=(1^2-{0.4}^2)\times \frac{d}{dt}{10}^{-3}\sin 100t$
$r=(1\times 4+0.4\times 4)\times {10}^{-3}\times 5\Omega$
$i=\frac{e}{r}=3A$