Question

A conducting square loop is placed in a magnetic field $B$ with its plane perpendicular to the field. The sides of the loop start shrinking at a constant rate $\alpha$/ The induced emf in the loop at an instant when its side is ${}^{\prime }{a}^{\prime }$ is

• A. $2a\alpha \beta$
• B. $a^2\alpha \beta$
• C. $2a^2\alpha \beta$
• D. $a\alpha \beta$

Answer 1

The correct option is A $2a\alpha \beta$

At any time $t$, the side of the square $a=(a_0-\alpha t)$, where $a_0=side$ at $t=0$.
At this instant, flux through the square:
$\varphi =BA\cos 0^{\circ }=B(a_0-\alpha t{)}^2$
$\therefore$ emf induced $E=-\frac{d\varphi }{dt}$
$\Rightarrow E=-B.2(a_0-\alpha t)(0-\alpha )=+2\alpha a\beta$.