Question

In the given arrangement, the loop is moved with constant velocity $v$ in a uniform magnetic field $B$ in a restricted region of width $a$. The time for which the emf is induced in the circuit is

• A. $\frac{2b}{v}$
• B. $\frac{2a}{v}$
• C. $\frac{(a+b)}{v}$
• D. $\frac{2(a+b)}{v}$

Answer 1

The correct option is B $\frac{2a}{v}$

as we know ,

$emf$ will change when flux changes and flux will change when area changes. see figures, in the given problem, flux changes from situation (1) to $\left(2\right)$ , but no flux will change from$\left(2\right)$ to$\left(3\right)$ finally, flux will change from $\left(3\right)$ to $\left(4\right)$.

now, total time taken from $\left(1\right)$ to $\left(4\right)$ , $T_1=(a+b)/v$

no flux will change from $\left(2\right)$ to $\left(3\right)$ , $T_1=(b-a)/v$

so, time taken to change flux ,$T=T_0-T_1$

$=\frac{\left(a+b\right)}{v}-\frac{\left(b-a\right)}{v}=\frac{2a}{v}$