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(B) An $emf$ is induced in the loop when the magnetic flux linked with it changes. This happens when the loop enters the magnetic field region and whe

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$\frac{2a}{v}$

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(B) An $emf$ is induced in the loop when the magnetic flux linked with it changes. This happens when the loop enters the magnetic field region and when it leaves the magnetic field region.$1$. When the leading edge of the loop enters the magnetic field region of width $a$,an $emf$ is induced until the entire width $a$ of the field is covered by the loop. The distance traveled by the loop during this phase is $a$. The time taken is $t_1 = \frac{a}{v}$.$2$. While the loop is completely inside the magnetic field region (since $b > a$),the flux linked with the loop remains constant,so no $emf$ is induced.$3$. When the trailing edge of the loop starts leaving the magnetic field region,the flux starts changing again,and an $emf$ is induced until the loop completely exits the region. The distance traveled by the loop during this phase is $a$. The time taken is $t_2 = \frac{a}{v}$.Therefore,the total time for which an $emf$ is induced is $t = t_1 + t_2 = \frac{a}{v} + \frac{a}{v} = \frac{2a}{v}$.

In the given arrangement,a loop of width $b$ is moved with constant velocity $v$ through a uniform magnetic field $B$ restricted to a region of width $a$ (where $b > a$). The total time for which an $emf$ is induced in the circuit is:

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