Question

The figure shows four wire loops, with edge lengths of either $lor2l$. All four loops will move through a region of uniform magnetic field $\overrightarrow{B}$(directed outwards from the plane of paper and perpendicular to it) at the same constant velocity. In which loop(s) the emf induced is maximum

• A. I
• B. II
• C. III
• D. IV

Answer 1

Answer: (A), (B)

The correct options are
A I
B II

In general, as the loop is entering the field



Emf generated
$|\epsilon |=|\frac{d\varphi }{dt}|=|\frac{d(\overrightarrow{B}.\overrightarrow{A})}{dt}||\epsilon |=\frac{d}{dt}\left[B\right(xy\left)\cos \theta \right]\left(\text{in magnitude}\right)|\epsilon |=By\frac{dx}{dt}|\epsilon |=BVy$
Since $B$ and $V$ are same for all the loops,
$\epsilon \propto y\underset{I}{y}=\underset{II}{y}>\underset{III}{y}=\underset{IV}{y}$
Thus $\epsilon$ genrated is maximum in loops $I$ and $II$