Question

Consider the situation shown in figure. The wire AB is slid on the fixed rails with a constant velocity. If the wire AB is replaced by a semicircular wire, the magnitude of the induced current will
(a) increase
(b) remain the same
(c) decrease
(d) increase or decrease depending on whether the semi-circle bulges towards the resistance or away from it.

Answer 1

The induced emf across ends A and B is given by
$E=Bvl$
This induced emf will serve as a voltage source for the current to flow across resistor R, as shown in the figure. The direction of the current is given by Lenz's law and it is anticlockwise.
$i=\frac{Bvl}{R}$
If the wire is replaced by a semicircular wire, the induced current will remain the same, as it depends on the length of the wire and not on its shape (when B, v and R are kept constant).