Question

A semicircular wire $PQ$ of radius $R$ is moved with a velocity $v$ in a transverse magnetic field, as shown in the figure. The value of induced emf across the ends of the wire is -

• A. $\pi BRv$ with the end $P$ at higher potential
• B. $\pi BRv$ with the end $P$ at lower potential
• C. $2BRv$ with the end $Q$ at higher potential
• D. $2BRv$ with the end $Q$ at lower potential

Answer 1

The correct option is C $2BRv$ with the end $Q$ at higher potential


For the wire with arbitrary shape, we take effective length between the ends.

Here, effective length $PQ=2R$ which is moving perpendicular to the magnetic field.

So, induced emf across the ends, $E=Bvl=2BRv$

Also, from right-hand rule, the end $Q$ will be at higher potential.