Question

A semi circular loop of radius R is placed in a uniform magnetic field as shown. It is pulled with a constantvelocity. The induced emf in the loop is

• A. Bv ($\pi$ R) cos $\theta$
• B. Bv ($\pi$ R) sin $\theta$
• C. Bv (2R) cos $\theta$
• D. Bv (2R) sin $\theta$

Answer 1

The correct option is D Bv (2R) sin $\theta$

Join $AB$ and then also make a segment $A^{\prime }{B}^{\prime }$.

There is no change in flux in the whole semicircular loop, thus no emf is generated in it. But a certain emf is induced in equivalent segment $A^{\prime }{B}^{\prime }$ which is same as in between $A$ and $B$.

Length of $A^{\prime }{B}^{\prime }$, $L=2R$

$\therefore$ EMF induced between $A^{\prime }$ and $B^{\prime }$, $E=B{v}_{\perp }L$

$E=B\left(vsin\theta \right)\left(2R\right)$