Question

A semicircular wire $PQ$, of radius $R=0.5\text{m}$, is moving in a uniform magnetic field of magnitude $2\text{T}$, as shown in the figure. If the velocity of the loop is $6\text{m/s}$, then calculate the emf developed across the ends of the wire $PQ$.

• A. $1.2\text{V}$
• B. $6.2\text{V}$
• C. $7.2\text{V}$
• D. $3.2\text{V}$

Answer 1

The correct option is C $7.2\text{V}$

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

Here, effective length is $PQ=2R=2\times 0.5=1\text{m}$

So, induced emf across the ends,

$E=Bvl\sin \theta =2\times 6\times 1\times \sin {37}^{\circ }$

$\therefore E=7.2\text{V}$

Hence, option $\left(C\right)$ is the correct answer.