Question

The figure shows an irregular shaped wire $acb$ moving with velocity $v$, in a direction as shown in the figure. What is the induced emf in the wire?

Take $ab=L$

• A. $BvL\cos \theta$
• B. $2BvL$
• C. $BvL$
• D. $BvL\sin \theta$

Answer 1

The correct option is D $BvL\sin \theta$


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

Here, effective length is $ab=L$.

So, induced emf, $E=(\overrightarrow{v}\times \overrightarrow{B}).\overrightarrow{L}=BvL\sin \theta$

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