Question

A semicircular conducting ring $acb$ of radius $R$ moves with constant speed $v$ in a plane perpendicular to the uniform magnetic field $B$ as shown in the figure. Identify the correct statement.

• A. $V_a-V_c=BRv$
• B. $V_b-V_c=BRv$
• C. $V_a-V_b=0$
• D. None of these

Answer 1

The correct option is C $V_a-V_b=0$


To calculate motional emf, we take the effective length between the two points if the conductor is curved.

For points $a$ and $b$, $ab=2R$ is the effective length which is moving without cutting the field lines.

So, $V_a-V_b=0$

Also, for points $a$ and $c$, effective length is $oc=R$.

Hence, $\epsilon =BRv$

From right-hand rule, $c$ is at the higher potential.

Therefore, $V_c-V_o=V_c-V_a=BRv$

Similarly, $V_c-V_b=BRv$

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