Question

A semi-circular conducting ring $acb$ of radius $R$ moves with constant speed $v$ in a plane perpendicular to uniform magnetic field $B$ as shown in 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 $V_a-V_b=0$

$E{=}_0^{\theta }\int \overrightarrow{B}.(\overrightarrow{v}\times dl)$
Consider a wire AB

$E{=}_0^{{180}^o}\int \overrightarrow{B}.(\overrightarrow{v}\times rd\theta sin\theta )$

$\overrightarrow{v}$ is parallel to $l$
Hence $V_A-V_B=0$
Also

$V_C-V_A{=}_0^{{90}^o}\int \overrightarrow{B}.(\overrightarrow{v}\times rd\theta sin\theta )$

$V_C-V_A=BvR$

$V_C-V_B=BvR$

$V_A-V_B=0$