Question

A metallic V shaped rod OAC is rotated with respect to one of its end in a uniform magnetic field, such that axis of rotation is parallel to the direction of magnetic field. Length of each arm of the rod is L and the angle between the arms is $60^\circ $ . P is the mid-point of section AC. The magnitude of the magnetic field is B. Then choose the incorrect relation.

• A. $V_{A}-V_{0}=\frac{\omega B L^{2}}{2}$
• B. $V_{A}-V_{C}=\frac{\omega B L^{2}}{2}$
• C. $V_{C}-V_{P}=\frac{\omega B L^{2}}{8}$
• D. $V_{A}-V_{P}=\frac{\omega B L^{2}}{8}$

Answer 1

Answer: (B)

$OA=OC=L;OP=\frac{\sqrt{3} L}{2}$
$V_{A}-V_{0}=\frac{\omega B L^{2}}{2} \, \, V_{A}-V_{C}=0$
$V_{C}-V_{0}=\frac{\omega B L^{2}}{2} \, \, \, V_{P}-V_{0}=\frac{\omega B}{2}\left(\frac{3 L^{2}}{4}\right)=\frac{3 \omega B L^{2}}{8}$
$V_{C}-V_{P}=\left(V_{C} - V_{0}\right)-\left(V_{P} - V_{0}\right)=\frac{\omega B L^{2}}{2}-\frac{3 \omega B L^{2}}{8}=\frac{\omega B L^{2}}{8}$
$V_{A}-V_{P}=\left(V_{A} - V_{0}\right)-\left(V_{P} - V_{0}\right)=\frac{\omega B L^{2}}{2}-\frac{2 \omega B L^{2}}{8}=\frac{\omega B L^{2}}{8}$