Question

A wheel having mass $m$ has charges $+q$ and $-q$ fixed at diametrically opposite ends. For the wheel to be in equilibrium on a rough inclined plane in the presence of uniform vertical electric field $E$ is

• A. $\frac{3mg}{2q}$
• B. $\frac{mg}{2q}$
• C. $\frac{\sqrt{3}mg}{2q}$
• D. $\frac{3mg}{4q}$

Answer 1

The correct option is B $\frac{mg}{2q}$


For system to be in equilibrium, $\tau =0$
Let us take the torque about the point $P$, so
$qE\left[2R\sin \right({30}^{\circ }\left)\right]=\left[mg\sin \right({30}^{\circ }\left)\right]R$
$\Rightarrow E=\frac{mg}{2q}$