Question

A charge $q$ is placed at some distance along the axis of a uniformly charged disc of surface charge density $\sigma$. The flux due to the charge $q$ through the disc is $\phi$. The electric force on charge $q$ exerted by the disc is

• A. $\sigma \phi$
• B. $\frac{\sigma \phi}{4 \pi}$
• C. $\frac{\sigma \phi}{2 \pi}$
• D. $\frac{\sigma \phi}{3 \pi}$

Answer 1

Answer: (A)

We know that if a point charge subtends a half-angle $\alpha$ on the circular cross-section of a disc, then flux passing through the disc is
$\phi=\frac{q}{2 \varepsilon_{o}}(1-\cos \alpha)$
Also, if a point charge $q$ lies on the axis of a charged disc of charge density $\sigma$ and subtends a half-angle $\alpha$, then it experiences a force
$F=\frac{q \sigma}{2 \varepsilon_{o}}(1-\cos \alpha)=\sigma \phi$