Question

A charged particle performs SHM in hole through uniformly charged solid sphere. Find frequency.

• A. \( \frac{1}{2\pi} \sqrt{\frac{Qq}{4\pi \varepsilon_0 R^3 m}} \)
• B. \( \frac{1}{2\pi} \sqrt{\frac{Qq}{4\pi \varepsilon_0 R m}} \)
• C. \( \frac{1}{2\pi} \sqrt{\frac{Qq}{4\pi \varepsilon_0 m R^2}} \)
• D. \( \frac{1}{2\pi} \sqrt{\frac{Qq}{4\pi \varepsilon_0 m R}} \)

Hint:

Electric field inside uniformly charged sphere is proportional to displacement \( r \), leading to SHM.

Answer 1

The Correct Option is A

Electric field inside solid sphere varies linearly: \[ E = \frac{1}{4\pi\varepsilon_0} \cdot \frac{Qr}{R^3} \Rightarrow F = qE = \frac{Qqr}{4\pi \varepsilon_0 R^3} \] This is like \( F = -kr \), so SHM with \[ \omega^2 = \frac{Qq}{4\pi \varepsilon_0 R^3 m} \Rightarrow f = \frac{1}{2\pi} \sqrt{\frac{Qq}{4\pi \varepsilon_0 R^3 m}} \]