Question

A metal sphere of radius 1 m is charged with \( 10^{-2} \) C in air. Its bulk modulus is \( \frac{10^{11}}{4\pi^2} \). The volume strain in the sphere is \( \epsilon_0 \) (permittivity of free space)

• A. \( \frac{10^{-1}}{6 \epsilon_0} \)
• B. \( \frac{10^{-14}}{8 \epsilon_0} \)
• C. \( \frac{10^{-15}}{8 \epsilon_0} \)
• D. \( \frac{10^{-12}}{4 \epsilon_0} \)

Hint:

Volume strain in a charged sphere is related to the electric field and the bulk modulus. The electric field produced by the charge causes the deformation in the material.

Answer 1

The Correct Option is C

Step 1: Understanding the relationship between charge and volume strain.
The volume strain \( \Delta V \) in the sphere is related to the charge and the electric field. The relationship between the electric field and the charge is governed by Gauss’s law. The strain in the material of the sphere is proportional to the applied electric field and the bulk modulus of the material. Step 2: Calculating the volume strain.
Using the given values, we can calculate the volume strain as: \[ \text{Volume strain} = \frac{10^{-15}}{8 \epsilon_0} \] Step 3: Conclusion.
Thus, the correct answer is (C) \( \frac{10^{-15}}{8 \epsilon_0} \).