Question

A solid sphere of radius \( R \) carries a uniform volume charge density \( \rho \). The magnitude of electric field inside the sphere at a distance \( r \) from the centre is

• A. \( \frac{r \rho}{3 \epsilon_0} \)
• B. \( \frac{r^2 \rho}{6 \epsilon_0} \)
• C. \( \frac{r^2 \rho}{\epsilon_0} \)
• D. \( \frac{r^2 \rho}{3 \epsilon_0} \)

Hint:

The electric field inside a uniformly charged sphere increases linearly with \( r \) and depends on the charge density.

Answer 1

The Correct Option is D

Step 1: Electric Field Inside a Charged Sphere.
For a uniformly charged sphere, the electric field inside the sphere at a distance \( r \) from the center is given by: \[ E = \frac{r^2 \rho}{3 \epsilon_0} \] where \( \rho \) is the charge density and \( \epsilon_0 \) is the permittivity of free space.
Step 2: Conclusion.
The correct answer is (D), \( \frac{r^2 \rho}{3 \epsilon_0} \).