Question

In a spherical shell, the potential at a point \( 2m \) from the center of the shell is equal to the potential due to a point charge \( q \) placed at the center of the shell. The potential at this point is:

• A. \( \frac{2qE_n}{m} \)
• B. \( \frac{qE_n}{2m} \)
• C. \( \frac{qE_n}{m} \)
• D. \( 2mE \)

Hint:

In spherical shells, the potential is the same as that due to a point charge located at the center of the shell.

Answer 1

The Correct Option is B

Step 1: Understanding the potential formula.
The electric potential \( V \) at a point due to a point charge \( q \) is given by: \[ V = \frac{kq}{r} \] where \( k \) is Coulomb's constant, \( q \) is the charge, and \( r \) is the distance from the charge.
Step 2: Applying the potential for a spherical shell.
For a spherical shell, the potential at a point is determined by the charge at the center and the distance from the center. Given that the potential due to the shell is equivalent to the potential due to a point charge at the center, the result will be \( \frac{qE_n}{2m} \).
Step 3: Conclusion.
Thus, the correct answer is (B) \( \frac{qE_n}{2m} \).