Question

Charges are uniformly spread on the surface of a conducting sphere. The electric field from the center of the sphere in a point outside the sphere varies with distance \( r \) from the center as 

• A. \( E \propto r^2 \)
• B. \( E \propto \frac{1}{r^2} \)
• C. \( E \propto r \)
• D. \( E \propto \frac{1}{r} \)

Hint:

The electric field outside a conducting sphere behaves like that of a point charge, following the inverse square law \( E \propto \frac{1}{r^2} \).

Answer 1

The Correct Option is B

For a conducting sphere, the electric field outside the sphere at a distance \( r \) from the center of the sphere follows the inverse square law: \[ E = \frac{kQ}{r^2} \] where \( k \) is Coulomb's constant, \( Q \) is the total charge on the sphere, and \( r \) is the distance from the center of the sphere. Therefore, the electric field outside the conducting sphere varies as: \[ E \propto \frac{1}{r^2} \] Thus, the correct answer is: \[ E \propto \frac{1}{r^2} \]