Question

Match List - I with List - II:

List - I: 

(A) Electric field inside (distance \( r > 0 \) from center) of a uniformly charged spherical shell with surface charge density \( \sigma \), and radius \( R \). 
(B) Electric field at distance \( r > 0 \) from a uniformly charged infinite plane sheet with surface charge density \( \sigma \). 
(C) Electric field outside (distance \( r > 0 \) from center) of a uniformly charged spherical shell with surface charge density \( \sigma \), and radius \( R \). 
(D) Electric field between two oppositely charged infinite plane parallel sheets with uniform surface charge density \( \sigma \). 

List - II: 

(I) \( \frac{\sigma}{\epsilon_0} \) 
(II) \( \frac{\sigma}{2\epsilon_0} \) 
(III) 0 
(IV) \( \frac{\sigma}{\epsilon_0 r^2} \) Choose the correct answer from the options given below:

• A. (A)-(IV),(B)-(II),(C)-(III),(D)-(I)
• B. (A)-(IV),(B)-(I),(C)-(III),(D)-(II)
• C. (A)-(III),(B)-(II),(C)-(IV),(D)-(I)
• D. (A)-(I),(B)-(II),(C)-(IV),(D)-(III)

Hint:

For spherical shells and infinite planes, Gauss's law is often the simplest method to find electric fields.

Answer 1

The Correct Option is A

- (A) Inside a uniformly charged spherical shell, the electric field is zero.
- (B) The electric field due to an infinite plane sheet is constant and given by \( \frac{\sigma}{2\epsilon_0} \).
- (C) Outside a uniformly charged spherical shell, the electric field is similar to that due to a point charge and is given by \( \frac{\sigma}{\epsilon_0 r^2} \).
- (D) The electric field between two oppositely charged infinite sheets is \( \frac{\sigma}{\epsilon_0} \).