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

To solve the given problem, we need to match the scenarios described in List I with their corresponding electric field expressions from List II. Let's analyze each scenario:

List I:

1. (A) Electric field inside a uniformly charged spherical shell: For a uniformly charged spherical shell, the electric field inside (distance \( r > 0 \) from the center) is zero, due to the symmetry of the shell. This matches with List II: (III).
2. (B) Electric field at distance \( r > 0 \) from a uniformly charged infinite plane sheet: The electric field due to an infinite plane sheet with surface charge density \( \sigma \) is given by \( \frac{\sigma}{2\epsilon_0} \), regardless of the distance from the sheet. This matches with List II: (II).
3. (C) Electric field outside a uniformly charged spherical shell: At a point outside a uniformly charged spherical shell, the electric field is the same as if all the charge were concentrated at the center, given by \( \frac{\sigma}{\epsilon_0 r^2} \). 
4. (D) Electric field between two oppositely charged infinite plane parallel sheets: The electric field between two oppositely charged infinite planes each with surface charge density \( \sigma \) results in a field \( \frac{\sigma}{\epsilon_0} \). This matches with List II: (I).

Matching results:

Thus, the matches are:

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

The correct answer from the options is:

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