JEE Main 2025 · 29 January · morning · Single correct · +4 / −1
Match List - I with List - II.
Choose the correct answer from the options given below :
| List - I | List - II |
|---|---|
| (A) Electric field inside (distance r > 0 from center) of a uniformly charged spherical shell with surface charge density σ, and radius R. | (I) σ/ε₀ |
| (B) Electric field at distance r>0 from a uniformly charged infinite plane sheet with surface charge density σ. | (II) σ/2ε₀ |
| (C) Electric field outside (distance r>0 from center) of a uniformly charged spherical shell with surface charge density σ, and radius R. | (III) 0 |
| (D) Electric field between 2 oppositely charged infinite plane parallel sheets with uniform surface charge density σ. | (IV) σ/(ε₀ r²) |
- (a) (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
- (b) (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
- (c) (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
- (d) (A)-(IV), (B)-(II), (C)-(III), (D)-(I)
Answer and solution
Answer (c) (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
Solution
Physics sir · 4 steps
Use Gauss's law on each charge layout and ask one thing: how much charge does the Gaussian surface enclose?
- Inside the shell. A sphere of radius r < R drawn inside the shell encloses no charge. By symmetry the field on it is the same everywhere, so it must be 0. That gives (A)-(III).
- Outside the shell. Outside, the shell acts like a point charge q = 4π R² σ at its centre, so E = q/(4πε₀ r²) = (σ R²)/(ε₀ r²). The list drops the R², but (IV) is the only entry that falls off as 1/r². That gives (C)-(IV).
- Sheets. A single infinite sheet sends half its flux to each side, so E = σ/2ε₀ at any distance. Between two oppositely charged sheets, the two fields point the same way and add.
Charge layout Field Match (A) Inside a charged shell 0 (III) (B) One infinite sheet σ/2ε₀ (II) (C) Outside a charged shell (σ R²)/(ε₀ r²), falls as 1/r² (IV) (D) Between two opposite sheets σ/2ε₀ + σ/2ε₀ = σ/ε₀ (I) - So. The matching is (A)-(III), (B)-(II), (C)-(IV), (D)-(I), which is option (c).
The idea to keep. No charge inside means no field inside a shell. One sheet gives σ/2ε₀. Two opposite sheets add up to σ/ε₀ between them and cancel outside.
Answer from the NTA final answer key. Solution by PrepWiser.