Q13 · Gauss Law

Problem

Cubical region side a, charges −q at (0,−a/4,0), +3q at origin, −q at (0,+a/4,0).

Options

Option	Value
(A)	Flux through x=±a/2 equal
(B)	Flux through y=+a/2 > y=−a/2
(C)	Total flux = q/ε₀
(D)	Flux through z=+a/2 equals x=+a/2

Key insight: Gauss’s law + symmetry: flux through symmetric planes is equal; total enclosed charge determines net flux.

Setup

flowchart TB
  S["Symmetric charge layout"] --> P["Equal flux through x = ±a/2 planes"]
  Q["Enclosed charge q_net"] --> F["Φ_total = q_net / ε₀"]

1. Symmetry

Charge config symmetric about x = ±a/2 planes.

$$\Phi_{x=+a/2} = \Phi_{x=-a/2} \Rightarrow (A)$$

2. Total flux

Enclosed: −q + 3q − q = q.

$$\Phi_{total} = q/\epsilon_0 \Rightarrow (C)$$

Hints

• Use symmetry of charge configuration.

Answer

(A), (C), (D)