Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is:

Solution

Physics sir · 3 steps

Do not count charges sitting on the cube as fully inside. Ask what share of the cube surrounds each one.

1. Charge at a vertex. Put 8 identical cubes together so that vertex A is at their common corner. The charge 2q then sits at the centre of a big closed cube, and each small cube gets an equal 1/8 share of its flux: 1/8 × 2q/ε₀ = q/4ε₀.
2. Charge on a face. The charge q at the centre of face CDEF is shared by 2 cubes, one on each side of that face. So this cube gets 1/2 × q/ε₀ = q/2ε₀.

   φ = 1/8·2q/ε₀ + 1/2·q/ε₀ = q/4ε₀ + 2q/4ε₀ = 3q/4ε₀

3. So. The total flux through the cube is 3q/4ε₀, which is option (b).

The idea to keep. For a charge on a cube, count how many identical cubes would surround it: 8 at a vertex, 4 on an edge, 2 on a face. This cube gets that fraction of q/ε₀.

Answer from the NTA final answer key. Solution by PrepWiser.