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Question:

A charge q is located at the centre of a cube. The electric flux through any face is :

πq/6(4πε₀)

q/6(4πε₀)

4πq/16(4πε₀)

4πq/6(4πε₀)

Solution:

Step 1: Charge inclosed in cube [Refer Fig.]
Charge enclosed in cube=q
Step 2: Apply Gauss Law
Assuming gaussian surface as the cube, Applying Gauss Law:
Electric flux passing through cube=Charge Enclosed/ε₀=q/ε₀
As charge is placed at the center, Therefore, due to symmetry, all the six faces of cube being equivalent, so same flux will pass through each face.
∴Flux through each face=Total flux through cube/6=q/6ε₀=4πq/6(4πε₀)
Hence Correct Option is C