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  4. A charge Q is situated at the corner of a cube, the electric flux passed through all the six faces of the cube is

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Q. A charge Q is situated at the corner of a cube, the electric flux passed through all the six faces of the cube is

AIPMTAIPMT 2000Electrostatic Potential and Capacitance

Solution:

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As at a comer, 8 cubes can be placed symmetrically, flux linked with each cube (due to a charge Q at the comer) will be $ \frac{Q} {8 \varepsilon_0}$.
Now for the faces passing through the edge A, electric field E at a face will be parallel to area of face and so flux for these three faces will be zero. Now as the cube has six faces and flux linked with three faces (through A) is zero, so flux linked with remaining three faces will be $ \frac{Q} {8 \varepsilon_0}$ Hence, electric flux passed through all the six faces of the cube is $ \frac{Q} {8 \varepsilon_0}$