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प्रश्न
Find out the outward flux to a point charge +q placed at the centre of a cube of side ‘a’. Why is it found to be independent of the size and shape of the surface enclosing it? Explain.
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उत्तर
Let a cube of side a enclose charge +q at its centre.
Because the electric flux through the square surface is `phi=q/(6in_0)`the square surfaces of cube are six. Hence, according to Gauss’s theorem in electrostatics, the total outward flux due to a charge +q of a cube is
`phi=6xx(q/(6in_0))=q/in_0`
The result shows that the electric flux passing through a closed surface is proportional to the charge enclosed. In addition, the result reinforces that the flux is independent of the shape and size of the closed surface.
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Mark the correct options:
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(a) the electric field must be zero everywhere on the surface
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(c) the charge inside the surface must be zero
(d) the charge in the vicinity of the surface must be zero
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- B: mid-point of an edge of the cube.
- C: centre of a face of the cube.
- D: mid-point of B and C.
