# A charge Q is placed at the centre of an imaginary hemispherical surface. Using symmetry arguments and the Gauss’s law, find the flux of the electric field due to this charge through the surface of the hemisphere (figure).

Given:

Charge Q placed at centre of imaginary hemispherical surface

Concept: Consider the hemisphere to be one half of an imaginary sphere in which charge Q is at the centre

We know that,

By Gauss’s law, flux of net electric field (E ) through a closed surface S equals the net charge enclosed (qin) by the surface divided by ϵ0

Net charge enclosed by the sphere Qin=Q

Therefore from Gauss’s law flux of electric field through this sphere

Since charge is symmetrically located with respect to sphere equal flux pass through each part of sphere of equal area. Therefore flux passing through both the hemispherical surfaces at the top and bottom are the same

So the flux passing through the hemispherical surface =

Therefore flux passing of electric field due to this charge through the surface of the hemisphere is Q/2ϵ0

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