4)a charge Q is placed at the centre of an imaginary hemispherical surfaces. 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.

Asked by Rohan Kumar | 2nd Jun, 2013, 01:24: PM

Expert Answer:

The charge of magnitude Q is inside the hemisphere. But it is not enclosed completely by the single hemispehere, so we imagine the other part of the hemisphere and we complete the sphere. Now the charge Q is inside the sphere. So, by symmetry, the total flux is equally distributed in the two hemispheres. So the flux through one hemisphere will be half of the total flux through the sphere.
 
Now applying Gauss law for a closed volume,
 
Due to Gauss law, the electric field will be due to the electric charge inside the sphere.
 
Now according to Gauss law,
 
Total flux=Qinside/?
= Q/?
 
So through one hemisphere, the flux will be half of total flux, that is
Q/2?

Answered by  | 9th Jun, 2013, 10:09: PM

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