a sphere of radius R has uniform distribution of electric charge in its volume .At s distance x from its center, for x
Dear student, A sphere of radius R has electric charge uniformly distributed in its entire volume.
Let charge Q is uniformly distributed in entire volume of sphere.
now at a distance x from the centre inside the sphere , charge will be q = Q/{4/3 πR³} × {4/3 π x³}
q = Qx³/R³ ..........(1)
from Gauss law,
electric flux through gaussian surface is the ratio of net charge enclosed inside the surface and permittivity of medium.
e.g., electric flux = q/€(epsilum) [ we assumed, medium is air or vaccum]
now, electric flux = electric field × area of gaussian surface = q/€(epsilum)
electric field × 4πx² = Qx³/R³/€(epsilum)
or, electric field , E = Qx/€4πR³
here it is clear that E is directly proportional to x.
All the best
Hope this helps
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