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a sphere of radius R has uniform distribution of electric charge in its volume .At s distance x from its center, for x
Spoorthi 6th Dec, 2019

Answer (1)
NAVEEN MEENA Student Expert 6th Dec, 2019

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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