# A spherical volume contains a uniformly distributed charge of density 2.0 × 10–4 C m–3. Find the electric field at a point inside the volume at a distance 4.0 cm from the centre.

Given:

Volume charge density ρ =2.0× 10-4C/m3

We have to find the electric field at a point at a distance 4cm from the centre.

Assume a spherical gaussian surface inside the sphere of radius 4cm=r

Volume of this spherical surface = Charge enclose by this gaussian spherical surface=(volume charge density)× (volume of gaussian surface containing charge) ……(i)

Surface area of this spherical gaussian surface=4πr2

All the points on this surface are equivalent and by symmetry we can say that field at every point on this surface is equal in magnitude and radial in direction.

Therefore flux through this surface can be written as …..(ii)

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 Using gauss’s law and eqn.(i) and eqn.(ii)  Putting the value of ρ, r and ϵ0 N/C N/C

Therefore electric field at a point inside volume at a distance 4cm from the centre is given by 3× 105N/C

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