A nuclear charge(Ze) is non uniformly distributed within a nucleus of Radius R .The charge density rho(r) is dependent only on the radial distance r from the centre of the nucleus as shown in the fig.The electric field is only along the radial direction.

Q1=FOr a =0,the value of d would be?Ans=3(Ze)/pie *R3

Q2=Show that at r=R the electric field is independent of a?

If a = 0 then we have a and d as x and y intercepts respectively,

By coordinate geometry from the graph we have 

For r = R

The total flux coming out of the sphere will be

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