A certain isolated spherical cloud of charge has radius R. The electric potentia

Question

A certain isolated spherical cloud of charge has radius R. The electric potential inside this cloud of charge depends only on r, the distance from the center of the spherical cloud. The electric potential inside the cloud of charge is given by the expression V =-a,2 + b where a and b are constants with the units V/m2 and V, respectively. Express your symbolic answers to the questions below in terms of a, b, r, R, and 0, as needed. Please report your answers only as fractions (ie., if the answer is R/2, do not use o.SR) (a) write an expression for the electric field within the cloud of charge. (Hint: E-0 at r-0.) (b) write an expression for the flux through a spherical Gaussian surface of radius r

Explanation / Answer

a)
we know, E = -dV/dr

= 2*a*r

b) flux through sperical gaussian surfcae = E.A

= (2*a*r)*(4*pi*r^2)

= 8*pi*a*r^3

c) we know, flux = Qin/epsilon

Qin = flux*epsilon

rho*Volume = flux*epsilon

rho*(4/3)*pi*r^3 = 8*pi*a*r^3*epsilon

rho = 6*a*epsilon

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