A hollow conducting sphere of inner radius r_{1}and outer radiusr_{2} has a charge Q on its surface. A point charge –q is also placed at the centre of the sphere.

(a) What is the surface charge density on the (i) inner and (ii) outer surface of the sphere ?

(b) Use Gauss’ law of electrostatics to obtain the expression for the electric field at a point lying outside the sphere.

 

 
 
 
 
 

Answers (1)

a)

i) Surface charge density on the inner surface

=\frac{q}{4\pi r_1^2}

ii) Surface charge density on the outer surface

=\frac{q-Q}{4\pi r_2^2}

b) 

Let the point outside be at a distance r from the center of the sphere, such that r>r2 

Consider a Gaussian surface of radius r, then by Gauss law

\int E.ds=\frac{Q-q}{\epsilon_0}

\\ E\times4\pi r^2=\frac{Q-q}{\epsilon_0}\\E=\frac{Q-q}{4\pi\epsilon_0 r^2}

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