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A charge Q is placed at the centre of an...

A charge Q is placed at the centre of an uncharged, hollow metallic sphere of radius a. (a) Find the surface charge density on the inner surface and on the outer surface. (b) If a charge q is put on the sphere, what would be the surface charge densities on the inner and the outer surface? (c) Find the electric field inside the sphere at a distance x from the centre in the situations (a) and (b).

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
a.
`sigma_i=(-Q)/(4pia^2)and `sigma_0=Q/(4pia^2)`
b.
`sigma_i=(-Q)/(4pia^2)`
and `sigma_0=((Q+q))/(4pia^2)`
c. According to Gauss's theorem,
`E=1/(4piepsilon_0) q_("in")/r^2`
For `xleR, q_("in")=Q`
and r=x both cases
`:. E=1/(4piepsilon_0) Q/x^2`
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