Question

An initially uncharged hollow metallic sphere with radius of 5 cm has a small object with a charge of +10 mC carefully placed at the center of the sphere through a hole in the latter's surface. With the charge in place, what charge is now present on the outside surface of the sphere? I know the answer 10uC, but do not understand how to get there. Please show work.

Answer 1

Since the small positively charge object is kept at centre of a metallic sphere, it will attract negative charges on the sphere towards itself.

the negative charges are electrons, and free electrons are present in metals so free electrons will go to the inner surface fo the sphere to shield the charge kept at the centre.

Since, the concentration of negative charge carriers decreases on the outer surface, positive charge appears there.

This positve charge is equal to the negative charge moving towards the inner surface, which in turn is controlled by the charge kept at the centre.

assuming electrostatic condition has been achieved , there must be no E? inside the conductor, in accordance with Gauss's Law. Thus net charge inside any gaussian surface you imagine is 0 .

Now imagining this physically , suppose the whole sphere is made up of very very thin infinitesimal shells , you can assume condition to be like this in every infinitesimal shell (assume these to bespheres).

But you know net charge of an isolated system is conserved , so on the outermost surface there will be net charge = the charge you put inside in the first place.

Equal in terms of magnitude and sign .

And it'll also be uniformly distributed .Because of the symmetric nature of the sphere.