Question

A negative charge is placed inside the cavity of a hollow metal solid. The outside of the solid is grounded by connecting a conducting wire between it and the earth. (a) Is there any excess charge induced on the inner surface of the piece of metal? If so, find its sign and magnitude. (b) Is there any excess charge on the outside of the piece of metal? Why or why not? (c) Is there an electric field in the cavity? Explain. (d) Is there an electric field within the metal? Why or why not? Is there an electric field outside the piece of metal? Explain why or why not. (e) Would someone outside the solid measure an electric field due to the charge Is it reasonable to say that the grounded conductor has shielded the region from the effects of the charge In principle, could the same thing be done for gravity? Why or why not?

Answer 1

a) +Q b) No. c) Yes. d) No e) No

Step-by-step explanation:

a) As charges can move freely on a conductor, any excess charge must be on the surface.

In this case, as charge must be conserved, a charge of opposite sign and equal magnitude to the one within the cavity must build on the inner surface of the metal.

b) If a charge + Q is built on the inner surface, charges inside must distribute in such a way that total charge, as looked from outside, must be the same, so a -Q charge should be on the outer surface.

However, as the outer surface is grounded, this means that there is a infinite source of sink of charge connected to the outer surface, which means that no excess charge can be on the outside side of the piece of metal.

c) As we have a charge -Q and a distributed +Q charge between the inner surface and the negative charge, there must exist an electric field inside, created by these charge distributions, going from the inner surface to the negative charge.

d) In electrostatic condition, no electric field can exist within a metal, as charges would move in order to do this field zero.

In this case, as the outer surface is grounded, no electric field can exist outside the metal.

e) As the conductor is grounded, no electric field can be measured from the outside of the metal (because the charge that creates this field, normal to the outer surface doesn't exist due to grounding), so it is reasonable to say that grounding has shielded the region from the effects of the charge.

This could not be possible to be done with gravity, due to while there are two types of charges, that attract or repel, masses only attract each other.