Question

A negative charge -Q 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. Is any excess charge induced on the inner surface of the metal? Is there any excess charge on the outside surface of the metal? Why or why not? Would someone outside the solid measure an electric field due to the charge -Q? Is it reasonable to say that the grounded conductor has shielded the region outside the conductor from the effects of the charge -Q? In principle, could the same thing be done for gravity? Why or why not?

Answer 1

There is excess charge on the outside surface of the metal, with a magnitude equal to -Q. The charge on the outer surface of the metal does shield the region outside the conductor from the effects of the charge -Q.

Step-by-step explanation:

When a negative charge -Q is placed inside the cavity of a hollow metal solid and the outside of the solid is grounded, no excess charge is induced on the inner surface of the metal. This is because the electric field inside a conductor is zero, causing the negative charge to distribute itself evenly on the outer surface of the solid.

As a result, there is excess charge on the outside surface of the metal, with a magnitude equal to -Q. Someone outside the solid would measure an electric field due to the charge -Q, as the electric field is not shielded by the grounded conductor. However, the charge on the outer surface of the metal does shield the region outside the conductor from the effects of the charge -Q.

In principle, the same thing cannot be done for gravity. Gravity is a non-electromagnetic force and cannot be shielded by conductive materials. Therefore, a grounded conductor would not be able to shield the region outside it from the effects of gravity.

Answer 2

a) + Q charge is inducce that compensates for the internal charge

b) There is no excess charge on the external face q_net = 0

c) E=0

Step-by-step explanation:

Let's analyze the situation when a negative charge is placed inside the cavity, it repels the other negative charges, leaving the necessary positive charges to compensate for the -Q charge. The electrons that migrated to the outer part of the sphere, as it is connected to the ground, can pass to the earth and remain on the planet; therefore on the outside of the sphere the net charge remains zero.

With this analysis we can answer the specific questions

a) + Q charge is inducce that compensates for the internal charge

b) There is no excess charge on the external face q_net = 0

c) If we create a Gaussian surface on the outside of the sphere the net charge on the inside of this sphere is zero, therefore there is no electric field, on the outside

d) If it is very reasonable and this system configuration is called a Faraday Cage

e) We cannot apply this principle to gravity since there are no particles that repel, in all cases the attractive forces.