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

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Asked Sep 14, 2019
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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.

A) Is any excess charge induced on the inner surface of the metal? Is there      any excess charge on the outside of the metal? Why or why not?

B) Can an electric field due to the charge -Q be measured from the                  outside of the solid? Is it reasonable to say that the grounded                      conductor has shielded the region outside the conductor from the              effects of -Q? In principle, could the same thing be done for gravity?            Why or why not?

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Expert Answer

Step 1

Consider a hollow metal solid has a charge of –Q inside the cavity. It can be of the form as given below.

The presence of negative charge in the cavity induces equal and opposite charge on the inner surface of the metal solid. So the inner surface will have uniform distribution of +Q charge over it.

+
-Q
+
+
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+ -Q + +

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Step 2

Since the solid is a neutral metal the induction of positive charges on the inner surface will cause the outer surface to have equal and opposite charge to keep the neutrality of the metal solid. The –Q charge will then be uniformly distributed on the outer surface of the solid. However the outer surface is grounded to the earth and it will cause the –Q charge produced on the outer surface to flow to the ground. Hence there will not be any excess charge on the outer surface of the solid.

Step 3

Consider a Gaussian surface of any arbitrary shape surrounding the hollow metal solid with the Q charge inside the cavity. The inner surface has +Q charge and the cavity has –Q charge and so the tota...

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