In this problem we will apply Gauss\'s law to a conducting shell that surrounds

Question

In this problem we will apply Gauss's law to a conducting shell that surrounds a charge. This problem is spherically symmetric, which makes it an ideal candidate for a Gauss's law analysis. A hollow conductor carries a net charge of +7 nC. In its cavity, insulated from the conductor, is a small, isolated sphere with a net charge of -5 nC. How much charge is on the outer surface of the hollow conductor? How much is on the inner surface of the cavity? SOLUTION SET UP (Figure 1) shows our sketch. We know that in this electrostatic situation the electric field in the conducting material must be zero. We draw a Gaussian surface within the material of the conductor and apply Gauss's law. SOLVE We apply Gauss's law Phi_E = Q_cncl/elementof_0 to the Gaussian surface shown in (Figure 1). The Gaussian surface lies within the conducting material, so E = 0 everywhere on that surface. By Gauss's law. Phi_E = Q_cncl/elementof. Thus, Phi_E = 0, so Q_cncl = 0. But then, in order to have Q_encl = 0, there must be a charge of +5 nC on the inner surface of the cavity, to cancel the charge in the cavity. The conductor carries a total charge of +7 nC, and all of its net charge is on its surfaces. So, if there is +5 nC on the inner surface, the remaining +2 nC must be on the outer surface, as shown in our sketch. REFLECT Field lines pass between the +5 nC on the inner surface of the cavity and the -5 nC on the object in the cavity. Each field line going to the -5 nC charge originated on the +5 nC charge; the field lines don't continue into the conducting material because E = 0 there. There is an electric field outside the conductor due to the +2 nC on its surface. Part A - Practice Problem: Determine the charge on the outer surface of the hollow conductor for the case where the conductor has a net charge of +3 nC. Express your answer in nanocoulombs to one significant figure. _____________ nC Part B - Practice Problem: Determine the charge on the inner surface of the cavity for the case where the conductor has a net charge of +3 nC. Express your answer in nanocoulombs to one significant figure.

Explanation / Answer

A) Charge on outer surface of hollow conductor = 3 - 5

                                                                              = - 2 nC

B) Charge on inner surface of cavity = + 5 nC

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