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? Figure Net charge - +7 nC +5 nC on cavity wall Gaussian surface +2 nC on outer surface 1 of 1 > 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 g = Qenel/€o 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, g = Qencl/co. Thus, g = 0, so Qencl = 0. But then, in order to have Qencl = 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 +2 nC. Express your answer in nanocoulombs. ΠΫΠΙ ΑΣΦ q= Submit ▾ Part B - Practice Problem: Request Answer q= Submit → Determine the charge on the inner surface of the cavity for the case where the conductor has a net charge of +2 nC. Express your answer in nanocoulombs. [95] ΑΣΦΑ @ Request Answer C ? nC C Q ? nC

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? Figure Net charge - +7 nC +5 nC on cavity wall Gaussian surface +2 nC on outer surface 1 of 1 > 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 g = Qenel/€o 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, g = Qencl/co. Thus, g = 0, so Qencl = 0. But then, in order to have Qencl = 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 +2 nC. Express your answer in nanocoulombs. ΠΫΠΙ ΑΣΦ q= Submit ▾ Part B - Practice Problem: Request Answer q= Submit → Determine the charge on the inner surface of the cavity for the case where the conductor has a net charge of +2 nC. Express your answer in nanocoulombs. [95] ΑΣΦΑ @ Request Answer C ? nC C Q ? nC

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter25: Gauss’s Law

Section: Chapter Questions

Problem 68PQ: Examine the summary on page 780. Why are conductors and charged sources with linear symmetry,...

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