18.3

Gauss' Law

Student Notes

With this simulation, you can investigate the implications of Gauss' Law as it applies to charged spheres made from conductive material. You can use a thin-walled spherical shell as well as a thick-walled shell - compare the fields obtained to the electric field from a point charge. The view shown in the simulation represents a two-dimensional slice through the center of the shells, which is why they look like circles.
Here are some things to consider. Gauss' Law states that inside a uniformly charged spherical shell, the electric field due to the charge on the shell is zero. Verify that with the simulation. Under what condition is it possible to have a non-zero electric field inside a uniformly charged spherical shell? Another implication of Gauss' Law is that the electric field outside a uniformly charged spherical shell, with a net charge Q, is the same as the field from a point charge Q. Verify that with the simulation by measuring the electric field created by the inner shell, and then replacing the inner shell by the point charge. If the point charge has the same charge as the inner shell did, is the field the same in the region outside the inner shell? Set the charge on the outer shell to -1 mC, and the other two charges to zero. How is the charge distributed on the outer shell? Keeping the charge on the outer shell at -1 mC, give the inner shell a charge of +1 mC. How is the charge distributed on the outer shell now? What happens if you increase the charge on the inner shell? Using both spherical shells as well as the point charge, arrange it so there is an electric field inside the inner shell pointing toward the center, no electric field between the inner and outer shells, and an electric field outside the outer shell that points away from the center of the shells. How can you maximize the magnitude of the electric field in the region outside the outer shell?

Self-test

When there are two uniformly charged spherical shells, one inside the other as in this simulation, does one exert a net force on the other? Set the charge on the inner shell to +3 mC and the charge on the outer shell to -2 mC (the charge of the point charge should be set to zero). The field in the thick wall of the outer shell is zero. For this to happen, what is the total charge on the inner surface of the outer shell? What is the total charge on the outer surface of the outer shells? In the previous simulation you learned some general things about electric fields from point charges that should hold true for the charged spheres in this simulation. Here, though, you should also recognize two additional facts about the field near a charged conductor. First, what direction is the electric field at the surface of a conductor? Second, paying particular attention to the thick-walled outer shell, what is the electric field in the solid part of a conductor? In this simulation, when the charge on the outer shell is set to zero the shell is removed from the picture. How would the field-line diagram change if the outer shell were left in the picture even when it had no net charge?

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