Question

(a) We have said that Gauss’s law is always true, but only useful for calculating the electric field created by source charge distributions that are spheres, infinite straight cylinders, and infinite flat sheets, and even those cases have additional restrictions. Explain why we are limited to those distributions. Discuss what additional restrictions apply. For example, can we use Gauss’s law to find the field of a sphere whose density depends on distance r from the center? Can we do it for a sphere whose density depends on angle (e.g. different at the poles from at the equator)?

(b) An insulating sphere carries a charge that is spread uniformly throughout its volume. A conducting sphere of the same size carries the same charge, but it is spread over its surface only with no charge in the interior (as it must for a conductor!) Compare the electric fields outside the insulator to the field outside the conductor. Compare the electric fields inside the insulator to the field inside the conductor.

(c) Suppose I draw some Gaussian surface that encloses some, but not all, of the source charge in some region. If we were to move the source charges but were careful not to move any of them in or out of the test surface, could the electric field at a point on the Gaussian surface change? Could the flux through some part of the Gaussian surface change? Could the total flux through the entire Gaussian surface change?

(d) Show that flux times 1/4pi has units of charge (ie check the units of Gauss’s law.)

Answer 1