## PHYS208 Fundamentals of Physics II

### Answer for Ch. 24, 25P

a) Consider a gaussian cylinder centered inside the negative charge distribution. With no net charge enclosed, the electric flux must be zero. Since the electric field must be constant everywhere on the tube wall, the electric field must be zero.

Note that the result is the same as if the charge were concentrated in a line along the axis.

### Answer for Ch. 24, 31P

Consider a gaussian cylinder of radius r and length L. The charge enclosed by the cylinder is given by

and the flux through the tube wall is given by

There is no flux contribution from the endcaps. By Gauss's law, the electric field is then proportional to the distance from the center and to the charge density:

pointing inward.

Outside the cylinder a "line of charge" result is obtained.

### Answer for Ch. 24, 32E

Using the result for a sheet of charge

along with the superposition principle, yields

directed outward, outside the sheets.

Inside the sheets the electric field is zero.

### Answer for Ch. 24, 52P

a) To find the total charge on the sphere, integrate over the charge density with spherical shells, from 0 to R, as shown:

b) Consider a gaussian sphere of radius r, centered in the charged sphere. Then the charge enclosed is given by:

Note the change to the dummy variable r' for integration.