1. Write down the elements of the stress tensor for an infinite solenoid carrying current I. What is the pressure on the curved surface of the solenoid whose cross section has a radius R?

2. Two opposite charges are at a distance q apart. Calculate the force between them using the stress tensor. (This is of course trivial but is primarily to test understanding of the method).

We will be calculating the force by integrating the stress tensor. In order to do so, we need the electric field expressions due to the two charges and also need to define a surface. Let us enclose the positive charge by a disk in the median plane and a hemisphere over it. The radius of the disk and hemisphere will be taken to be infinitely large so that the fields vanish. As a result the integration over the curved surface gives zero.

The net electric field on the median plane must be towards left (along .Thus only needs to be considered.

If we take an annular region at a distance y from the midpoint, the field strength is

Thus and the surface integral is