1. Plates of a parallel plate capacitor, of area A and separation d, have charge densities with the electric field being directed along the y direction.  A small solenoid of radius is placed symmetrically within the capacitor so that its axis is along the z axis. The solenoid carries n turns per unit length and has a current I flowing in its turns. Calculate the  momentum contained in the system, ignoring  fringe effect.

The electric field is given by ,the magnetic field is confined to the solenoid and is The momentum is confined to the volume of the solenoid and is given by per unit volume.

2. A solenoid with n turns per unit length is wound over a non-magnetic core. A current is switched on at time t=0.  The radius of cross section of the solenoid is R. Calculate the amount of momentum stored in a unit length of the solenoid.

In this case the field in the solenoid is . As the current in the turns vary with time, there is an electric field which is circumferential and is obtained by calculating the line integral over a circle of radius r and equating it with the flux through the circular path

which gives .The Poynting vector points inward towards the axis along the polar r direction and the momentum density is given by

The total momentum stored per unit length is thus given by integrating this expression over the circular cross section,