1. Plates of a parallel plate capacitor, of area A and separation d, have charge densities
![](Self Assesment_clip_image002.gif)
with the electric field being directed along the y direction. A small solenoid of radius
![](Self Assesment_clip_image002_0000.gif)
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.
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
![](Self Assesment_clip_image002_0006.gif)
which gives
.The Poynting vector points inward towards the axis along the polar r direction and the momentum density is given by
![](Self Assesment_clip_image002_0008.gif)
The total momentum stored per unit length is thus given by integrating this expression over the circular cross section,
![](Self Assesment_clip_image002_0009.gif)