In the region shown in cross-section in Fig. P5.6.4, the charge density is where and are…
In the region shown in cross-section in Fig. P5.6.4, the charge density is
where and are constants. Electrodes at constrain the potential there to be cos and given constants, while an electrode at makes .
(a) Find a particular solution that satisfies Poisson’s equation everywhere between the electrodes.
(b) What boundary conditions must the homogeneous solution satisfy at and ?
(c) Find in the region .
(d) The force density (force per unit volume) acting on the charge is . Find the total force acting on a section of the charge spanning the system from to , of unit length in the direction and of length in the direction.