The cross-section of a two-dimensional system is shown in Fig. P7.9.9. The parallel plate…
The cross-section of a two-dimensional system is shown in Fig. P7.9.9. The parallel plate capacitor to the left of the plane 0 extends to with the lower electrode at potential and the upper one grounded. This upper electrode extends to the right to the plane , where it is bent downward to and inward to the plane along the surface . Region (a) is free space while region (b) to the left of the plane has uniform permittivity and conductivity . The applied voltage is a step function of magnitude Vo.
(a) The voltage has been on for a long-time. What are the field and potential distributions in region (b)? Having determined , what is the potential in region (a)?
(b) Now, is to be found for . Example 6.6.3 illustrates the approach that can be used. Show that in the limit becomes the result of part (a).
(c) In the special case where = , sketch the evolution of the field from the time just after the voltage is applied to the long-time limit of part (a).