P.24 |
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P.25 Dielectric Filled Capacitor |
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Statement
Two parallel conducting disks are separated by d and contain a dielectric with relative permittivity e. The upper disk is at a potential V1, and the lower disk at potential V2. Determine the charge densities on the disks.
System Parameters
Permittivity of free space:
Solution
As in the previous problem (Problem 8.1), neglect fringing so the potential will be a function in z only.
The difference between the potential at the upper plate and the potential at the lower plate gives the equation for A:
The electric field is given by
By the boundary conditions on conductors given in Chapter 6,
The charge density is positive on the upper plate and negative on the lower plate, since the potential drops from V1 to V2, and flux always originates on positive charges. Notice the sign on the fields is negative, since the unit vector in z points up and the field points down.
