There exist two perfectly conducting spherical shells with radii a and b which form a capacitor and are designed by ITU Honeycomb. There is a potential difference V between the shells as shown in the figure. For 0 ≤0 ≤0, the region between the conductors is filled with an inhomogeneous dielectric of the permittivity (0) = (1 + cose) and the rest of the region for which 0 ≤0 ≤ π is filled with permittivity €0.

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There exist two perfectly conducting spherical shells with radii a and b which form a
capacitor and are designed by ITU Honeycomb. There is a potential difference V between the shells
as shown in the figure. For 0 ≤0 ≤0, the region between the conductors is filled with an
inhomogeneous dielectric of the permittivity (0) = (1 + cose) and the rest of the region for
which 0 ≤ ≤ is filled with permittivity €0.
a) Find E-field and D-field vectors, everywhere
b) Find the free surface charge density everywhere
c) Find the capacitance of the structure
€0
€ (0)
a
Z
00
5
Figure 3. The geometry of Q-4.
Transcribed Image Text:There exist two perfectly conducting spherical shells with radii a and b which form a capacitor and are designed by ITU Honeycomb. There is a potential difference V between the shells as shown in the figure. For 0 ≤0 ≤0, the region between the conductors is filled with an inhomogeneous dielectric of the permittivity (0) = (1 + cose) and the rest of the region for which 0 ≤ ≤ is filled with permittivity €0. a) Find E-field and D-field vectors, everywhere b) Find the free surface charge density everywhere c) Find the capacitance of the structure €0 € (0) a Z 00 5 Figure 3. The geometry of Q-4.
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