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Suppose the space between the two inner shells of the previous problem is filled with a dielectric of dielectric constant K. Find the capacitance of the system between A and B.
Sol. Here we should consider two spherical capacitor of capacitance cab and cbc in series Cab = 4πε base 0abk/(b - a) Cbc = 4πε base 0bc/(c - b) 1/C = 1/Cab + 1/Cbc = (b - a)/4πε base 0abk + (c - b)/4πε base 0bc = c(b - a) + ka(c - b)/k4πε base 0abc C = 4πε base 0kabc/c(b - a) + ka(c - b)
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