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Q.

A capacitor is formed by two square metal-plates of edge a, separated by a distance d. Dielectrics of dielectric constants K1 and K2 are filled in the gap as shown in fig. Find the capacitance.

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a

ε0K1+K2a2lnK1K2K1K2d

b

ε0K1K2a2lnK1K2K1K2d

c

ε0K1K2a2lnK2K1K1K2d

d

ε0K1+K2a2lnK2K1K1K2d

answer is A.

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Detailed Solution

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AB = x tan θ, BC = d - x tan θ,,

Capacitance of the strip is   

dC=ε0AsABK1+BCK20CdC=0ε0bdxxtanθK1+dxtanθK2C=ε0bK1K2K2K1tanθlogeK1d+K2K1ltanθK1d

But tan θ=dl and A = l x b

C=ε0AK1K2K2K1dlogeK2K1=ε0K1K2a2lnK1K2K1K2d

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