A capacitor is made of two square plates each of side ′a′ making a very small angle a between them, as shown in figure. The capacitance will be close to
A
ϵ0a2d(1−3αa2d)
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B
ϵ0a2d(1−αa4d)
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C
ϵ0a2d(1+αad)
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D
ϵ0a2d(1−αa2d)
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Solution
The correct option is Dϵ0a2d(1−αa2d)
Consider an infinitesimal strip of capacitor of thickness dx at a distance x as shown
Capacitance of parallel plate capacitor of area A is given by C=ϵ0At
[Here t = seperation between plates]
So, capacitance of thickness dx will be
∴dC=ϵ0adxd+xtanα
Total capacitance of system can be obtained by integrating with limits x=0tox=a