The capacitance of a parallel plate air capacitor is C. The capacitor is immesed half way into an oil of dielectric constant 1.6 with the plates perpendicular to the surface of the oil. What will be the capacitance of this capacitor?

Explanation

The capacitance of the half of the capacitor immersed in oil,
`C_1 = (k in_0)/(d)*(alpha)/(2)= (1.6 in_0)/(d)*(alpha)/(2)`
The capacitance of the other half of the capacitor in air,
`C_2 = (in_0)/(d)*(alpha)/(2)`
Net capacitance `=C_1+C_2= (1.6 in_0)/(d)*(alpha)/(2)+(in_0)/(d)*(alpha)/(2) = (2.6 in_0)/(d)* (alpha)/(2)`
`=(1.3 in_0)/(d)* alpha= 1.3C[ :. C =(in_0 alpha)/(d)]`.