Question

Derive the expression for the capacitance of a parallel plate capacitor.

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Solution

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Let be the separation of two conducting parallel plates , each of area .
If charge is given to first plate , then charge is induced on inner surface of second plate and charge induced on the outer surface , is earthed .
Now , the electric field between the two plates will be ,
            
or        ...........eq1
If is he surface density of the plates , then the electric field between two plates is given by ,
            ...............eq2
where absolute permittivity of the free space.
Putting the value of from eq2 to eq1 , we get
           ................eq3
but we have ,
           
hence ,
Now , capacitance of parallel capacitor ,
             
or        

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