Derive an expression for energy stored in a parallel plate capacitor fo capacitane C with air as medium between the plates having charges `Q and -Q`. Show that this energy can be expressed in terms of electric field as `(1)/(2) in_(0) E^(2)` Ad, where A is area of each plate and d is the separation between the plates. How will the energy stored in a fully charged capacitor chanege when the separation between the plates is doubled and the dielectric medium of constant 4 is introduced between the plates ?

Explanation

For energy stored in the capacitor, refer to Art.
`U = (Q^(2))/(2C) = ((CV)^(2))/(2C) = (1)/(2) CV^(2)`
Now, `C = (in_(0) A)/(d) and E = (V)/(d)`
`:. U = (1)/(2) (in_(0) A)/(d) (Ed)^(2) = (1)/(2) in_(0) E^(2) Ad`
When separation between the plates is doubled `d' = 2d`, and
dielectric medium of constant 4 is intorduced ,
new capacity, `C' = (4)/(2) C = 2C`
As charged Q remains uncharged,
`:. U' = (Q^(2))/(2C') = (1)/(2) (Q^(2))/((2C)) = (1)/(2) U`