Two conductors carrying equal and opposite charges produce a non uniform electric field along X- axis given by `E=(Q)/(in_(0)A)(1+Bx^(2))` where `A` and `B` are constant. Separation between the conductors along X-axis is `X`. Find the capacitance of the capacitor formed.

Explanation

Potential difference between the conductors is given by `V=V_(+) -V_(-) = underset(0) overset(x) int Edx`
`rArr V= underset(0) overset(x) int (Q)/(in_(0)A)(1-Bx^(2))dx`
or `V=(Q)/(in_(0) A)(x-(Bx^(3))/(3))_(O)^(X)=(Q)/(in_(0)A) (X+(BX^(3))/(3))`
Capacity `C=(Q)/(V) =(in_(0) A)/(X(1+(BX^(2))/(3)))`.