# 3. Physics | Capacitance | Non-uniform Electric Field in a Capacitor | by Ashish Arora (GA)

in this illustration, we’ll see about non

uniform electric field in a capacitor. here the figure shows 2 conductors ay and b of

a capacitor which is charged. and due to the shape of these conductors their exist a non

uniform electric field between conductors which is given as q by b, 1 plus ay x square.

where ay and b are constants, and here we are required to find the capacitance of this

capacitor. now in this situation to find the capacitance we can first find out the potential

difference between the 2 conductors. which can be calculated as potential difference

between. ay and b is given as v ay minus v b as field exist from left to right ay will

be at higher potential. this is integration of e d x from zero to d, as separation between

the conductors is, taken as d. so, this will be integration from zero to d, electric field

we can write as q by b. 1 plus, ay x square, d x. which on integration gives q by b. x

plus, ay x cube by, 3. and limits, we substitute from zero to d. so this is q d by b. multiplied

by 1 plus, ay d square by 3, so if this is the potential difference we can directly find

out the capacitance between. ay and b which is given as c, that is. the charge, of capacitor

plate divided by the potential difference across, the 2 conductors of capacitor. so

on substituting here q gets cancelled out this will give us 3 b. divided by d. 3 plus.

ay d square, that is, the result of this problem.

## One Reply to “3. Physics | Capacitance | Non-uniform Electric Field in a Capacitor | by Ashish Arora (GA)”

how to find the capacitance of the electrodes of spark gap having spherical shape ??