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

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.

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