Question

two parallel plates have area Aand seperation d they are given charges q1 and q2 they repel each other by a force
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Answer 1

Given that,

Area = A

First charge = q₁

Second charge = q₂

Separation = d

The charges repel each other by a force.

We need to calculate the charge density

Using formula of charge density

$\sigma=\dfrac{q}{A}$

put the value into the formula

$\sigma_{1}=\dfrac{q_{1}}{A}$

We need to calculate the field due to first plate on second plate

Using formula of electric field

$E=\dfrac{\sigma_{1}}{2\epsilon_{0}}$

Put the value into the formula

$E=\dfrac{q_{1}}{2A\epsilon_{0}}$

We need to calculate the force on second plate due to first plate

Using formula of force

$F=Eq_{2}$

Put the value into the formula

$F=\dfrac{q_{1}}{2A\epsilon_{0}}\times q_{2}$

$F=\dfrac{q_{1}q_{2}}{2A\epsilon_{0}}$

Hence, The force is $\dfrac{q_{1}q_{2}}{2A\epsilon_{0}}$