Question

four point charges Q,q,Q,q are placed at the corners of a square of side a find the resultant electric force on a charge Q

Answer 1

Resultant force on Q is
$\frac{kQ^2}{2a^2}+\sqrt{2}\frac{kQq}{a^2}$

Answer 2

Resultant electric force on charge Q is $\bold{F_{n e t}=\left[\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{a^{2}}\left(\frac{Q}{2}+q \sqrt{2}\right)\right] N}$

Solution:

The net force resulting on charge Q at the center by the four point charges at corner of the square of length a are calculated as follows,

Given: Point charges as “Q, q Q and q”.

Square side = a

Force on charge Q imposed by charge q will be, $F=\frac{1}{4 \pi \varepsilon_{0}} \frac{q Q}{a^{2}}$

Force on charge Q imposed by charge Q will be, $F=\frac{1}{4 \pi \varepsilon_{0}} \frac{Q^{2}}{\sqrt{2} a^{2}}$

Force on charge Q imposed by charge q and q will be, $F=\frac{1}{4 \pi \varepsilon_{0}} \frac{q Q}{a^{2}} \sqrt{2}$

Therefore, Net resultant of force acting on charge Q by all the four point charges be –

$\bold{F_{n e t}=\left[\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{a^{2}}\left(\frac{Q}{2}+q \sqrt{2}\right)\right] N}$