Question

Four charges q, 2q, 3q and 4q are placed at corners A, B, C and D of a square as shown in the figure below. Find the direction of electric field at the centre P of the square.

Answer 1

We can draw a figure representing the electric field

Let each side of the square be $a$.

Then distance of the center of the square from each vertices will be $\frac{a}{\sqrt{2}}$
From the figure,

Electric field due to charge q at the center
$E_A=\frac{kq}{{\left(\frac{a}{\sqrt{2}}\right)}^2}=\frac{2kq}{a^2}$

Electric field due to charge 2q at the center
$E_B=\frac{2kq}{{\left(\frac{a}{\sqrt{2}}\right)}^2}=2\left(\frac{2kq}{a^2}\right)$

Electric field due to charge 3q at the center
$E_C=3\left(\frac{2kq}{a^2}\right)$

Electric field due to charge 4q at the center
and $E_D=4\left(\frac{2kq}{a^2}\right)$

Now,

Resultant of $E_{C}and{E}_A$ will be in the direction of $E_C$ because its value is greater

The resultant of $E_{B}and{E}_D$ is in the direction of $E_D$ because its value is greater

Now from the figure, we can say that the results of electric field in the direction of $E_{C}and{E}_D$ will be along CB
So, the resultant is along CB.