Question

Four point charges +q, +q, -q and -q are placed on the corners of a square of side length ${}^{\prime }{a}^{\prime }$ as shown in the figure. Magnitude of electric field at a point which is at a distance $x$(>>$a$) from the centre along a line perpendicular to the plane of square and passing through the center is

• A. $\frac{\sqrt{2}qa}{4\pi {\epsilon }_0{x}^3}$
• B. $\frac{qa}{2\pi {\epsilon }_0{x}^3}$
• C. $\frac{\sqrt{2}qa}{2\pi {\epsilon }_0{x}^3}$
• D. $\frac{qa}{4\pi {\epsilon }_0{x}^3}$

Answer 1

The correct option is B $\frac{qa}{2\pi {\epsilon }_0{x}^3}$

Consider the two charges in a column to form a dipole.
Field due to each of these dipoles at asked position is
$E=\frac{KP}{x^3}$ [since x >> a] in the same direction.
So the field due to both the dipoles is
$E_{net}=2E=\frac{2KP}{x^3}=\frac{qa}{2\pi {\epsilon }_0{x}^3}$