Question

Four identical charges Q are fixed at the four corners of a square of side a. The electric field at a point P located symmetrically at a distance a/$\sqrt{2}$ from the center of the square is:

• A. $\frac{Q}{2\sqrt{2}\pi {\epsilon }_0{a}^2}$
• B. $\frac{Q}{\sqrt{2}\pi {\epsilon }_0{a}^2}$
• C. $\frac{2\sqrt{2}Q}{\pi {\epsilon }_0{a}^2}$
• D. $\frac{\sqrt{2}Q}{\pi {\epsilon }_0{a}^2}$

Answer 1

The correct option is B $\frac{Q}{\sqrt{2}\pi {\epsilon }_0{a}^2}$

as shown in horizontal components of the forces cancel each other but vertical components are in same direction and of equal magnitude $Ecos\theta$ hence,

$E_{net}=4Ecos\theta =\frac{4}{4\pi {\epsilon }_0}\frac{Q}{a^2}\frac{1}{\sqrt{2}}=\frac{Q}{\sqrt{2}\pi {\epsilon }_0{a}^2}$