Question

Four point charges are individually brought from infinity and placed at the corners of a square. Each charge has the identical value +Q. The length of the diagonal of the square is 2a. What is the electric potential at P, the center of the square?
a. kQ/4a
b. kQ/a
c. zero volts
d. 2kQ/a
e. 4kQ /a

Answer 1

To solve this problem we will apply the concept of voltage given by Coulomb's laws. From there we will define the charges and the distance, and we will obtain the total value of the potential difference in the system.

The length of diagonal is given as

$l = 2a$

The distance of the center of the square from each of the corners is

$r = \frac{2a}{2}= a$

The potential electric at the center due to each cornet charge is

$V_1 = \frac{kQ_1}{r_1}$

$V_2 = \frac{kQ_2}{r_2}$

$V_3 = \frac{kQ_3}{r_3}$

$V_4 = \frac{kQ_4}{r_4}$

The total electric potential at the center of the given square is

$V = V_1+V_2+V_3+V_4$

$V = \frac{kQ_1}{r_1}+ \frac{kQ_2}{r_2}+\frac{kQ_3}{r_3}+\frac{kQ_4}{r_4}$

Al the charges are equal, and the distance are equal to a, then

$V = \frac{kQ}{a}+ \frac{kQ}{a}+\frac{kQ}{a}+\frac{kQ}{a}$

$V = \frac{4kQ}{a}$

Therefore the correct option is E.