Question

Four charges of equal magnitude q = 2.16 µC are situated as shown in the diagram below. If d = 0.88 m, find the electric potential at location A due to the four charges. (enter the magnitude only)

Answer 1

Answer:

The total potential (magnitude only) is 11045.45 V

Explanation:

Electric Potential

The total electric potential at location A is the sum of all four individual potentials produced by the charges, including the sign since the potential is a scalar magnitude that can be computed by

$\displaystyle V=\frac{kq}{r}$

Where k is the Coulomb's constant, q is the charge, and r is the distance from the charge. Let's find the potential of the rightmost charge:

$\displaystyle V_1=\frac{9\cdot 10^{9}\times -2.16\cdot 10^{-6}}{0.88}=-22090.91\ V$

The potential of the leftmost charge is exactly the same as the above because the charges and distances are identical

$V_2=-22090.91\ V$

The potential of the topmost charge is almost equal to the above computed, is only different in the sign:

$V_3=+22090.91\ V$

The bottom charge has double distance and the same charge, thus the potential's magnitude is half the others':

$\displaystyle V_4=\frac{9\cdot 10^{9}\times 2.16\cdot 10^{-6}}{1.76}=+11045.45 \ V$

The total electric potential in A is

$V=-22090.91\ V-22090.91\ V+22090.91\ V+11045.45 \ V$

$V=-11045.45 \ V$

The total potential (magnitude only) is 11045.45 V