Question

Four point charges of magnitudes 3q q 2q and 4q are arranged in the corners of a square of side length L.The charge q creates a potential of 1 V relative to infinity in the center of the square.
What is the total potential created in the center of a square by all 4 charges?

a. 1V
b. 10V
c. It is impossible to determine without knowing the exact arrangement.
d. 0V
e. 5V

Answer 1

Answer:

d. 0V

Explanation:

The magnitude of four point charges are +3q, -q, +2q and -4q. I think you forget to mention the signs.

As we know that the potential due to the point charge that has traveled the distance d can be represented mathematically as,

$V = k\frac{q}{r}$

$k$ = 1/4λε = 9×$10^{9}$ Nm²/C²

Now as it is mentioned in the question that all four charges are arranged in the corners of a square so there distance from the center is same. We can rewrite the above potential equation as follows.

$V = \frac{k}{d} (q_{1} + q_{2} +q_{3} +q_{4} )$        (1)

We can find out d by the pythagoras theorem, as we are dealing with square so d is a semi diagonal.

$d = \sqrt{\frac{L^{2} }{4}+\frac{L^{2} }{4} } = \frac{\sqrt{2} }{2} L$

by putting all values in equation (1)

V = $\frac{9*10^{9} }{\frac{\sqrt{2} }{2} L } (+3q-q+2q-4q)$

V = 0V