Three point charges +q are placed at corners

of a square with sides of length L.
+
+
+
A B
L
O
What is the potential at point A?

To determine the potential at point A due to the three point charges, we need to consider the principle of superposition. The potential at a given point is the sum of the potentials due to each individual charge.

The potential due to a point charge is given by the formula:
V = k * q / r

where V is the potential, k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2), q is the charge, and r is the distance from the charge to the point where the potential is being calculated.

In this case, point A is equidistant from the three point charges. Let's label the charges as q1, q2, and q3.

To calculate the potential at point A, we need to find the distance between a charge and point A. In this square arrangement, since the distance between charges is equal to the side length (L), each charge is at a distance L from point A.

Using the formula for potential due to a point charge, the potential V1 at point A due to charge q1 is given by:
V1 = k * q1 / L

Similarly, the potential V2 at point A due to charge q2 is given by:
V2 = k * q2 / L

And the potential V3 at point A due to charge q3 is given by:
V3 = k * q3 / L

To find the total potential at point A, we sum up the potentials due to each charge:
V_total = V1 + V2 + V3

Substituting the given charge value (+q) for all three charges, we can write the expression for the potential at point A as:
V_total = k * q / L + k * q / L + k * q / L

Simplifying the expression:
V_total = 3 * k * q / L

So, the potential at point A due to the three charges located at the corners of the square is 3 times the potential due to a single charge q, divided by the side length L.