Question

Consider four charges,
q₁ = 0.5 μC, q₂ = 0.3 μC, q₃ = -1.3 μC and q₄ = 1.5 μC, arranged at the corners of square, as shown in the figure below. If the side length of the square is 47.00 cm calculate the potential at the center of the square.

Answer 1

Answer 2

To calculate the potential at the center of the square, we need to calculate the contribution of each charge to the potential at that point and then add them up. The formula for the potential due to a point charge is:

V = k * q / r

where k is the Coulomb's constant (k = 9 x 10^9 N m^2 / C^2), q is the charge, and r is the distance between the charge and the point where we want to calculate the potential.

Let's call the center of the square point P. The distance between P and each charge is the diagonal of the square, which can be calculated using the Pythagorean theorem:

d = √(a^2 + a^2) = a√2

where a is the side length of the square.

So, the distance between P and each charge is:

d = 47 cm * √2 = 66.52 cm = 0.6652 m

Now, we can calculate the potential due to each charge:

V1 = k * q1 / d = 9 x 10^9 N m^2 / C^2 * 0.5 x 10^-6 C / 0.6652 m = 3.383 V V2 = k * q2 / d = 9 x 10^9 N m^2 / C^2 * 0.3 x 10^-6 C / 0.6652 m = 2.030 V V3 = k * q3 / d = 9 x 10^9 N m^2 / C^2 * (-1.3 x 10^-6 C) / 0.6652 m = -8.809 V V4 = k * q4 / d = 9 x 10^9 N m^2 / C^2 * 1.5 x 10^-6 C / 0.6652 m = 10.149 V

The total potential at the center of the square is the sum of these individual potentials:

Vtotal = V1 + V2 + V3 + V4 = 3.383 V + 2.030 V - 8.809 V + 10.149 V = 6.753 V

Therefore, the potential at the center of the square is 6.753 V.