The drawing shows a square, each side of which has a length of L = 0.25 m. Two different positive charges q1 and q2 are fixed at the corners of the square. Find the electric potential energy of a third charge q3 = -5 x 10-9 C placed at corner A and then at corner B. q1= 1.5e-9 and q2=4.0e-9

To find the electric potential energy of charge q3 placed at the corners of the square, we need to calculate the electric potential energy between q3 and charges q1 and q2 separately.

The formula for the electric potential energy between two charges is given by:
U = k * (q1 * q2) / r

Where:
U is the electric potential energy
k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2)
q1, q2 are the magnitudes of the respective charges
r is the distance between the charges

Let's calculate the electric potential energy for each scenario:

1. Charge q3 placed at corner A:
a) Calculate the distance between q3 and q1 (diagonal of the square):
The diagonal of a square can be calculated using the Pythagorean theorem. Since each side of the square has a length of L = 0.25m, the diagonal can be calculated as follows:
d = √(L^2 + L^2) = √(0.25^2 + 0.25^2) = √(0.125) ≈ 0.354m

b) Now, we can calculate the electric potential energy between q3 and q1:
U1 = (k * q1 * q3) / r1 = (9 x 10^9 Nm^2/C^2) * (1.5 x 10^-9 C) * (-5 x 10^-9 C) / (0.354m)
U1 ≈ -17 J

2. Charge q3 placed at corner B:
a) Calculate the distance between q3 and q2 (side of the square):
The distance between q3 and q2 is simply the length of one side of the square:
r2 = L = 0.25m

b) Now, we can calculate the electric potential energy between q3 and q2:
U2 = (k * q2 * q3) / r2 = (9 x 10^9 Nm^2/C^2) * (4 x 10^-9 C) * (-5 x 10^-9 C) / (0.25m)
U2 ≈ -72 J

Therefore, the electric potential energy of q3 placed at corner A is approximately -17 Joules, while the electric potential energy of q3 placed at corner B is approximately -72 Joules.