Four identical charged particles (q = +18.0 µC) are located on the corners of a rectangle as shown in the figure below. The dimensions of the rectangle are L = 61.0 cm and W = 11.0 cm. Calculate the change in electric potential energy of the system as the particle at the lower left corner in the figure is brought to this position from infinitely far away. Assume the other three particles in the figure below remain fixed in position.

To solve this problem, we need to calculate the potential energy change for each pair of charges as one charge is brought from infinity to its position. The formula for potential energy (U) between two point charges is given by:

U = kq1q2/r

where:

• k is Coulomb's constant (8.9910^9 Nm^2/C^2),
• q1 and q2 are the charges,
• r is the distance between the charges.

Given that the charge q = +18.0 µC = 18.0*10^-6 C, the length L = 61.0 cm = 0.61 m, and the width W = 11.0 cm = 0.11 m, we can calculate the potential energy for each pair:

1. The charge at the lower left corner and the charge at the upper left corner: U1 = kqq/L = 8.9910^9 * 18.010^-6 * 18.0*10^-6 / 0.61 = 0.47 J

2. The charge at the lower left corner and the charge at the upper right corner: U2 = kqq/(L^2 + W^2)^0.5 = 8.9910^9 * 18.010^-6 * 18.0*10^-6 / (0.61^2 + 0.11^2)^0.5 = 0.42 J

3. The charge at the lower left corner and the charge at the lower right corner: U3 = kqq/W = 8.9910^9 * 18.010^-6 * 18.0*10^-6 / 0.11 = 2.68 J

The total change in potential energy as the charge is brought from infinity to the lower left corner is the sum of these three energies:

ΔU = U1 + U2 + U3 = 0.47 J + 0.42 J + 2.68 J = 3.57 J

So, the change in electric potential energy of the system as the particle at the lower left corner is brought to this position from infinitely far away is 3.57 Joules.