Rank the electric potential energies of the systems of charges shown in the figure below from largest to smallest. Indicate equalities if appropriate. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.)

Question

Incorrect: Your answer is incorrect.

Four figures show four different charge distributions.
Figure a. An equilateral triangle of side length d has a positive charge Q at each of its three vertices.
Figure b. An equilateral triangle of side length d has a positive charge Q at two of its vertices and a negative charge, −Q, at its third vertex on the bottom right of the triangle.
Figure c. A square of side length d has a positive charge Q at each of its four vertices.
Figure d. A square of side length d has a positive charge Q at three of its vertices and a negative charge, −Q, at its fourth vertex on the bottom right of the square.

Answer 1

To compare the electric potential energies for the given charge distributions, we need to consider how the arrangement and magnitude of the charges influence the potential energy of each system.

1. Figure a: All three charges are positive \( Q \) at the vertices of the triangle. The potential energy is positive and relatively high due to the repulsive nature of the positive charges.

2. Figure b: Two positive charges \( Q \) and one negative charge \( -Q \) create an attraction between the positive and negative charges, which decreases the total potential energy compared to Figure a.

3. Figure c: All four charges are positive \( Q \) at the corners of the square. This system similarly has positive potential energy due to repulsion, and because there are four charges, the total potential energy is higher than that in Figure a.

4. Figure d: This arrangement consists of three positive charges \( Q \) and one negative charge \( -Q \). Like in Figure b, the negative charge will result in a lower potential energy compared to the previous examples because of the attractive interaction with the positive charges.

Based on this reasoning, we can rank the electric potential energies from largest to smallest:

1. Figure c (all positive charges, maximum positive potential)
2. Figure a (all positive charges, high positive potential)
3. Figure d (three positive charges, one negative charge lowers potential)
4. Figure b (two positive charges, one negative charge lowers potential even more)

Thus, the ranking from largest to smallest electric potential energies is:

c > a > d > b