50 POINTS! please help asap!

Two point charges, each of magnitude +a, are separated by a distance d. Refer to the diagram for a model of the point charges.

The point charges are allowed to move in the electric field that they generate. Which describes their movement and change in electric potential energy?
A: They move toward each other, and their electric potential energy increases.
B: They move away from each other, and their electric potential energy decreases.
C: They move toward each other, and their electric potential energy decreases.
D: They move away from each other, and their electric potential energy increases.



Answer :

Answer:

Explanation:

Given that both charges have the same sign (+a), they will experience a repulsive force due to the like charges. This force will cause them to move away from each other.

The electric potential energy (U) between two point charges can be calculated using the formula:

\[ U = \frac{k \cdot |q_1 \cdot q_2|}{r} \]

where:

- \( k \) is Coulomb's constant (\(8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2\))

- \( q_1 \) and \( q_2 \) are the magnitudes of the charges

- \( r \) is the distance between the charges

Since both charges are positive, the product \( |q_1 \cdot q_2| \) is positive.

When the charges move away from each other, the distance \( r \) in the denominator increases. Since \( r \) is in the denominator, increasing it will decrease the overall potential energy.

So, the correct answer is:

B: They move away from each other, and their electric potential energy decreases.