How does the electric potential energy (EPE) between two point charges depend upon their separation s?
a. EPE ∝ 1/s
b. EPE ∝ s
c. EPE ∝ 1/s2
d. EPE ∝ s2
I want to say it's a. since it's part of the formula UE = kq1q2/s but I'm not too sure if that logic is correct.
Your logic is correct, and the answer is indeed option a. The electric potential energy (EPE) between two point charges depends inversely on their separation, s.
To explain this further, we can consider Coulomb's Law, which states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of their charges (q1 and q2) and inversely proportional to the square of their separation (s):
F = k * (q1 * q2) / s^2
Here, k is the electrostatic constant.
To calculate the electric potential energy, we can integrate the electrostatic force over the separation distance:
∆PE = ∫ F * ds
Since the formula for electrostatic force is F = k * (q1 * q2) / s^2, we can substitute it into the equation:
∆PE = ∫ (k * (q1 * q2) / s^2) * ds
Simplifying further, we have:
∆PE = k * q1 * q2 ∫ ds / s^2
The integral of ds / s^2 is -1/s, which results in:
∆PE = -k * q1 * q2 / s
Therefore, the electric potential energy (EPE) between two point charges is directly proportional to the inverse of their separation:
EPE ∝ 1/s
So, you were correct in selecting answer option a.