Question

If the distance between the two charges is increased, then the electrostatic potential energy of the charges

• A. decreases
• B. increases
• C. may increase or decrease
• D. remains the same

Hint:

Think of it like forces: separating two things that repel each other (like charges) is "easy" and releases energy, so potential energy decreases. Separating two things that attract each other (unlike charges) requires work, so potential energy increases.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Electrostatic potential energy (\(U\)) of a system of two point charges is the work done in assembling the charges from an infinite separation to their current positions.
Step 2: Key Formula or Approach:
The formula for the electrostatic potential energy between two point charges \(q_1\) and \(q_2\) separated by a distance \(r\) is:
\[ U = k \frac{q_1 q_2}{r} \] where \(k\) is Coulomb's constant.
Step 3: Detailed Explanation:
The change in potential energy when the distance \(r\) is increased depends on the product of the charges \(q_1 q_2\), which is determined by whether the charges are like (both positive or both negative) or unlike (one positive, one negative).
Case 1: Like Charges
If both charges are positive or both are negative, their product \(q_1 q_2\) is positive.
In this case, \(U = k \frac{|q_1 q_2|}{r}\) is positive. As the distance \(r\) increases, the value of the fraction \(\frac{1}{r}\) decreases. Consequently, the potential energy \(U\) decreases. This makes sense, as the repulsive force does positive work when the charges move apart.
Case 2: Unlike Charges
If one charge is positive and the other is negative, their product \(q_1 q_2\) is negative.
In this case, \(U = -k \frac{|q_1 q_2|}{r}\) is negative. As the distance \(r\) increases, the value of \(\frac{1}{r}\) decreases, making \(U\) less negative (i.e., it moves closer to zero). A change from a more negative value to a less negative value is an increase. This makes sense, as work must be done against the attractive force to separate the charges.
Step 4: Final Answer:
Since the question does not specify whether the charges are like or unlike, the potential energy may either increase (for unlike charges) or decrease (for like charges) when the distance is increased. Thus, option (C) is correct.