Question

Which of the following statements is true for two point charges of opposite sign?

• A. The potential energy is always negative
• B. The potential energy is always positive
• C. The potential energy can be either positive or negative
• D. The potential energy is zero

Hint:

Opposite charges = attractive interaction = negative potential energy. Same sign charges = repulsive interaction = positive potential energy.

Answer 1

The Correct Option is A

Step 1: Electric potential energy between charges.
The potential energy between two point charges is given by the formula: \[ U = \frac{{k \cdot q_1 \cdot q_2}}{{r}} \] where \(k\) is the Coulomb constant, \(q_1\) and \(q_2\) are the charges, and \(r\) is the distance between them.
Step 2: Analyzing the sign of potential energy.
- When two point charges have opposite signs (one positive and one negative), their potential energy is always negative because the product of \(q_1 \cdot q_2\) will be negative. This indicates an attractive interaction between the charges.
Step 3: Explanation of each option.
- (A) The potential energy is always negative: Correct. For opposite charges, the potential energy is negative due to the attractive force.
- (B) The potential energy is always positive: Incorrect. This happens only for like charges.
- (C) The potential energy can be either positive or negative: Incorrect for opposite charges, where the energy is always negative.
- (D) The potential energy is zero: Incorrect. The potential energy is not zero for opposite charges unless the charges are at infinite distance.
Step 4: Conclusion.
For two point charges of opposite signs, the potential energy is always negative.