For two point charges of opposite sign, the electric potential energy of the system is

For two point charges of opposite sign, the electric potential energy of the system is

• A. Negative
• B. Positive
• C. Zero
• D. Undefined

Answer: (A)

The key idea is that the potential energy of two point charges depends on the product q1 q2 and the separation r: U = k q1 q2 / r. When the charges have opposite signs, their product is negative, so the potential energy is negative. This reflects the attractive interaction: bringing opposite charges from infinity to a finite separation releases energy, so the system’s potential energy decreases (becomes more negative) as they get closer. At infinite separation the energy is defined as zero; as the distance shrinks, |U| grows and U becomes more negative, approaching negative infinity as r → 0 in the ideal point-charge model. That’s why the correct answer is negative. (Zero would occur only at infinite separation, and undefined would only arise at r = 0 within the point-charge model.)

The key idea is that the potential energy of two point charges depends on the product q1 q2 and the separation r: U = k q1 q2 / r. When the charges have opposite signs, their product is negative, so the potential energy is negative. This reflects the attractive interaction: bringing opposite charges from infinity to a finite separation releases energy, so the system’s potential energy decreases (becomes more negative) as they get closer. At infinite separation the energy is defined as zero; as the distance shrinks, |U| grows and U becomes more negative, approaching negative infinity as r → 0 in the ideal point-charge model. That’s why the correct answer is negative. (Zero would occur only at infinite separation, and undefined would only arise at r = 0 within the point-charge model.)