For two point charges q1 and q2 separated by r12, what is their electric potential energy U12?

For two point charges q1 and q2 separated by r12, what is their electric potential energy U12?

• A. U12 = (1/(4π ε0)) (q1 q2 / r12^2)
• B. U12 = (1/(4π ε0)) (q1 q2 / r12)
• C. U12 = (1/(4π ε0)) (q1 q2 r12)
• D. U12 = (1/(4π ε0)) (q1 q2 / r12^3)

Answer: (B)

The potential energy between two point charges depends on their separation and on the product of the charges. This energy is the work required to assemble the pair from infinity, and it scales with 1 over the distance between them. Using k = 1/(4π ε0), the expression for two charges q1 and q2 separated by r12 is U12 = k q1 q2 / r12. So the correct form is (1/(4π ε0)) (q1 q2 / r12). Note how the energy changes with sign: same-sign charges give positive energy, opposite signs give negative energy. The other forms would imply different distance dependencies (like 1/r^2, 1/r^3, or a direct proportionality to r), which do not describe the potential energy between two static point charges.

The potential energy between two point charges depends on their separation and on the product of the charges. This energy is the work required to assemble the pair from infinity, and it scales with 1 over the distance between them. Using k = 1/(4π ε0), the expression for two charges q1 and q2 separated by r12 is U12 = k q1 q2 / r12. So the correct form is (1/(4π ε0)) (q1 q2 / r12).

Note how the energy changes with sign: same-sign charges give positive energy, opposite signs give negative energy. The other forms would imply different distance dependencies (like 1/r^2, 1/r^3, or a direct proportionality to r), which do not describe the potential energy between two static point charges.