What is the potential energy U of two point charges q1 and q2 separated by distance r12?

What is the potential energy U of two point charges q1 and q2 separated by distance r12?

• A. U = k q1 q2 r12
• B. U = k q1 q2 / r12
• C. U = k q1 q2 / r12^2
• D. U = k (q1 + q2) / r12

Answer: (B)

Potential energy between two point charges comes from the work required to assemble them from infinity against the electrostatic force. For two charges q1 and q2 separated by a distance r12, the energy stored is U = k q1 q2 / r12, where k = 1/(4π ε0). This shows energy is proportional to the product of the charges and inversely proportional to their separation. If the charges have the same sign, U is positive, meaning you must do positive work to bring them together. If the charges have opposite signs, U is negative, indicating energy would be released when they’re brought to that separation. The other forms don’t fit because they either give the wrong distance dependence (multiplying by r12 or squaring r12) or combine the charges in a way that doesn't reflect the interaction energy between two point charges.

Potential energy between two point charges comes from the work required to assemble them from infinity against the electrostatic force. For two charges q1 and q2 separated by a distance r12, the energy stored is U = k q1 q2 / r12, where k = 1/(4π ε0).

This shows energy is proportional to the product of the charges and inversely proportional to their separation. If the charges have the same sign, U is positive, meaning you must do positive work to bring them together. If the charges have opposite signs, U is negative, indicating energy would be released when they’re brought to that separation.

The other forms don’t fit because they either give the wrong distance dependence (multiplying by r12 or squaring r12) or combine the charges in a way that doesn't reflect the interaction energy between two point charges.