The work required to assemble two charges q1 and q2 from infinity to separation r12 is:

The work required to assemble two charges q1 and q2 from infinity to separation r12 is:

• A. W = - k q1 q2 / r12
• B. W = (1/2) k q1 q2 / r12
• C. W = k q1 q2 / (2 r12)
• D. W = k q1 q2 / r12

Answer: (D)

When you assemble two charges from infinity, the work you do equals the potential energy stored in the final arrangement. For two point charges, that potential energy is U(r) = k q1 q2 / r. Since U(∞) = 0, the external work required is W = U(r12) − U(∞) = k q1 q2 / r12. So the correct expression is W = k q1 q2 / r12. The sign of the result follows the product q1 q2: like charges give positive work by you, opposite charges give negative work (the field does the work). The other options misstate the sign or magnitude by misapplying the integral of the Coulomb force.

When you assemble two charges from infinity, the work you do equals the potential energy stored in the final arrangement. For two point charges, that potential energy is U(r) = k q1 q2 / r. Since U(∞) = 0, the external work required is W = U(r12) − U(∞) = k q1 q2 / r12. So the correct expression is W = k q1 q2 / r12. The sign of the result follows the product q1 q2: like charges give positive work by you, opposite charges give negative work (the field does the work). The other options misstate the sign or magnitude by misapplying the integral of the Coulomb force.