Write the potential at a point P due to two point charges q1 at r1 and q2 at r2.

Write the potential at a point P due to two point charges q1 at r1 and q2 at r2.

• A. V(P) = (1/(4π ε0)) [ q1/|P − r1| − q2/|P − r2| ]
• B. V(P) = (1/(4π ε0)) [ q1|P − r1| + q2|P − r2| ]
• C. V(P) = (1/(4π ε0)) [ q1/|P − r1| + q2/|P − r2| ]
• D. V(P) = (1/(4π ε0)) [ q1/|P + r1| + q2/|P + r2| ]

Answer: (C)

Electric potential from multiple point charges adds up. For a single charge q at position r0, the potential at P is V = (1/(4π ε0)) q / |P − r0|. With two charges at r1 and r2, the total potential is the sum of their contributions: V(P) = (1/(4π ε0)) [ q1 / |P − r1| + q2 / |P − r2| ]. This follows the superposition principle: potentials are scalar and simply add, and each distance is the magnitude of the vector from the charge to the point, |P − ri|. The sign of each term comes from the charge value itself, so negative charges contribute negative terms automatically. Expressions that use distances in the numerator, or distances like |P + r1|, or insert a fixed minus between terms, do not correctly represent the distance to the charges or the additive nature of the potential.

Electric potential from multiple point charges adds up. For a single charge q at position r0, the potential at P is V = (1/(4π ε0)) q / |P − r0|. With two charges at r1 and r2, the total potential is the sum of their contributions: V(P) = (1/(4π ε0)) [ q1 / |P − r1| + q2 / |P − r2| ]. This follows the superposition principle: potentials are scalar and simply add, and each distance is the magnitude of the vector from the charge to the point, |P − ri|. The sign of each term comes from the charge value itself, so negative charges contribute negative terms automatically. Expressions that use distances in the numerator, or distances like |P + r1|, or insert a fixed minus between terms, do not correctly represent the distance to the charges or the additive nature of the potential.