Which expression correctly gives the potential at a point due to two charges q1 and q2 at distances r1 and r2 from the point?

Which expression correctly gives the potential at a point due to two charges q1 and q2 at distances r1 and r2 from the point?

• A. V = k (q1 / r1) + k (q2 / r2)
• B. V = k (q1 / r2) + k (q2 / r1)
• C. V = k (q1 / r1 + q2 / r2)
• D. V = k (q1 r1 + q2 r2)

Answer: (C)

The key idea is that electric potential adds. Each point charge creates a potential that falls off as 1/r, specifically V = k q / r. To get the total potential at a point due to two charges, you add the contributions from each charge: V = k q1 / r1 + k q2 / r2. You can factor out the constant k to get the compact form V = k (q1 / r1 + q2 / r2). This form correctly assigns each charge its own distance to the point and then sums the two contributions, which is how potentials from multiple charges combine. Forms that mix distances between charges or multiply the distances would misrepresent how each charge contributes, and would not match how the 1/r dependence works.

The key idea is that electric potential adds. Each point charge creates a potential that falls off as 1/r, specifically V = k q / r. To get the total potential at a point due to two charges, you add the contributions from each charge: V = k q1 / r1 + k q2 / r2. You can factor out the constant k to get the compact form V = k (q1 / r1 + q2 / r2). This form correctly assigns each charge its own distance to the point and then sums the two contributions, which is how potentials from multiple charges combine. Forms that mix distances between charges or multiply the distances would misrepresent how each charge contributes, and would not match how the 1/r dependence works.