The electric potential at distance r from a point charge q is V(r) = ?

The electric potential at distance r from a point charge q is V(r) = ?

• A. V(r) = k q r
• B. V(r) = k q / r^2
• C. V(r) = k q / r
• D. V(r) = k / r

Answer: (C)

The main idea is that the potential from a point charge falls off with distance as 1/r. The electric field of a point charge is E(r) = k q / r^2 directed radially. To get the potential, use V(r) − V(∞) = −∫∞^r E·dr'. With the usual reference V(∞) = 0, this becomes V(r) = −∫∞^r (k q / r'^2) dr' = k q / r. So the potential decreases inversely with distance and scales with the charge q. This matches the chosen form because it has the correct inverse-distance dependence and the correct q factor, with k being 1/(4πε0). The other forms don’t fit the physics: one would grow with distance, another would correspond to the field rather than the potential, and one would miss the charge factor and have inconsistent units.

The main idea is that the potential from a point charge falls off with distance as 1/r. The electric field of a point charge is E(r) = k q / r^2 directed radially. To get the potential, use V(r) − V(∞) = −∫∞^r E·dr'. With the usual reference V(∞) = 0, this becomes V(r) = −∫∞^r (k q / r'^2) dr' = k q / r. So the potential decreases inversely with distance and scales with the charge q.

This matches the chosen form because it has the correct inverse-distance dependence and the correct q factor, with k being 1/(4πε0). The other forms don’t fit the physics: one would grow with distance, another would correspond to the field rather than the potential, and one would miss the charge factor and have inconsistent units.