Electric potential at distance r from a point charge q located at the origin is:

Electric potential at distance r from a point charge q located at the origin is:

• A. V(r) = k q / r
• B. V(r) = k q r
• C. V(r) = r / (k q)
• D. V(r) = ε0 q / r

Answer: (A)

Electric potential from a point charge falls off with distance as 1/r. For a charge q located at the origin, the electric field is radial: E = k q / r^2, where k = 1/(4π ε0). The potential difference between infinity and a point at distance r is V(r) = -∫∞^r E · dr. Since E points radially, this becomes V(r) = ∫∞^r (k q / r′^2) dr′ = k q / r. This uses the common convention V(∞) = 0, so the potential decreases as you move away from the charge and scales as 1/r. If q is negative, V(r) is negative accordingly, and as r → 0 the potential diverges. The other forms don’t fit because they either grow with distance (which would imply increasing potential with separation, not true for a point charge), have the wrong units, or miss the correct constant 1/(4π ε0) in favor of ε0 alone.

Electric potential from a point charge falls off with distance as 1/r. For a charge q located at the origin, the electric field is radial: E = k q / r^2, where k = 1/(4π ε0). The potential difference between infinity and a point at distance r is V(r) = -∫∞^r E · dr. Since E points radially, this becomes V(r) = ∫∞^r (k q / r′^2) dr′ = k q / r. This uses the common convention V(∞) = 0, so the potential decreases as you move away from the charge and scales as 1/r. If q is negative, V(r) is negative accordingly, and as r → 0 the potential diverges.

The other forms don’t fit because they either grow with distance (which would imply increasing potential with separation, not true for a point charge), have the wrong units, or miss the correct constant 1/(4π ε0) in favor of ε0 alone.