For a positive point charge q, what is the potential at distance r from the charge?

For a positive point charge q, what is the potential at distance r from the charge?

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

Answer: (A)

Electric potential from a point charge scales with the amount of charge and decreases with distance. For a point charge q, the potential at distance r is V(r) = k q / r, where k = 1/(4πε0). Since the charge is positive, the potential is positive at any r. If you check with E = -dV/dr, you get E_r = k q / r^2 pointing away from the charge, which matches Coulomb’s law. The other forms don’t fit because a negative sign would give negative potential for a positive charge, and forms like k/(q r) or k q r either miss the 1/r distance dependence or produce incorrect units and behavior.

Electric potential from a point charge scales with the amount of charge and decreases with distance. For a point charge q, the potential at distance r is V(r) = k q / r, where k = 1/(4πε0). Since the charge is positive, the potential is positive at any r. If you check with E = -dV/dr, you get E_r = k q / r^2 pointing away from the charge, which matches Coulomb’s law. The other forms don’t fit because a negative sign would give negative potential for a positive charge, and forms like k/(q r) or k q r either miss the 1/r distance dependence or produce incorrect units and behavior.