Electric Potential Calculator
Calculate the electric potential at a distance from a point charge.
Uses Coulomb's constant k = 8.9875×10⁹ N·m²/C².
Electric Potential
The electric potential at a distance r from a point charge Q is:
V = kQ/r
Where:
- V = Electric potential in volts (V)
- k = Coulomb’s constant = 8.9875 × 10⁹ N·m²/C²
- Q = Charge in coulombs (C)
- r = Distance from the charge in meters (m)
Electric potential vs. electric field:
- Electric potential V is a scalar — just a number at each point
- Electric field E is a vector — both magnitude and direction at each point
- They are related: E = −dV/dr (the field points from high to low potential)
What does electric potential mean?
Electric potential is the potential energy per unit charge. If you place a small test charge q at a point where the potential is V, it has potential energy U = qV.
This is why we measure voltage in volts — “volts” are joules per coulomb.
Superposition: If multiple charges are present, the total potential is just the sum: V_total = V₁ + V₂ + V₃ + …
This is simpler than adding electric fields (which require vector addition).
Practical reference:
- Near a proton (1.6 × 10⁻¹⁹ C) at the Bohr radius (5.29 × 10⁻¹¹ m): V ≈ 27.2 V
- This is the “Hartree” unit of energy = 27.2 eV, fundamental to atomic physics