Electric Potential Calculator

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