2.10 Electric Potential due to a Point Charge

Electric Potential from a Point Charge

The electric potential created by a point charge is given by V = kQ/r, where k is Coulomb's constant, Q is the source charge, and r is the distance from it. Unlike electric field, potential is a scalar — it has magnitude and sign but no direction. V = 0 is defined at r = infinity.

Sign and Superposition

Positive charges create positive potential; negative charges create negative potential. To find potential at a point due to multiple charges, simply add the scalar values algebraically (no vector components needed), unlike electric field calculations.

Potential vs. Distance

V is inversely proportional to r (not r² like electric field). As you move farther from a point charge, potential decreases toward zero, but more slowly than the field does. Potential energy of a second charge q placed at that point is U = qV = kQq/r.

Key terms

Electric potential due to point charge formula

V = kQ/r, where k is Coulomb's constant, Q is source charge, r is distance.

Is electric potential a scalar or vector?

Scalar — it has magnitude and sign, but no direction.

How does V depend on distance r compared to E?

V is proportional to 1/r; E is proportional to 1/r². Potential falls off more slowly.

Reference point where V = 0 for a point charge

At r = infinity (infinitely far from the charge).

Potential energy of charge q in potential V

U = qV = kQq/r, combining potential with the placed charge.

Try an AP-style question

What is the potential 0.30 m from a 2.0 μC charge? (k = 9.0 × 10⁹)

1. 1.8 × 10⁴ V
2. 6.0 × 10³ V
3. 2.0 × 10⁵ V
4. 6.0 × 10⁴ V