Electric Potential Formula

The Formula

V = \frac{kQ}{r} (potential due to a point charge at distance r).

When to use: Electric potential is like altitude on a hill — charges 'roll downhill' from high potential to low potential, just as balls roll from high ground to low ground.

Quick Example

A point 1 m from a +1 \muC charge has a potential of about 9000 V. A second positive charge placed there would be pushed away (rolling downhill).

Notation

V is the electric potential in volts (V = J/C), Q is the source charge in coulombs, r is the distance in metres, and \epsilon_0 is the permittivity of free space. \nabla V denotes the gradient of the potential.

What This Formula Means

The electric potential energy per unit charge at a point in an electric field. Measured in volts (V).

Electric potential is like altitude on a hill — charges 'roll downhill' from high potential to low potential, just as balls roll from high ground to low ground.

Formal View

The electric potential at a point P due to a point charge Q is V = \frac{1}{4\pi\epsilon_0}\frac{Q}{r}, where r is the distance from Q to P. The potential is related to the field by \vec{E} = -\nabla V, and the work done moving a charge q from A to B is W = q(V_A - V_B).

Worked Examples

Example 1

medium
What is the electric potential 0.3 \text{ m} from a point charge of 6 \times 10^{-6} \text{ C}? Use k = 9 \times 10^9 \text{ N m}^2/\text{C}^2.

Solution

  1. 1
    Use the electric potential formula for a point charge: V = k\dfrac{q}{r}, where k = 9 \times 10^9\,\text{N m}^2/\text{C}^2.
  2. 2
    Identify given values: q = 6 \times 10^{-6}\,\text{C}, r = 0.3\,\text{m}. Compute \dfrac{q}{r} = \dfrac{6 \times 10^{-6}}{0.3} = 2 \times 10^{-5}.
  3. 3
    Multiply by k: V = 9 \times 10^9 \times 2 \times 10^{-5} = 1.8 \times 10^5\,\text{V}

Answer

V = 1.8 \times 10^5 \text{ V}
Electric potential is the electric potential energy per unit charge. Unlike the electric field (a vector), potential is a scalar quantity, making it easier to work with in many calculations.

Example 2

hard
How much work is needed to move a 3 \times 10^{-6} \text{ C} charge from a point at 200 \text{ V} to a point at 500 \text{ V}?

Common Mistakes

  • Confusing electric potential (scalar, at a single point) with potential difference (between two points) — potential alone does not tell you about energy transfer.
  • Using the electric field formula E = kQ/r^2 when the potential formula V = kQ/r is needed — potential falls off as 1/r, not 1/r^2.
  • Forgetting that potential is a scalar: contributions from multiple charges are added algebraically (with signs), not as vectors.

Why This Formula Matters

Electric potential simplifies force calculations and connects field theory to circuit analysis through voltage.

Frequently Asked Questions

What is the Electric Potential formula?

The electric potential energy per unit charge at a point in an electric field. Measured in volts (V).

How do you use the Electric Potential formula?

Electric potential is like altitude on a hill — charges 'roll downhill' from high potential to low potential, just as balls roll from high ground to low ground.

What do the symbols mean in the Electric Potential formula?

V is the electric potential in volts (V = J/C), Q is the source charge in coulombs, r is the distance in metres, and \epsilon_0 is the permittivity of free space. \nabla V denotes the gradient of the potential.

Why is the Electric Potential formula important in Physics?

Electric potential simplifies force calculations and connects field theory to circuit analysis through voltage.

What do students get wrong about Electric Potential?

Potential is defined at a single point, but only the difference between two points (voltage) does physical work.

What should I learn before the Electric Potential formula?

Before studying the Electric Potential formula, you should understand: electric field, coulombs law.

← Back to Electric Potential See All Examples Practice Problems