Electric Potential Formula

The electric potential energy per unit charge at a point in an electric field.

The Formula

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

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

Notation

VV is the electric potential in volts (V = J/C), QQ is the source charge in coulombs, rr is the distance in metres, and ϵ0\epsilon_0 is the permittivity of free space. ∇V\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 PP due to a point charge QQ is V=14πϵ0QrV = \frac{1}{4\pi\epsilon_0}\frac{Q}{r}, where rr is the distance from QQ to PP. The potential is related to the field by E⃗=−∇V\vec{E} = -\nabla V, and the work done moving a charge qq from AA to BB is W=q(VA−VB)W = q(V_A - V_B).

Worked Examples

Example 1

medium
What is the electric potential 0.3 m0.3 \text{ m} from a point charge of 6×10−6 C6 \times 10^{-6} \text{ C}? Use k=9×109 N m2/C2k = 9 \times 10^9 \text{ N m}^2/\text{C}^2.

Answer

V=1.8×105 VV = 1.8 \times 10^5 \text{ V}

First step

1
Use the electric potential formula for a point charge: V=kqrV = k\dfrac{q}{r}, where k=9×109 N m2/C2k = 9 \times 10^9\,\text{N m}^2/\text{C}^2.

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Example 2

hard
How much work is needed to move a 3×10−6 C3 \times 10^{-6} \text{ C} charge from a point at 200 V200 \text{ V} to a point at 500 V500 \text{ V}?

Example 3

medium
An electron is accelerated through 250 V250\ \text{V}. Find its kinetic energy gain.

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. - Fix this by naming the system, checking "Am I using a field or potential to explain how one object influences another across space?", and attaching units or direction to the final statement.
  • Using the electric field formula E=kQ/r2E = kQ/r^2 when the potential formula V=kQ/rV = kQ/r is needed — potential falls off as 1/r1/r, not 1/r21/r^2. - Fix this by naming the system, checking "Am I using a field or potential to explain how one object influences another across space?", and attaching units or direction to the final statement.
  • Forgetting that potential is a scalar: contributions from multiple charges are added algebraically (with signs), not as vectors. - Fix this by naming the system, checking "Am I using a field or potential to explain how one object influences another across space?", and attaching units or direction to the final statement.
  • Using electric potential from a keyword alone - Signal words like field, charge, magnet only point to a possible model; the system must match too.

Common Mistakes Guide

If this formula feels simple in isolation but keeps breaking during real problems, review the most common errors before you practice again.

Coulomb's Law Mistakes

Why This Formula Matters

Electric Potential gives students a way to explain non-contact forces and energy changes. It connects electricity, magnetism, gravitation, induction, motors, generators, and orbital motion through a shared spatial model.

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?

VV is the electric potential in volts (V = J/C), QQ is the source charge in coulombs, rr is the distance in metres, and ϵ0\epsilon_0 is the permittivity of free space. ∇V\nabla V denotes the gradient of the potential.

Why is the Electric Potential formula important in Physics?

Electric Potential gives students a way to explain non-contact forces and energy changes. It connects electricity, magnetism, gravitation, induction, motors, generators, and orbital motion through a shared spatial model.

What do students get wrong about Electric Potential?

Students often know a formula related to electric potential but skip the recognition step: Am I using a field or potential to explain how one object influences another across space? That leads to a correct-looking substitution attached to the wrong physical model.

What should I learn before the Electric Potential formula?

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

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