Electric Potential

Fields
definition

Also known as: voltage at a point, V

Grade 9-12

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The electric potential energy per unit charge at a point in an electric field. Electric potential simplifies force calculations and connects field theory to circuit analysis through voltage.

Definition

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

💡 Intuition

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.

🎯 Core Idea

Potential is a scalar — no direction, just a number at each point. The difference in potential between two points drives current.

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).

Formula

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

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.

🌟 Why It Matters

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

💭 Hint When Stuck

When solving an electric potential problem, identify the source charge and the distance to the point of interest. Then apply V = kQ/r — note there is no squaring of r unlike the field formula. If multiple charges are present, add their potentials as scalars (no vector addition needed).

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).

🚧 Common Stuck Point

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

⚠️ 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.

Common Mistakes Guides

Coulomb's Law

Frequently Asked Questions

What is Electric Potential in Physics?

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

What is the Electric Potential formula?

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

When do you use Electric Potential?

When solving an electric potential problem, identify the source charge and the distance to the point of interest. Then apply V = kQ/r — note there is no squaring of r unlike the field formula. If multiple charges are present, add their potentials as scalars (no vector addition needed).

How Electric Potential Connects to Other Ideas

To understand electric potential, you should first be comfortable with electric field and coulombs law. Once you have a solid grasp of electric potential, you can move on to potential difference.

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