Physics / core

Electric Potential

Also known as: voltage at a point, V

definition

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.

💡 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.

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).

🔬 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).

🎯 Why It Matters

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

⚠️ Common Confusion

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

💭 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).

Related Concepts

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.

Go Deeper

Worked Examples

Step-by-step solved problems

Practice Problems

Test your understanding

Formula Explained

Notation, derivation, and common mistakes

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).

Why is Electric Potential important?

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

What do students usually 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 Electric Potential?

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