Potential Difference

Fields
definition

Also known as: voltage drop, pd

Grade 9-12

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The difference in electric potential between two points, equal to the work done per unit charge moving between them. Links the abstract concept of electric field to the practical concept of voltage used in circuits and power systems.

Definition

The difference in electric potential between two points, equal to the work done per unit charge moving between them.

💡 Intuition

Potential difference is the 'height drop' that makes charges flow — the bigger the drop, the harder the push.

🎯 Core Idea

Potential difference is what actually drives current in circuits — it's the 'voltage' engineers measure.

Example

The potential difference across a 9 V battery's terminals is 9 V. Each coulomb of charge gains 9 J of energy passing through the battery.

Formula

\Delta V = V_B - V_A = -\int_A^B \vec{E} \cdot d\vec{l}

Notation

\Delta V is the potential difference in volts (V), \vec{E} is the electric field vector, d\vec{l} is an infinitesimal displacement along the path, and q is the charge in coulombs.

🌟 Why It Matters

Links the abstract concept of electric field to the practical concept of voltage used in circuits and power systems.

💭 Hint When Stuck

When solving a potential difference problem, identify the two points you are comparing. First, find the electric potential at each point (or the work done moving a charge between them). Then subtract: \Delta V = V_B - V_A. Finally, use \Delta V = W/q to relate voltage to energy and charge.

Formal View

The potential difference between points A and B is defined as \Delta V = V_B - V_A = -\int_A^B \vec{E} \cdot d\vec{l}, equal to the work done per unit positive charge moved from A to B.

Related Concepts

Electric PotentialVoltage

🚧 Common Stuck Point

Voltage is always measured between two points — saying 'the voltage at this wire' implicitly means relative to ground.

⚠️ Common Mistakes

  • Confusing electric potential (at one point) with potential difference (between two points) — voltage is always a difference.
  • Forgetting that potential difference is measured in volts (joules per coulomb), not in joules alone.
  • Mixing up the sign convention: work done by the field on a positive charge moving from high to low potential is positive.

Frequently Asked Questions

What is Potential Difference in Physics?

The difference in electric potential between two points, equal to the work done per unit charge moving between them.

What is the Potential Difference formula?

\Delta V = V_B - V_A = -\int_A^B \vec{E} \cdot d\vec{l}

When do you use Potential Difference?

When solving a potential difference problem, identify the two points you are comparing. First, find the electric potential at each point (or the work done moving a charge between them). Then subtract: \Delta V = V_B - V_A. Finally, use \Delta V = W/q to relate voltage to energy and charge.

How Potential Difference Connects to Other Ideas

To understand potential difference, you should first be comfortable with electric potential and voltage.

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