📘 Chapter 18: Potential Difference (Class XII)

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🔷 1. Introduction

The concept of potential difference is fundamental in electrostatics and electric circuits. It tells us how much work is required to move a charge between two points in an electric field.

While electric potential refers to a single point, potential difference compares two different points in space.

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🔷 2. Definition of Potential Difference

Potential difference between two points A and B is defined as the work done per unit charge in moving a test charge from point A to point B.

ΔV = V_B − V_A = W / q

Where:

• ΔV = potential difference
• W = work done
• q = charge

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📦 3. Important Results (Must Remember)

• Definition: ΔV = W/q
• Unit: Volt (V)
• 1 Volt = 1 Joule/Coulomb
• Scalar quantity
• Independent of path (electrostatic field)

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🔷 4. Relation with Electric Field

Potential difference is related to electric field as:

ΔV = − ∫ E⃗ · dl⃗

For uniform electric field:

ΔV = − E d

Where d is displacement along field.

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🔷 5. Physical Interpretation

Potential difference represents the energy change per unit charge between two points.

• Higher potential → more energy
• Charge moves naturally from higher to lower potential

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🔷 6. Sign Convention

• If work is done by field → ΔV negative
• If work is done against field → ΔV positive

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🔷 7. Potential Difference for Point Charge

Between two points at distances r₁ and r₂:

ΔV = (1 / 4πε₀) q (1/r₂ − 1/r₁)

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🔷 8. Equipotential Surfaces

Points having same potential form an equipotential surface.

• No work required along this surface
• Electric field is perpendicular

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🔷 9. Applications in Circuits

In electrical circuits, potential difference is commonly known as voltage.

• Drives current in circuits
• Measured using voltmeter

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🧠 10. Solved Numerical Problems

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🔹 Q1

Find potential difference when 10 J work is done to move 2 C charge.

Solution:

ΔV = W/q = 10 / 2

ΔV = 5 V

Answer: 5 Volt

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🔹 Q2

Find ΔV across 2 m in uniform field of 50 N/C.

Solution:

ΔV = −Ed = −50 × 2

ΔV = −100 V

Answer: −100 Volt

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🔹 Q3

Why is potential difference path independent?

Answer:

Because electrostatic field is conservative.

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🔹 Q4

What is potential difference in equipotential surface?

Answer:

Zero

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🔹 Q5

Does charge affect potential difference?

Answer:

No, potential difference is independent of test charge.

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🔷 11. Advanced Conceptual Insight

Potential difference is central to both electrostatics and circuit theory. It connects field theory with energy concepts and forms the basis of electrical power systems.

It is also essential in understanding capacitors, resistors, and current flow.

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🔷 12. Applications

• Electric circuits and electronics
• Power transmission
• Capacitor operation
• Electrochemical cells

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🔷 13. Summary

Potential difference measures the work done per unit charge between two points. It is a scalar quantity, independent of path, and plays a key role in both electrostatics and electrical circuits.

✨ End of Chapter 18: Potential Difference ✨