Electric Charge

Electric charge is a fundamental property of matter. There are two types: positive (protons) and negative (electrons). Opposite charges attract; like charges repel. Charge is measured in coulombs (C). An electron carries a charge of −1.6 × 10⁻¹⁹ C.

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Like charges — REPEL

Two positive or two negative charges push each other away.

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Opposite charges — ATTRACT

A positive and a negative charge pull each other together.

Coulomb's Law

Coulomb's law states that the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

F = k × q₁q₂ / r²

F = force (N)

k = 9 × 10⁹ N m² C⁻²

q₁, q₂ = charges (C)

r = distance (m)

Doubling the distance: If r doubles, r² increases by 4, so the force decreases to 1/4 of its original value (inverse square law).

Doubling one charge: If q₁ doubles, the force doubles.

Electric Field Strength and Field Lines

An electric field is a region of space around a charged object where another charged object would experience a force. The electric field strength (E) at a point is the force per unit positive charge placed at that point.

E = F / q

E = electric field strength (N/C or V/m) F = force (N) q = charge (C)

Electric field lines show the direction a positive test charge would move in the field:

Around a positive charge

Lines radiate outward from the charge. A positive test charge would be pushed away.

Around a negative charge

Lines point inward toward the charge. A positive test charge would be attracted in.

Rules for field lines: They never cross each other. Closer lines indicate a stronger field. They are perpendicular to the surface of a conductor.

Electric Potential and Potential Difference

Electric potential (V) at a point is the work done per unit positive charge to move a small test charge from infinity to that point. It is measured in volts (V).

Potential difference (voltage) between two points is the work done per unit charge to move a charge between those points:

W = qV

W = work done (J) q = charge (C) V = potential difference (V)

Example: A charge of 2 C moves through a potential difference of 12 V. Work done = 2 × 12 = 24 J. This is the same principle as the voltage rating of a battery — a 12 V car battery does 12 J of work for every coulomb of charge that flows through the circuit.

Key Vocabulary

Term	Definition
Coulomb (C)	The SI unit of electric charge. One coulomb is the charge carried by approximately 6.24 × 10¹⁸ electrons.
Electric field	A region of space around a charged object where a force acts on other charged objects.
Coulomb's law	The electrostatic force between two charges is proportional to their charges and inversely proportional to the square of the distance between them.
Potential difference	The work done per unit charge to move a charge between two points; measured in volts (V).

Worked Examples

1

Calculate the force between two charges of +3 × 10⁻⁶ C and −2 × 10⁻⁶ C separated by 0.5 m.

Given: q₁ = 3 × 10⁻⁶ C, q₂ = 2 × 10⁻⁶ C, r = 0.5 m, k = 9 × 10⁹ N m² C⁻².

Formula: F = k × |q₁q₂| / r²

Substitute: F = (9 × 10⁹) × (3 × 10⁻⁶ × 2 × 10⁻⁶) / (0.5)²

F = (9 × 10⁹) × (6 × 10⁻¹²) / 0.25 = 54 × 10⁻³ / 0.25 = 0.216 N

The force is attractive (opposite charges). Answer: F = 0.216 N attraction.

2

A force of 4 N acts on a charge of 0.5 C. Find the electric field strength at that point.

Formula: E = F / q

Substitute: E = 4 / 0.5 = 8 N/C

Answer: The electric field strength is 8 N/C (or 8 V/m).

3

How much work is done moving a charge of 4 × 10⁻³ C through a potential difference of 50 V?

Formula: W = qV

Substitute: W = 4 × 10⁻³ × 50 = 0.2 J

Answer: 0.2 joules of work is done on the charge.

Knowledge Check

Select the correct answer for each question.

Question 1

According to Coulomb's law, if the distance between two charges is doubled, the force between them becomes:

Twice as large One-quarter as large Four times as large One-half as large

Question 2

Electric field lines around a positive point charge point:

Toward the charge from all directions In a circle around the charge Outward from the charge in all directions Horizontally only

Question 3

A charge of 0.01 C is placed in an electric field of 200 N/C. What force does it experience?

0.02 N 20,000 N 200 N 2 N

Question 4

What is the unit of electric potential difference?

Volt (V) Watt (W) Ampere (A) Coulomb (C)

Question 5

Two positive charges are placed near each other. What happens to the force between them if one charge is tripled?

The force decreases by a factor of 3 The force triples The force remains the same The force increases by a factor of 9

Electric Fields

Electric Charge

Coulomb's Law

Electric Field Strength and Field Lines

Around a positive charge

Around a negative charge

Electric Potential and Potential Difference

Key Vocabulary

Worked Examples

Calculate the force between two charges of +3 × 10⁻⁶ C and −2 × 10⁻⁶ C separated by 0.5 m.

A force of 4 N acts on a charge of 0.5 C. Find the electric field strength at that point.

How much work is done moving a charge of 4 × 10⁻³ C through a potential difference of 50 V?

Knowledge Check

Key Concepts Summary

Electric Fields

Electric Charge

Coulomb's Law

Electric Field Strength and Field Lines

Around a positive charge

Around a negative charge

Electric Potential and Potential Difference

Key Vocabulary

Worked Examples

Calculate the force between two charges of +3 × 10−6 C and −2 × 10−6 C separated by 0.5 m.

A force of 4 N acts on a charge of 0.5 C. Find the electric field strength at that point.

How much work is done moving a charge of 4 × 10−3 C through a potential difference of 50 V?

Knowledge Check

Key Concepts Summary

Calculate the force between two charges of +3 × 10⁻⁶ C and −2 × 10⁻⁶ C separated by 0.5 m.

How much work is done moving a charge of 4 × 10⁻³ C through a potential difference of 50 V?