ما هو قانون كولوم وطريقة حسابه؟ How to calculate electric force using Coulomb Law?

يحسب قانون كولوم بالقانون: F = k(|q₁q₂|)/r²، حيث تتناسب القوة طردياً مع حاصل ضرب مقدار الشحنتين وعكسياً مع مربع المسافة الفاصلة بينهما. [الصيغة الرمزية الموزونة: F = k × (|q₁ × q₂|) / r² (k = 8.99 × 10⁹ N·m²/C²)]

Theme D — Fields

D.2.4 Coulomb’s Law — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 19 of 39 1 quiz

📚 IB Physics HL Hub / Topical Revision

Curriculum Equation Key قانون كولوم للقوة الكهربائية - Coulomb Law FormulaFast Exam Solution

F = k × (|q₁ × q₂|) / r²  (k = 8.99 × 10⁹ N·m²/C²)

Word Equation & Conditions: القوة الكهربائية المتبادلة = ثابت كولوم × حاصل ضرب الشحنتين ÷ مربع المسافة بينهما

Location & Specifications: الكهرومغناطيسية والتحصيلي وفيزياء 3 ثانوي و AP Physics.

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Lesson summary

D.2.4 Coulomb's Law — IB PHYSICS SL notes: State Coulomb's law and calculate electrostatic forces, including resultant forces from several charges and comparisons with gravity.Coulomb's law — the electric force between two point charges is directly proportional to the product of …

What the symbols mean
Permittivity of free space
Using signs
Irregular objects
Separation
Permittivity (ε)

Part 1 of 8Statement of the law

Statement of the law

Coulomb's law

Coulomb's law the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of their separation
F = kq₁q₂ / r²
What the symbols mean: F = electric force (N) · Q₁, Q₂ = charges (C) · r = separation (m) · k = 1/4πε₀ = 8.99 × 10⁹ N m² C⁻²

Symbols

F is the force in N and q₁, q₂ are the charges in C.
r is the separation of the centres in m.
k = 1/(4πε₀) = 8.99 × 10⁹ N m² C⁻².

Permittivity of free space

ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻², referring to charges in a vacuum
Unless stated, charges are assumed to be in a vacuum.
Both constants are given in the data booklet.

Direction

Direction the force acts along the line joining the charges
Unlike charges attract and like charges repel.
The two forces are equal and opposite (Newton's third law).

Using signs

Using signs use magnitudes for the size of the force and decide direction from the signs
A positive product q₁q₂ means repulsion and a negative product means attraction.

Part 2 of 8Validity

Point charges

Point charges the law holds for charges small compared with their separation

Spheres

Spheres uniformly charged spheres are treated as point charges at their centres, with r from centre to centre

Irregular objects

Irregular objects it cannot be used for charge spread over irregularly shaped objects

Part 3 of 8Inverse-square behaviour

Separation

Separation doubling it reduces the force to a quarter

Charge

Charge doubling one charge doubles the force

Graphs

F against r is a decaying curve and F against 1/r² is a straight line through the origin

Part 4 of 8Permittivity of materials

Permittivity of materials

Permittivity (ε)

Permittivity (ε) a measure of how easily an electric field can be generated in a material

Relative permittivity (εr)

Relative permittivity (εr) the ratio of the permittivity of a material to that of free space, ε_r = ε/ε₀
It has no units and is also called the dielectric constant.

Effect on the force

Effect on the force in a material k = 1/(4πε) with ε = ε_rε₀, so the force is reduced

Air

Air its relative permittivity is taken as 1, so air behaves like a vacuum

Other materials

Other materials they have higher permittivity, and k is lower

Material	Relative permittivity
Vacuum	1
Air	1.0005
Paraffin	2.3
Polystyrene	3
Paper	4
Pure water	80
Ceramic	100 to 15 000

Part 5 of 8Superposition of forces

Several charges

Several charges the net force on one charge is the vector sum of the individual Coulomb forces
Each pair acts independently of the others.

Straight line

Straight line choose a positive direction and add forces with their signs

Two dimensions

Two dimensions treat each force as a vector

Part 6 of 8Resolving forces in two dimensions

Find the size of the force from each charge using Coulomb's law.

Sketch the directions, towards for attraction and away for repulsion.

Resolve each force into horizontal and vertical components.

Add the components.

Combine them with Pythagoras and a tangent to find the magnitude and direction of the resultant.

Symmetry

Symmetry for three equal charges at the corners of an equilateral triangle, the resultant on one charge points along the bisector from the opposite side

Field link

Field link the force on a charge q is F = qE, where E is the field of all the other charges (D.2.5)

Part 7 of 8Comparison with gravity

Same form

Same form both are inverse-square laws

Strength

Strength between a proton and an electron in hydrogen the electric force is about 10³⁹ times the gravitational force

Nature

Nature gravity is always attractive, whereas electric forces can attract or repel and can be cancelled by oppositely charged bodies

Scale

Scale large bodies are almost neutral and so are dominated by gravity
At atomic scale electric forces control the structure of matter, chemical bonds and everyday contact forces.

Part 8 of 8More from the specification

1Coulomb's Law of Electrostatic Force

Coulomb's law states that the electrostatic force between two stationary point charges Q₁ and Q₂ separated by distance r in vacuum is F = (1 / 4πε₀) * (Q₁ Q₂ / r²),
where ε₀ is the permittivity of free space.

2Uniform Electric Fields Between Parallel Plates

When two flat parallel conducting plates are connected across an electric potential difference V and separated by distance d, a uniform electric field of magnitude E = V / d is produced with parallel field lines.

3Magnetic Field Lines and North Poles

Magnetic field lines represent the direction of magnetic flux density B, defined as pointing from a magnetic north pole to a south pole outside the magnet, with line density indicating field strength.

4Magnetic Field Around a Current-Carrying Conductor

An electric current flowing through a straight wire generates concentric circular magnetic field lines around the wire, whose strength and flux density follow Ampere's relation B = μ₀I / (2πr).

5Parallel

Components on separate branches, each with the full e.m.f.

6Current

Flow of electrons in a circuit.

7Density

Mass per unit volume.

8Distance

Total length of path travelled, a scalar.

9Field lines

Lines showing the direction and strength of a magnetic field.

10Magnetic field

Area around a magnet where its effects can be detected.

11Potential difference

Work done by a unit charge passing through a component.

12W = mg

What the symbols mean: W = weight (N) · m = mass (kg) · g = gravitational field strength (9.81 N kg⁻¹ on Earth)

Key terms

Term	Meaning
Coulomb's law	F = kq₁q₂/r², the force between two point charges.
Coulomb constant k	8.99 × 10⁹ N m² C⁻², equal to 1/(4πε₀).
Permittivity ε₀	8.85 × 10⁻¹² C² N⁻¹ m⁻², a constant describing electric fields in vacuum.
Relative permittivity	Ratio of the permittivity of a material to that of free space.
Point charge	A charge whose size is negligible compared with the distances involved.
Superposition	The net force is the vector sum of the forces from each charge.

Avoid these mistakes

Putting the signs of the charges into the formula and then misreading a negative force — use magnitudes, then add direction.

Using r in centimetres without converting to metres.

Forgetting to square r or squaring only part of the product of charges.

Thinking the larger charge exerts the larger force — both feel equal forces.

Adding forces as scalars when they are not collinear.

Last updated: 15 October 2026