4.2.4Tools and Inquiry — IB Physics skills
Coulomb’s Law — IB Physics SL Revision Notes & Topical Questions
5 min read 5 parts Lesson 32 of 33 Unit quiz
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.
Part 1 of 5The Law
Charged particles exert forces on each other without touching, and the force depends on their charges and separation.
Statement
- Statement The force between two point charges is proportional to the product of the charges and inversely proportional to the square of their separation.
Equation
- Equation F = kq₁q₂/r², where k = 8.99 × 10⁹ N m² C⁻², which is equal to 1/(4πε₀).
Direction
- Direction Like charges repel and unlike charges attract, and the two forces are equal and opposite.
Point charges
- Point charges The law applies to point charges, and to charged spheres with distances measured between their centres.
Part 2 of 5Using Coulomb's Law
1
Convert charges to coulombs, for example 2.0 μC = 2.0 × 10⁻⁶ C, and distances to metres.
2
Substitute the magnitudes of the charges into F = kq₁q₂/r² to find the size of the force.
3
Decide the direction from the signs of the charges: away from each other if the signs are the same.
4
For several charges, find each force separately and add them as vectors.
5
Use ratios when the separation changes, since doubling r reduces the force to one quarter.
Part 3 of 5Comparisons
Comparisons
With gravity
- With gravity Both are inverse square laws, but electric forces can attract or repel while gravity only attracts.
Strength
- Strength The electric force between two protons is vastly greater than their gravitational force.
Field strength
- Field strength The electric field of a point charge is E = kQ/r², directed away from a positive charge.
Medium
- Medium The value of k is for a vacuum; in air it is almost the same.
| Property | Gravitational force | Electrostatic force |
|---|---|---|
| Source | Mass | Charge |
| Direction | Attractive only | Attractive or repulsive |
| Constant | G = 6.67 × 10⁻¹¹ | k = 8.99 × 10⁹ |
Part 4 of 5Worked Example
Question
- Two small spheres carry charges of +2.0 μC and +3.0 μC and are 0.30 m apart in a vacuum.
- Calculate the force between them and state whether it is attractive or repulsive.
- Chargesq₁ = 2.0 × 10⁻⁶ C and q₂ = 3.0 × 10⁻⁶ C.
- F = kq₁q₂/r² = (8.99 × 10⁹ × 2.0 × 10⁻⁶ × 3.0 × 10⁻⁶) / (0.30)².
- Numerator = 5.39 × 10⁻² ; denominator = 0.090 ; F = 0.60 N.
- Both charges are positive, so the force is repulsive.
Answer F = 0.60 N, repulsive.
Part 5 of 5Exam Checklist & Tips
4.2.4 – Key Points for the Exam
- Coulomb's law The force between point charges is proportional to q₁q₂/r².
- Coulomb The unit of charge, equal to the charge flowing in one second at a current of one ampere.
- Point charge A charged object small enough that its size can be ignored.
- Permittivity of free space The constant ε₀ that appears in k = 1/(4πε₀).
Common Mistakes
- Leaving charges in microcoulombs and not converting to coulombs.
- Forgetting to square the distance in the denominator.
- Including the signs of charges in the magnitude of the force and so getting a negative force size.
- Saying that unlike charges repel.
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