Coulomb's law (A-level only) — AQA A-Level Physics
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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 = kQ1Q2/r^2, where k = 1/(4*pi*epsilon0). It is a fundamental inverse-square law in AQA A-Level Physics, essential for understanding electric fields, potential, and the behaviour of charged particles.
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Coulomb's law (A-level only) explained
Coulomb's law (A-level only) covers 2 specification points, including For a charged sphere, charge may be considered… and Comparison of magnitude of gravitational and….
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Open a point below for its explanation and revision guidance.
For a charged sphere, charge may be considered to be at the centre.
A uniformly charged conducting sphere behaves, for points outside it, as though all its charge were concentrated at its centre. This follows from the spherical symmetry of the charge distribution: every shell of charge contributes as a point charge at the centre, so the field outside is radial and Coulomb's law applies with r measured from the centre. For a point charge Q, the force on q is F = kQq/r², where k = 1/(4πε₀). The same result lets you treat a charged sphere as a point charge when finding force or field outside it. Inside a conductor in electrostatic equilibrium the field is zero, so the result is used only for external points.
Comparison of magnitude of gravitational and electrostatic forces between subatomic particles.
For two charged particles, the electrostatic force magnitude is F = kQ₁Q₂/r², where k = 1/(4πε₀), while the gravitational force magnitude is F = Gm₁m₂/r². Because both obey an inverse-square law, their ratio simplifies to (kQ₁Q₂)/(Gm₁m₂), independent of separation. For two protons, Q₁ = Q₂ = 1.60 × 10⁻¹⁹ C and m₁ = m₂ = 1.67 × 10⁻²⁷ kg, giving an electrostatic-to-gravitational ratio of order 10³⁶. Electrostatic forces therefore dominate between subatomic particles, yet gravity dominates on astronomical scales because bulk matter is almost exactly charge-neutral, so the much weaker gravitational attraction accumulates without cancellation.
Your focus
- Explain why a uniformly charged sphere may be treated as a point charge at its centre for external points.
- Apply Coulomb's law using the centre-to-centre separation of charged spheres.
- Recognise the conditions under which the point-charge approximation is valid.
Show all 6 objectives
- Write and apply the equations for gravitational and electrostatic force between two point particles.
- Derive and evaluate the ratio of electrostatic to gravitational force for a named pair of subatomic particles.
- Explain why gravity dominates on astronomical scales despite being far weaker between individual particles.
Which command word is this?
A numerical answer is required. You must show your working, including the equation, substitution, and final answer with correct units and significant figures. Method marks are awarded for correct rearrangement and substitution.
Coulomb's law (A-level only) exam tips
Topic Overview
Coulomb's law describes the electrostatic force between two point charges. It is an inverse-square law, meaning the force is proportional to the product of the charges and inversely proportional to the square of the distance between them. This law is fundamental to understanding electric fields, electric potential, and the behaviour of charged particles in fields, forming a cornerstone of AQA A-Level Physics Unit 3.4.1.
In the wider subject, Coulomb's law is analogous to Newton's law of gravitation, both being inverse-square laws. It is essential for analysing phenomena such as the motion of charged particles in electric fields, the stability of atoms, and the behaviour of capacitors. Mastery of this law is crucial for tackling more advanced topics like electric potential energy and Gauss's law.
Key Concepts
- →Coulomb's law: F = kQ1Q2/r^2, where k = 1/(4*pi*epsilon0) = 8.99e9 N m^2 C^-2 in a vacuum.
- →The force is a vector: attractive for opposite charges, repulsive for like charges. Always consider direction when multiple charges are present.
- →The law applies to point charges or spherically symmetric charge distributions (treat as point charges at their centres).
- →The inverse-square relationship means that doubling the distance reduces the force to one quarter.
- →The permittivity of free space, epsilon0, is a fundamental constant that appears in Coulomb's law and relates to the strength of the electric force.
Marking Points
- For a uniformly charged sphere, external field lines are radial and appear to come from the centre.
- Coulomb's law may be applied with r measured from the centre of the sphere, not from its surface.
- The force between two charged spheres is F = kQ₁Q₂/r² when r is the centre-to-centre distance and the spheres do not overlap.
- The result depends on spherical symmetry and uniform charge distribution.
- Inside a conducting sphere in electrostatic equilibrium, the electric field is zero.
- State Coulomb's law as F = kQ₁Q₂/r² with k = 1/(4πε₀) ≈ 8.99 × 10⁹ N m² C⁻².
- State Newton's law of gravitation as F = Gm₁m₂/r² with G ≈ 6.67 × 10⁻¹¹ N m² kg⁻².
- Recognise that both forces obey an inverse-square law, so the ratio of electrostatic to gravitational force is independent of separation.
- Calculate the ratio for two protons as (kQ₁Q₂)/(Gm₁m₂) ≈ 10³⁶, showing substitution of charge and mass values.
- Explain that gravity dominates on astronomical scales because large bodies are approximately charge-neutral, so electrostatic forces largely cancel.
Examiner Tips
- 💡Mark the centre of each sphere on a diagram and label r as the centre-to-centre distance.
- 💡State that the sphere behaves as a point charge at its centre before substituting into F = kQ₁Q₂/r².
- 💡Check whether the question asks for force or field, and use the appropriate equation.
- 💡Keep charges in coulombs and distances in metres before calculating.
- 💡Write the ratio as a single expression before substituting numbers, so the cancellation of r² is visible.
- 💡Quote k and G to the precision given in the data sheet and keep units consistent throughout.
- 💡When asked to compare, give both the numerical ratio and a physical reason for the difference in dominance at different scales.
- 💡Always write the full equation and substitute values with units. Show intermediate steps clearly to gain method marks even if the final answer is wrong.
- 💡When dealing with multiple charges, draw a diagram and use vector addition. State the direction of the net force (e.g., 'to the left') to secure the final mark.
- 💡Remember that Coulomb's law gives the magnitude of the force. Use the signs of the charges to determine whether it is attractive or repulsive, but use absolute values in the calculation.
Common Mistakes
- Measuring r from the surface of the sphere instead of its centre; correct by using the centre-to-centre distance.
- Applying the point-charge result inside the sphere; correct by noting that the field inside a conductor in equilibrium is zero.
- Assuming the result holds for a non-uniformly charged or irregular object; correct by restricting it to a uniformly charged sphere.
- Treating the ratio as dependent on separation; correct by cancelling the common r² factor before substituting.
- Using the electron mass for a proton calculation; correct by selecting the mass of the particle named in the question.
- Claiming gravity is always negligible; correct by noting that on astronomical scales, charge neutrality allows gravity to dominate.
- Students often think that the force between two charges is affected by the presence of a third charge. In fact, the force between any two charges is independent of other charges, though the net force on a charge is the vector sum of individual forces.
- Students may confuse the distance r with the diameter of a sphere or the distance between surfaces. For spherical charges, r is the centre-to-centre distance.
- Some students believe that Coulomb's law only applies to charges in a vacuum. It also applies in other media, but with a different permittivity (epsilon = epsilon_r * epsilon0), which reduces the force.
Revision Plan
- 1Day 1-2: Learn the equation F = kQ1Q2/r^2 and the meaning of each term. Memorise the value of k and epsilon0. Practice simple calculations with two point charges.
- 2Day 3-4: Study the vector nature of the force. Solve problems involving three or more charges, drawing free-body diagrams and using vector addition.
- 3Day 5-6: Explore the analogy with Newton's law of gravitation. Compare and contrast the two inverse-square laws.
- 4Day 7-8: Work through exam-style questions, including those involving equilibrium (e.g., charged spheres on threads) and electric fields.
- 5Day 9-10: Review common misconceptions and examiner tips. Complete a past paper question on Coulomb's law under timed conditions.
Exam Question Types
- 📋Calculation of force between two point charges: Often asks for magnitude and direction. Use F = kQ1Q2/r^2, square the distance, and state attractive/repulsive.
- 📋Vector addition of forces from multiple charges: Requires drawing a diagram, calculating individual forces, and resolving components. Watch for cancellation.
- 📋Equilibrium problems with charged spheres: Combine Coulomb's law with mechanics (resolving forces, moments). Often asks for charge or angle.
- 📋Comparison with gravitational force: Discuss similarities and differences, such as the relative strength and the role of mass vs charge.
Command Word Expectations (AQA)
A numerical answer is required. You must show your working, including the equation, substitution, and final answer with correct units and significant figures. Method marks are awarded for correct rearrangement and substitution.
You must provide a reasoned argument, often linking cause and effect. For example, explaining why the force decreases with distance squared, or why the force is attractive. Use precise physics terminology.
You must find a value or state a conclusion, often from given data or a graph. Show logical steps and justify your answer. This may involve using the gradient of a graph or solving an equation.
How Students Lose Marks (Examiner Pitfalls)
Step-by-Step Worked Solutions
Question: Calculate the electrostatic force between two point charges of +2.0 microC and -3.0 microC separated by a distance of 0.15 m in a vacuum. State whether the force is attractive or repulsive.
- 1.Step 1: Identify given values: Q1 = +2.0e-6 C, Q2 = -3.0e-6 C, r = 0.15 m, k = 8.99e9 N m^2 C^-2.
- 2.Step 2: Apply Coulomb's law: F = k|Q1Q2|/r^2 = (8.99e9 * 2.0e-6 * 3.0e-6) / (0.15)^2.
- 3.Step 3: Calculate numerator: 8.99e9 * 6.0e-12 = 0.05394 N m^2. Divide by r^2: 0.05394 / 0.0225 = 2.397 N.
- 4.Step 4: Determine direction: charges have opposite signs, so force is attractive.
Question: Two identical small conducting spheres, each with mass 0.10 g, are suspended from the same point by insulating threads of length 0.50 m. When each sphere carries the same charge Q, they repel and come to rest with their centres 0.20 m apart. Calculate the magnitude of Q.
- 1.Step 1: Draw a free-body diagram for one sphere. Forces: weight mg downward, tension T along thread, electrostatic repulsion F horizontally.
- 2.Step 2: The spheres are in equilibrium. Resolve vertically: T cos(theta) = mg. Resolve horizontally: T sin(theta) = F.
- 3.Step 3: Divide horizontal by vertical: tan(theta) = F / (mg).
- 4.Step 4: Geometry: half the distance between centres = 0.10 m. Thread length = 0.50 m. So sin(theta) = 0.10 / 0.50 = 0.20, theta = 11.54 degrees, tan(theta) = 0.204.
- 5.Step 5: F = mg tan(theta) = (0.10e-3 kg * 9.81 m s^-2) * 0.204 = 2.00e-4 N.
- 6.Step 6: Coulomb's law: F = kQ^2 / r^2, so Q^2 = F r^2 / k = (2.00e-4 * (0.20)^2) / 8.99e9 = 8.90e-16 C^2.
- 7.Step 7: Q = sqrt(8.90e-16) = 2.98e-8 C.