AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
For a charged sphere, charge may be considered to be at the centre.
Full specification wording
Coulomb's law (A-level only): 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.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 1 of 2
- 2 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
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.
What earns the marks
- 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.
Common mistakes and how to put them right
Measuring r from the surface of the sphere instead of its centre.
Put it right by using the centre-to-centre distance.
Applying the point-charge result inside the sphere.
Put it right by noting that the field inside a conductor in equilibrium is zero.
Assuming the result holds for a non-uniformly charged or irregular object.
Put it right by restricting it to a uniformly charged sphere.
Exam 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.
Try the lesson
The start of the Coulomb's law (A-level only): For a charged sphere, charge may be considered to be at the centre. lesson, made from checked teaching notes for this specification point.
Have a go first
When using Coulomb's law to find the force between two charged spheres, where may the charge on each sphere be considered to act?
Listen
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. A strong answer earns marks for these 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. A common slip: Measuring r from the surface of the sphere instead of its centre. Instead, using the centre-to-centre distance. Exam tip: Mark the centre of each sphere on a diagram and label r as the centre-to-centre distance.
See it
Key words
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Coulomb's law for point charges
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Spherical symmetry and equivalent point charge
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See every definition
- Coulomb's law for point charges
- For a point charge Q, the force on q is F = kQq/r², where k = 1/(4πε₀).
- Spherical symmetry and equivalent point charge
- For a uniformly charged sphere, charge may be considered to be at the centre, so it can be treated as a point charge for external points.
Label the diagram
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1Box 1
2Box 2
3Box 3
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