AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Similarities and differences between gravitational and electrostatic…
Full specification wording
Fields (A-level only): Similarities and differences between gravitational and electrostatic forces: Similarities: Both have inverse-square force laws that have many characteristics in common, eg use of field lines, use of potential concept, equipotential surfaces etc Differences: masses always attract, but charges may attract or repel
Gravitational and electrostatic forces share a common mathematical structure.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 4 of 4
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Gravitational and electrostatic forces share a common mathematical structure. Both obey inverse-square laws: F = Gm₁m₂/r² and F = Q₁Q₂/(4πε₀r²). Both can be represented by field lines, and both have a potential concept, with gravitational potential V = -GM/r and electric potential V = Q/(4πε₀r). Equipotential surfaces are perpendicular to field lines in each case, and moving along an equipotential requires no work. The key difference is sign and direction: mass is always positive, so gravity is always attractive, whereas charge can be positive or negative, so the electrostatic force may be attractive or repulsive. This sign difference also changes the sign of potential energy and the shape of potential graphs.
What earns the marks
- States both inverse-square laws, F = Gm₁m₂/r² and F = Q₁Q₂/(4πε₀r²), and identifies the constant in each.
- Explains that both fields can be represented by field lines whose direction shows the force on a test mass or positive test charge, and whose spacing shows relative strength.
- Defines potential in each case as work done per unit mass or per unit charge, and gives V = -GM/r and V = Q/(4πε₀r) for a point source.
- Describes equipotential surfaces as surfaces of constant potential, perpendicular to field lines, with no work done when a test quantity moves along them.
- Contrasts the always-attractive nature of gravity, because mass is always positive, with the attractive or repulsive nature of electrostatic force, because charges can be positive or negative.
Common mistakes and how to put them right
Stating that gravitational potential is positive near a point mass.
Put it right: Gravitational potential is negative, V = -GM/r, because the zero is taken at infinity and gravity is attractive.
Claiming that electrostatic forces are always attractive.
Put it right: Like charges repel and opposite charges attract, so the force can be either.
Treating equipotential surfaces as parallel to field lines.
Put it right: Equipotential surfaces are perpendicular to field lines.
Assuming the inverse-square law applies inside a uniform sphere or near a charged plate.
Put it right: The inverse-square form applies to point masses and point charges, while other geometries need their own field expressions.
Exam tips
- When comparing the two forces, structure the answer as similarities first, then differences, and support each point with an equation or a diagram feature rather than a general statement.
- Use the sign of the source quantity to predict the sign of potential and the direction of force before doing any calculation; this catches sign errors early.
- If asked about equipotential surfaces, state the perpendicular relationship to field lines and explain that potential difference is zero along the surface, so no work is done.
Try the lesson
The start of the Fields (A-level only): Similarities and differences between gravitational and electrostatic forces: Similarities: Both have inverse-square force laws that have many characteristics in common, eg use of field lines, use of potential concept, equipotential surfaces etc Differences: masses always attract, but charges may attract or repel lesson, made from checked teaching notes for this specification point.
Have a go first
Two isolated point masses and two isolated point charges are each separated by the same distance. Which comparison of the forces is correct?
Listen
Gravitational and electrostatic forces share a common mathematical structure. Both obey inverse-square laws: F = Gm₁m₂/r² and F = Q₁Q₂/(4πε₀r²). Both can be represented by field lines, and both have a potential concept, with gravitational potential V = -GM/r and electric potential V = Q/(4πε₀r). Equipotential surfaces are perpendicular to field lines in each case, and moving along an equipotential requires no work. The key difference is sign and direction: mass is always positive, so gravity is always attractive, whereas charge can be positive or negative, so the electrostatic force may be attractive or repulsive. This sign difference also changes the sign of potential energy and the shape of potential graphs. A strong answer earns marks for these points. States both inverse-square laws, F = Gm₁m₂/r² and F = Q₁Q₂/(4πε₀r²), and identifies the constant in each. Explains that both fields can be represented by field lines whose direction shows the force on a test mass or positive test charge, and whose spacing shows relative strength. Defines potential in each case as work done per unit mass or per unit charge, and gives V = -GM/r and V = Q/(4πε₀r) for a point source. Describes equipotential surfaces as surfaces of constant potential, perpendicular to field lines, with no work done when a test quantity moves along them. A common slip: Stating that gravitational potential is positive near a point mass. Instead, gravitational potential is negative, V = -GM/r, because the zero is taken at infinity and gravity is attractive. Exam tip: When comparing the two forces, structure the answer as similarities first, then differences, and support each point with an equation or a diagram feature rather than a general statement.
See it
Key words
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Inverse-square force laws
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Field lines and potential
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Equipotential surfaces
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Attractive versus attractive-or-repulsive forces
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See every definition
- Inverse-square force laws
- Both gravitational and electrostatic forces have inverse-square force laws that have many characteristics in common.
- Field lines and potential
- Both fields can be represented by field lines, and both have a potential concept.
- Equipotential surfaces
- Surfaces of constant potential, perpendicular to field lines, with no work done when a test quantity moves along them.
- Attractive versus attractive-or-repulsive forces
- Masses always attract, but charges may attract or repel.
Label the diagram
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1Box 1
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3Box 3
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