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Revision guide · A-Level

A-Level Physics gravitational and electric fields: field strength, potential and orbits

A field is a region where an object feels a force: masses in a gravitational field, charges in an electric field. Field strength is force per unit mass (g = F/m) or per unit positive charge (E = F/q). Both point-mass and point-charge fields follow an inverse-square law, g = GM/r^2 and E = Q/(4πε0 r^2), and both have potentials that fall off as 1/r. Between parallel plates the electric field is uniform, E = V/d. In Cambridge 9702 these are A Level topics 13 and 18. In Edexcel IAL, electric fields are in Unit 4 (WPH14) and gravitational fields in Unit 5 (WPH15). Marks are lost on r^2, on using height instead of orbital radius, and on signs.

Facts checked:

At a glance

Cambridge 9702
A Level topic 13 (gravitational), topic 18 (electric)
Edexcel IAL
Electric fields Unit 4 (WPH14); gravitational fields Unit 5 (WPH15)
Data sheet values
G = 6.67 × 10^-11 N m^2 kg^-2; e = 1.60 × 10^-19 C
Key idea
Both point fields are inverse-square

Where fields sit in each specification

Board and unitContent
Cambridge 9702 topic 13 (A Level)Gravitational field as force per unit mass, field lines, Newton's law of gravitation, circular orbits and geostationary satellites, g = GM/r^2, gravitational potential φ = -GM/r and potential energy -GMm/r
Cambridge 9702 topic 18 (A Level)Electric field as force per unit positive charge, F = qE, uniform fields E = ΔV/Δd and charged particles in them, Coulomb's law, field of a point charge, electric potential and potential energy, field as negative potential gradient
Edexcel IAL Unit 4 (WPH14)Electric fields: definition, E = F/Q, Coulomb's law, point charge fields, E = V/d between parallel plates, radial and uniform fields, link between field and potential; capacitors and magnetic fields in the same unit
Edexcel IAL Unit 5 (WPH15)Gravitational fields: definition, g = F/m, g = GM/r^2, V = -GM/r, comparing electric and gravitational fields, Newton's laws applied to orbits

The key ideas

Newton's law of gravitation: F = GMm/r^2, always attractive, where r is the distance between centres. Divide by m to get the field strength g = GM/r^2. Coulomb's law: F = Qq/(4πε0 r^2), attractive or repulsive depending on the signs; 1/(4πε0) = 8.99 × 10^9 N m^2 C^-2. The field strength of a point charge is E = Q/(4πε0 r^2). Doubling the distance quarters the field.

Potential at a point is the work done per unit mass (or per unit positive charge) bringing a small test object from infinity to that point. Gravitational potential is always negative, φ = -GM/r, because work is done by the field as a mass moves in. Electric potential V = Q/(4πε0 r) is positive near a positive charge. Field strength is the negative of the potential gradient.

For a circular orbit, gravity provides the centripetal force: GMm/r^2 = mv^2/r = mω^2 r. This gives v = sqrt(GM/r) and T^2 = 4π^2 r^3/(GM). A geostationary satellite has a period of 24 hours, orbits above the equator from west to east, and stays above the same point. Between parallel plates, a charged particle feels a constant force qE and follows a parabolic path, like a projectile.

Worked example 1: the radius of a geostationary orbit

  1. Data: G = 6.67 × 10^-11 N m^2 kg^-2, mass of Earth M = 5.97 × 10^24 kg, T = 24 hours = 86 400 s.
  2. From GMm/r^2 = m(2π/T)^2 r, r^3 = GMT^2/(4π^2).
  3. r^3 = 6.67 × 10^-11 × 5.97 × 10^24 × 86 400^2 ÷ (4π^2) = 7.53 × 10^22 m^3.
  4. r = 4.22 × 10^7 m from the centre of the Earth.
  5. Height above the surface = 4.22 × 10^7 - 6.37 × 10^6 = 3.59 × 10^7 m. The orbital speed is 2πr/T = 3.07 × 10^3 m s^-1.

Worked example 2: an electron between parallel plates

  1. Two plates 20 mm apart have a p.d. of 500 V.
  2. E = V/d = 500 ÷ 0.020 = 2.5 × 10^4 V m^-1 (equivalently N C^-1).
  3. Force on an electron: F = eE = 1.60 × 10^-19 × 2.5 × 10^4 = 4.0 × 10^-15 N, towards the positive plate.
  4. Acceleration: a = F/m = 4.0 × 10^-15 ÷ 9.11 × 10^-31 = 4.4 × 10^15 m s^-2. Gravity on the electron is negligible by comparison.

Worked example 3: field of a point charge

  1. Find the field strength 0.10 m from a +4.0 nC point charge.
  2. E = Q/(4πε0 r^2) = 8.99 × 10^9 × 4.0 × 10^-9 ÷ 0.10^2.
  3. E = 3.6 × 10^3 N C^-1, directed away from the charge.
  4. At 0.20 m the field is a quarter of this, 9.0 × 10^2 N C^-1.

Common mistakes that cost marks

  • Using the height above the surface instead of the distance from the centre.
  • Forgetting to square r, or squaring it in the potential formula.
  • Writing gravitational potential as positive.
  • Confusing field strength (a vector) with potential (a scalar).
  • Using the wrong distance unit: convert mm and cm to m before calculating E = V/d.
  • Definitions without 'per unit mass' or 'per unit positive charge', or without 'from infinity' for potential.

Exam technique and how a tutor helps

Learn the definitions exactly; they are regularly worth 1 or 2 marks. Questions often ask you to compare the two fields: both are inverse-square, both have potentials proportional to 1/r, but gravity is only attractive while electric forces can attract or repel, and the electric force between particles is far stronger. For orbit questions, write the equation of gravitational force to centripetal force first, then rearrange before substituting.

Graph questions are common: the gradient of a potential-distance graph gives the negative of the field strength, and the area under a field strength-distance graph gives the potential difference.

In one-to-one lessons a tutor works through orbit and field calculations side by side with the student, so the parallels between the two fields become a single method rather than two topics, and checks each definition against the mark scheme wording.

Self-check: can you do these?

  • Define gravitational field strength. (Answer: force per unit mass)
  • The field 1.0 m from a charge is 800 N C^-1. What is it at 2.0 m? (Answer: 200 N C^-1)
  • Why is gravitational potential negative? (Answer: zero is at infinity and work is done by the field as a mass moves closer)
  • State two properties of a geostationary orbit. (Answer: period 24 hours, above the equator, west to east)
  • What is the unit of electric field strength besides N C^-1? (Answer: V m^-1)

Common questions

Are fields AS or A Level?

A Level in both boards. In Cambridge 9702 they are topics 13 and 18. In Edexcel IAL electric fields are in Unit 4 and gravitational fields in Unit 5.

Are G and the Coulomb constant given?

Yes. The data lists for both boards give G = 6.67 × 10^-11 N m^2 kg^-2, e = 1.60 × 10^-19 C and the Coulomb law constant (8.99 × 10^9). Planet masses and radii are given in the question.

What is the difference between field strength and potential?

Field strength is the force per unit mass or charge at a point, a vector. Potential is the work done per unit mass or charge bringing an object from infinity, a scalar. Field strength equals the negative of the potential gradient.

Do I need to derive orbit equations?

Cambridge 9702 asks you to analyse circular orbits by relating gravitational force to centripetal acceleration, and to derive g = GM/r^2. Edexcel IAL asks you to apply Newton's laws and gravitation to orbital motion. Practise the derivation of T^2 against r^3.

How much do LiveTutor A-Level Physics lessons cost?

Every lesson is one to one, online and 60 minutes, at one flat rate of $15 a lesson for every subject and level. Families choose a weekly plan of 1 to 5 lessons billed monthly, and the first lesson is a free trial.

Sources

Dates and figures on this page come from these official and published sources. Always confirm deadlines on the official page before acting on them.

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