Fields (A-level only) — AQA A-Level Physics

This topic introduces the concept of a field as a region where a non-contact force acts, covering gravitational, electric and magnetic fields. You will learn to represent fields using field lines, define field strength and potential, and apply inverse-square laws to calculate forces, field strengths and potentials for point masses and point charges.

Fields are fundamental to understanding orbits, capacitors, particle accelerators and electromagnetic induction. AQA examines this topic through calculations, graph interpretation and explanations of field behaviour, often linking to circular motion and energy conservation. Mastering fields is essential for later topics such as electromagnetic induction and nuclear physics.

• →A field is a region where a force acts on a suitable object; gravitational fields act on mass, electric fields on charge, and magnetic fields on moving charges or magnetic materials.
• →Field strength is a vector: gravitational field strength g = F/m (N kg^-1), electric field strength E = F/Q (N C^-1 or V m^-1). Field lines show the direction of the force on a positive test charge or mass.
• →Potential is a scalar: gravitational potential V = -GM/r (J kg^-1), electric potential V = kQ/r (J C^-1 or V). Potential is zero at infinity and negative for attractive fields.
• →For radial fields, field strength follows an inverse-square law: g = GM/r^2 and E = kQ/r^2. For uniform fields, E = V/d.
• →Equipotential surfaces are always perpendicular to field lines; no work is done moving along an equipotential. The potential gradient equals the negative of field strength: g = -dV/dr and E = -dV/dr.

• Defines a force field as a region in which a non-contact force acts on a body placed there.
• Identifies that the field is produced by a source such as a mass, charge or magnet and exists in the surrounding space.
• States that the force is non-contact, so the interacting bodies need not touch.
• Gives a correct example such as gravitational attraction between a mass and a planet, electric force between charges, or magnetic force on a compass needle.
• Recognises that the force can be attractive or repulsive and may vary in magnitude and direction across the region.
• Explains that the field is a vector quantity at each point, with both magnitude and direction.
• Distinguishes a field from a contact force such as friction or normal contact force.
• States that a force field can be represented by a vector at each point in the region.
• Explains that the magnitude of the vector represents the strength of the field at that point.
• Explains that the direction of the vector represents the direction of the force on a suitable test body.
• Determines direction by inspection, for example gravitational field towards the centre of a planet.
• Determines electric field direction as the force on a positive test charge, away from a positive source and towards a negative source.
• Determines magnetic field direction using the direction in which the north pole of a compass needle points.
• Interprets field-line diagrams, using arrows for direction and spacing for relative magnitude.
• Defines a field as a region where a test mass, test charge or moving charge experiences a force, and distinguishes the three sources: mass, static charge, moving charge.
• Uses g = F/m for gravitational field strength and E = F/q for electric field strength, stating that both are vector quantities with direction given by the force on a positive test quantity.
• Explains that field lines show the direction of the force on a positive test charge or on a test mass, and that line spacing indicates relative field strength.
• Applies F = BIL sin θ to a current-carrying conductor and F = Bqv sin θ to a moving charge, noting the force is perpendicular to both the field and the velocity or current.
• Describes how field strength decreases with distance for point mass and point charge, linking to inverse-square behaviour, and contrasts this with the uniform field between parallel plates.
• Interprets a described practical arrangement, such as a mass on a spring balance near a large mass, a charged sphere on a balance near another charged sphere, or a wire on a top-pan balance in a magnetic field, to identify the field type and calculate a field strength.
• 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.
• Links the sign of charge to the sign of potential energy and to whether potential is positive or negative near an isolated point charge, and compares this with the always-negative gravitational potential near a point mass.

• 💡Define the term precisely, including the words region and non-contact force, before giving an example.
• 💡Use a named example such as the gravitational field of a planet or the electric field of a point charge to show understanding.
• 💡When asked to explain, link the source, the field in the surrounding space and the force on a test body in a clear chain.
• 💡State the test body you are using, such as a positive test charge or a compass needle, when justifying a direction.
• 💡Sketch a simple field-line diagram with arrows to support your written direction.
• 💡Check the sign of the source before deciding whether the field points towards or away from it.
• 💡When asked to compare fields, name the source, the test quantity and the defining equation before substituting numbers; this makes the physics explicit and avoids vague descriptions.
• 💡For magnetic force questions, sketch the field direction, the current or velocity direction and the force direction, then apply Fleming's left-hand rule to check the direction before calculating magnitude.
• 💡If a question gives a graph of force against distance or against 1/r², state the relationship shown and use the gradient or area only where the axes make that physically meaningful.
• 💡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.
• 💡Always define the direction of a field or force relative to a positive test charge or mass. For electric fields, state 'away from positive, towards negative'. For gravitational fields, always attractive.
• 💡When sketching field lines, ensure they are perpendicular to the surface of the mass or charge, never cross, and have arrows showing direction. For uniform fields, draw equally spaced parallel lines.
• 💡In calculations, keep signs consistent: use negative for attractive potentials and positive for repulsive. Show all working and give units in your final answer.

• Thinking a force field requires the two bodies to touch: correct this by stressing that the force acts at a distance through the field.
• Believing the field only exists where a test body is present: correct this by explaining the field is a property of the space around the source and exists independently.
• Confusing the field with the force itself: correct this by stating the field is defined at a point and the force depends on the body placed there.
• Assuming the field vector always points away from the source: correct this by checking the type of field and the sign of the source, since gravitational and electric fields can point towards the source.
• Using the force on a negative test charge to define electric field direction: correct this by defining the direction using a positive test charge.
• Treating field lines as paths that a body follows: correct this by explaining that field lines show the direction of the field vector at each point, not the trajectory of a moving body.
• Treating the electric field direction as the direction of force on a negative charge; the correction is that E points in the direction of force on a positive test charge, so a negative charge feels force opposite to E.
• Assuming a magnetic force acts on a stationary charge in a magnetic field; the correction is that a magnetic force requires relative motion, so F = Bqv sin θ is zero when v = 0.
• Confusing field strength with potential or with force; the correction is that field strength is force per unit test quantity, whereas potential is energy per unit test quantity, and the two are related but distinct.
• Using F = BIL without the sin θ factor when the conductor is not perpendicular to the field; the correction is to include sin θ, which equals 1 only at 90°.
• Stating that gravitational potential is positive near a point mass; the correction is that 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; the correction is that like charges repel and opposite charges attract, so the force can be either.
• Treating equipotential surfaces as parallel to field lines; the correction is that equipotential surfaces are perpendicular to field lines.
• Assuming the inverse-square law applies inside a uniform sphere or near a charged plate; the correction is that the inverse-square form applies to point masses and point charges, while other geometries need their own field expressions.
• Students often think gravitational potential is positive because they confuse it with potential energy. Correction: gravitational potential is negative because the field is attractive and the zero is at infinity.
• Many believe that field strength and potential are the same thing. Correction: field strength is a vector (force per unit mass/charge) while potential is a scalar (work done per unit mass/charge); they are related by a gradient.
• Students frequently apply E = V/d to radial fields. Correction: E = V/d only applies to uniform fields; for radial fields use E = kQ/r^2 and V = kQ/r.

1. 1Days 1-2: Revise the definitions of field, field strength and potential for gravitational and electric fields. Learn the equations and their units, and practise drawing field lines for point masses, point charges and uniform fields.
2. 2Days 3-4: Work through calculations using inverse-square laws for radial fields and E = V/d for uniform fields. Focus on orbital motion and charged particle motion in electric fields.
3. 3Days 5-6: Study the relationship between field strength and potential gradient. Plot and interpret graphs of g against r and V against r, and practise deriving E = -dV/dr.
4. 4Days 7-8: Attempt past paper questions on fields, including multiple-choice, structured calculations and 6-mark explanations. Mark your answers using the mark scheme and note recurring errors.
5. 5Days 9-10: Create a summary sheet of key definitions, equations and graphs. Use active recall to test yourself on definitions and derivations, and revisit any weak areas.

• 📋Definition and explanation questions: e.g., 'Define gravitational potential' or 'Explain why the electric field inside a hollow charged sphere is zero'. Use precise wording and refer to the reference point (infinity) and sign.
• 📋Calculation questions: e.g., 'Calculate the orbital speed of a satellite' or 'Determine the electric field strength at a point due to two charges'. Show all steps, use standard form and give units.
• 📋Graph interpretation: e.g., 'Sketch a graph of gravitational potential against distance from a point mass' or 'Explain the shape of the graph of field strength against distance'. Label axes and key features.
• 📋Six-mark structured questions: e.g., 'Describe and explain the motion of a charged particle entering a uniform electric field'. Structure your answer with clear points, using correct terminology and equations.