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Gravitational and electric field questions

Distinguish field strength from potential; use centre distances, charge signs and circular orbits.

Practise

Circular orbital speed

A satellite of negligible mass follows a circular orbit of radius 9000000 m about a spherical planet of mass 6 × 10+24 kg. Find its orbital speed. Ignore other bodies and use G = 6.67 × 10⁻¹¹ N m² kg⁻². Give your answer to 3 significant figures.

Treat the given values as exact unless an uncertainty is stated.

Use decimals or e notation, e.g. 4.2e-3. Enter the unit separately.

Hint

Gravity supplies centripetal force: GMm/r² = mv²/r.

Worked solution
  1. v² = GM/r.
  2. v = √(6.67 × 10⁻¹¹ × 6 × 10+24/9000000) m s⁻¹.
  3. Answer: 6.67 × 103 m s⁻¹ (3 significant figures).
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Question type: Mixed practice
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Measure radius from the centre

Outside a spherical planet, g = GM/r². For height h above a planet of radius R, use r = R + h. Gravitational field strength points towards the planet; its magnitude is positive. In a circular orbit, gravity provides centripetal force, giving speed √(GM/r).

Field strength and potential are different quantities

Gravitational potential is energy per unit mass: V = −GM/r, taking zero at infinity. It is measured in J kg⁻¹. Gravitational field strength is force per unit mass, measured in N kg⁻¹. Do not use the inverse-square field equation to calculate potential.

Keep the charge sign

For a point charge in vacuum, field magnitude E = k|Q|/r² and signed potential V = kQ/r. Field points away from positive charge and towards negative charge. Between parallel plates, E = ΔV/d away from the positive plate, ignoring edge effects. Force F = qE reverses direction for a negative charge.

What this practice covers

Selected spherical gravitational fields, circular orbital speeds, point-charge electric fields and potentials, and forces in uniform fields. No field superposition, magnetic fields, escape speed, equipotential plotting or charged-particle trajectories are included.

A-level relevance

AQA 7408: 3.7.2.1–4; 3.7.3.2–3 (selected); OCR A H556: 5.4.1–4; 6.2.1–4 (selected). Tasks cover the selected skills listed above.

AQA specification · OCR A specification

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