AQA A-level Physics 7408 · Paper 2 · Spec 3.7.5.1–3.7.5.2
Magnetic Fields
On this page: — field B · → force F · → velocity v · ⊗ into the page · ⊙ out of the page
Force on a wire: the motor effect
A wire carrying a current across a magnetic field feels a force F = BIl sin θ, at right angles to both the field and the wire. Drag the diagram to turn it round in 3D. Turn the wire, change the current, the field or the length, and watch the force and your left hand follow.
Left hand: first finger = field (N to S) · second finger = current (+ to −) · thumb = motion (the force). The rule uses the current, not the electron flow.
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Drag either diagram to turn both round together (on a phone, swipe sideways across it). Press a Predict the force button for a random wire, then click the pink direction (A to F) you think the force acts along. With the wire at an angle, resolve the current: only the part across the field, I sin θ, gives a force. You get two tries, then the force and the hand appear. Change anything or press Reset to go back to free play. The magnets get thicker and the field lines closer together as B increases. The force arrow is drawn to scale: its length is proportional to F (a very small force is shown with a short minimum arrow so its head is visible).
Required practical 10: weigh the force
The magnets sit on a top-pan balance. The force on the wire has an equal and opposite partner on the magnets (Newton’s third law), so the reading changes. The flux density between the poles is hidden: find it from the gradient of F against I, then reveal it.
| I / A | Reading / g | Δm / g | F / mN |
|---|---|---|---|
| No results yet. Tare the balance, set a current, then press Record result (top of the balance). | |||
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The balance reads to 0.01 g, and g = 9.81 N kg−1. If you leave a large current on, the wire warms up and the reading creeps up slowly: that is why you switch off between readings.
Charged particles in a field
The force BQv is always at right angles to the velocity, so a charged particle moves in a circle at constant speed. Choose a particle, its speed and the field, or compare two particles fired in at the same speed.
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Masses used: proton 1.673 × 10−27 kg, electron and positron 9.11 × 10−31 kg, deuteron 3.344 × 10−27 kg, alpha particle 6.64 × 10−27 kg; charge e = 1.60 × 10−19 C. The motion is slowed down hugely: use the readouts for the real times. In Compare mode both paths share one scale unless the radii differ by more than 20 times; then the smaller path is shown in a zoom box with its own scale bar.
The cyclotron
Protons gain energy QV each time they cross the gap, and the field turns them round inside the dees. Every half-turn takes the same time, so a pd of fixed frequency keeps in step. Tune it, then try it slightly out of tune.
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Each crossing is exact: the gain is QV cos(πkδ), where k is the crossing number and δ the fractional frequency error, so a tuned pd always gives the full QV. Proton mass 1.673 × 10−27 kg. The drawing shows the last 12 half-turns; speeds are far below the real ones, which are given in the readouts.
Key equations for magnetic fields
Quick catch
Three rounds of five multiple-choice questions, each round harder than the last. Pick A, B, C or D and the reasons appear straight away. Get 4 of 5 right to unlock the next round.
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Where it comes from
Three short derivations, each with a live diagram. Move the slider and every number in the steps updates.
Test yourself
35 exam-style questions in three levels: Core, Exam-style and Stretch for A*. Each level shows a few at a time. Press Try another question for a different one. Type numbers without units. For the explain parts, write your answer, then mark it against the mark scheme.
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Download the booklet
Notes, worked examples, equation cards, 15 quick checks and 31 exam-style questions on the force on a current, required practical 10, charged particles and the cyclotron, to print and write on. The answers are at the back.
Magnetic Fields: notes and practice booklet
Print it, write in the spaces, then check your answers at the back.
It opens in a new tab. Use the download or print button in the PDF viewer to keep a copy. Print it double-sided and write in the spaces. In the PDF, each question links to its answer and back again.
Teachers: free for classroom use. Please share this page link rather than the file, so students always get the latest version.
Magnetic fields: common questions
Why is it the left hand?
Fleming’s left-hand rule is for the motor effect: a current in a field feels a force. First finger Field, seCond finger Current, thuMb Motion.
Fleming’s right-hand rule is for the generator effect: a wire moved through a field has a current induced in it. There the thumb is the motion and the second finger gives the induced current. You meet it with electromagnetic induction.
The right-hand grip rule is different again: it gives the direction of the field around a wire, not a force.
Exam trap. Using the right hand for a force on a current, or pointing the second finger along an electron beam instead of the conventional current.
Why doesn’t a magnetic field speed a particle up?
The force BQv is always at right angles to the velocity. A force at right angles to the motion does no work, so the kinetic energy and the speed stay the same. Only the direction changes.
Exam trap. Saying the magnetic field accelerates the protons in a cyclotron. The pd across the gap does the work; the field only turns them round.
Why can a cyclotron’s frequency stay fixed?
The time for one orbit does not depend on the speed:
A faster proton moves on a bigger semicircle in exactly the same time, so it always arrives at the gap when the pd is the right way round. (At speeds close to the speed of light this stops being true.)
What does a balance reading in grams tell me in required practical 10?
Multiply the change in reading by 10−3 to get kilograms, then by g = 9.81 N kg−1 to get the force in newtons. That is the force on the magnets, equal and opposite to the force on the wire.
Exam trap. Leaving the change in grams, or using the whole reading instead of the change.