IB, A-Level & GCSE Physics
Fleming’s left hand rule tells you which way a current-carrying wire is pushed when it sits in a magnetic field. Hold out your left hand, point three fingers at right angles, and the rule gives you the answer in a second.
The hard part is not the hand. It is remembering which finger stands for what, and knowing when to use the left hand rather than the right. Both are below, with the physics behind them.
Put a wire carrying a current into a magnetic field and the wire is pushed. That push is called the motor effect, and Fleming’s left hand rule tells you which way it acts.
Scroll the diagram sideways.
The rule
On your left hand, held with the thumb, first finger and second finger all at right angles: the thuMb gives the direction of the Motion or force, the First finger gives the Field, and the seCond finger gives the Current.
The mnemonic is built into the words themselves. Each finger contains the first letter of what it stands for, which is why the rule sticks once you have seen it written out.
| Finger | Stands for | Pointing which way |
|---|---|---|
| thuMb | Motion, meaning the force on the wire | The way the wire is pushed |
| First finger | Field, the magnetic field | Always from north to south |
| seCond finger | Current, conventional current | From positive to negative |
Three things that are easy to get wrong
Exam diagrams are flat, but the three directions in this rule are not. Something always has to point into or out of the page, and there is a standard way of drawing that.
Scroll the diagram sideways.
A dot means out of the page, towards you. A cross means into the page, away from you. The same two marks are used for current in a wire and for magnetic field, so always read the label next to them.
Watch the symbol in the middle of a circle
A circle with a dot in it can be a wire carrying current out of the page. A grid of crosses across the whole diagram is a magnetic field going into the page. They look similar at a glance and mean different quantities, so check what the question has labelled.
Here is the arrangement that turns up most often: a wire running between the poles of a magnet, at right angles to the field.
Scroll the diagram sideways.
Do it with your actual hand. Reading about it is not the same thing, and in an exam you will have your hand but not this page.
What happens when something reverses
The hand gives you the direction. For the size of the force you need the equation.
F = B I L
force = magnetic flux density × current × length of wire in the field
| Symbol | Quantity | Unit |
|---|---|---|
| F | Force on the wire | newtons, N |
| B | Magnetic flux density, or field strength | tesla, T |
| I | Current in the wire | amps, A |
| L | Length of wire inside the field | metres, m |
A wire of length 0.25 m carries a current of 4.0 A at right angles to a magnetic field of flux density 0.30 T. Find the force on the wire.
The current is at 90° to the field, so use F = BIL directly
F = 0.30 × 4.0 × 0.25
F = 0.30 N
If the wire sits at an angle to the field, only the part of the current perpendicular to the field produces a force. The equation gains a sine term.
F = B I L sin θ
θ is the angle between the current and the field
| Angle to the field | sin θ | Force |
|---|---|---|
| 90° | 1 | Maximum, F = BIL |
| 45° | 0.71 | About 71% of the maximum |
| 30° | 0.5 | Half the maximum |
| 0° | 0 | No force at all |
The case worth remembering
A wire running parallel to the field feels no force, because sin 0° = 0. Examiners like this one, and students who have only ever seen the perpendicular case tend to answer that the force is simply BIL.
There is a second rule with the same three fingers, on the other hand. Students mix them up constantly, and the fix is to ask one question before you lift either hand: what is causing what?
Scroll the diagram sideways.
| Which hand | The situation | What you are finding | Device |
|---|---|---|---|
| LEFT hand | A current is already flowing, and the field pushes the wire | The direction of the force | Motor |
| RIGHT hand | You move the wire through the field, and a current appears | The direction of the induced current | Generator |
One line that settles it
A motor is the left hand rule applied twice at once. Put a loop of wire in a magnetic field and the two sides of the loop carry current in opposite directions — so the force on one side is opposite to the force on the other.
Scroll the diagram sideways.
Check it with your hand. On the left side the current comes out of the page and the field points right, so the force is up. On the right side the current goes into the page, everything else unchanged, so the force is down. One side rises, the other falls, and the coil rotates.
Why a motor needs a split-ring commutator
After half a turn the two sides have swapped places, so the forces would now push the coil back the way it came and it would rock instead of spin. A split-ring commutator reverses the current every half turn, which reverses both forces at exactly the right moment and keeps the coil turning the same way.
| The mistake | What goes wrong | Do this instead |
|---|---|---|
| Using the right hand for a motor | The force comes out exactly backwards. | Current in, motion out: left hand. |
| Drawing the field south to north | The first finger points the wrong way, so the thumb does too. | Field lines leave the north pole and enter the south. |
| Using electron flow as the current | Electrons travel the opposite way to conventional current, so the force reverses. | Conventional current: positive to negative. |
| Fingers not at right angles | A vague hand position gives a vague answer, and in three dimensions that usually means a wrong one. | All three mutually perpendicular, every time. |
| Forgetting sin θ | F = BIL only applies when the wire is at 90° to the field. | Angled wire: F = BIL sin θ. Parallel wire: no force. |
| Using the whole length of the wire | Only the part sitting inside the field is pushed. | L is the length in the field, not the length of the wire. |
Use your actual left hand. Answer each one before tapping to check.
Upwards. First finger right for the field, second finger towards you for the current, and the left thumb points up.
Downwards. Only the current has reversed, so the force reverses with it.
Perpendicular, so F = BIL
F = 0.20 × 2.5 × 0.40
F = 0.20 N
Zero. The angle between the current and the field is 0°, and sin 0° = 0, so F = BIL sin 0° = 0. A wire parallel to the field feels no force.
Not perpendicular, so include sin θ
F = 0.50 × 6.0 × 0.30 × sin 30°
F = 0.90 × 0.5
F = 0.45 N
Right hand. The movement is causing the current, so this is a generator situation. The left hand is for the opposite case, where a current already flowing causes movement.
The same way as before. Reversing the current flips the force, and reversing the field flips it back, so the two changes cancel.
L is the length inside the field, so L = 0.60 m, not 2.0 m
F = 0.40 × 3.0 × 0.60
F = 0.72 N
It is a way of finding the direction of the force on a current-carrying wire placed in a magnetic field. Hold your left hand with the thumb, first finger and second finger at right angles to each other: the thumb gives the force, the first finger gives the field, and the second finger gives the current. It was devised by the English engineer John Ambrose Fleming as a teaching aid.
The first finger is the Field and the seCond finger is the Current. The letters are in the words, which is what makes the rule memorable: thuMb for Motion, First for Field, seCond for Current.
Ask what is causing what. If a current is already flowing and you want to know which way the wire is pushed, use the left hand — that is a motor. If you are moving a wire through a field and want to know which way the induced current flows, use the right hand — that is a generator.
Because of how the three directions relate to one another mathematically. The force, field and current form a set of three perpendicular directions whose handedness is fixed by the physics, and with the finger meanings Fleming chose, that handedness matches the left hand for the motor case and the right hand for the generator case. It is not an arbitrary convention you can swap.
Outside a magnet, field lines run from the north pole to the south pole. Inside the magnet they run south to north, completing the loop, but exam diagrams almost always show the outside region. Point your first finger from N towards S.
Conventional current, which runs from positive to negative. Electrons actually drift the other way. If a question describes electron flow, reverse it before pointing your second finger, or your force will come out backwards.
A dot means out of the page, towards you; a cross means into the page, away from you. Think of an arrow: you see its point coming towards you and its tail flights going away. The notation is used for both current and magnetic field, so read the label.
F = BIL when the current is at right angles to the field, where B is the magnetic flux density in tesla, I the current in amps and L the length of wire inside the field in metres. At any other angle, F = BIL sin θ, where θ is the angle between the current and the field.
It is the name for the force experienced by a current-carrying conductor placed in a magnetic field. The field of the magnet and the field around the current interact, and the wire is pushed. Fleming’s left hand rule gives the direction of that push, and F = BIL gives its size.
Because the force depends on sin θ, and when the current runs along the field lines θ = 0°, so sin θ = 0. Physically, there is no component of the current cutting across the field, so there is nothing for the field to push against. You also cannot hold three fingers at right angles in that arrangement, which is the hand telling you the same thing.
A split-ring commutator reverses the current through the coil every half turn. Without it, once the coil had turned 180° the forces would act to push it back, and it would simply rock. Reversing the current at that point reverses both forces so they keep driving the coil the same way round.
Increase any of the three things in F = BIL: a larger current, a stronger magnetic field, or more turns of wire in the coil, since each turn adds its own length inside the field. All three increase the force on the coil and so the turning effect.
Yes. IB Physics at both SL and HL covers the force on a current-carrying conductor in a magnetic field, with F = BIL sin θ for the magnitude and the left hand rule for the direction. The same material appears on A‑level and GCSE physics papers, so one understanding serves all three courses.
They are different rules that both use the right hand. Fleming’s right hand rule uses three fingers at right angles to find an induced current in a moving wire. The right hand grip rule uses a closed fist: point your thumb along the current in a wire and your curled fingers show the direction of the circular magnetic field around it. One is about induction, the other about the field a current creates.
Write the three letters in the margin as soon as you start: Motion, Field, Current, matching thuMb, First, seCond. Then put your left hand on the desk and actually point the fingers. Students who try to do it in their heads are the ones who get the direction backwards.
Getting the hand right is the easy part. The marks sit in explaining why the coil turns, what the commutator does, and what happens when you change the field — and those are the parts students lose. Our tutors teach IB and A‑level physics and work through your own past papers, so the gaps we close are the ones costing you marks right now.
Book a free 30-minute meetingRevising the whole subject? Our IB revision notes cover physics topic by topic at SL and HL, or read about our online physics tutors.
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