Fleming’s Rules Simulator
Left-hand & right-hand rules in 3D — Simulate • Explain • Practice • Quiz
Display Controls
Σ Live equation — values from the set-up on screen
1 Overview
The simulator demonstrates Fleming’s left-hand rule (the motor effect) and Fleming’s right-hand rule (the generator effect) on three classic experiments: a copper rod catapulted along rails by a current, the same rod pushed to induce a current, and a straight wire turned through an angle in a field. It has four modes: Simulate, Explore, Practice and Quiz.
2 Getting Started
Follow the three numbered cards beside the canvas: 1 choose an experiment (Motor, Generator or Angle), 2 press the green action button (Close the switch, Push the rod or Switch the current on) or 🎓 Explain, and 3 change the conditions with the buttons and sliders. The line under the canvas always says, in words, which way the field, current and force point.
The page opens in the 3D view on a computer or tablet and in the 2D view on a phone. The 2D | 3D switch is at the bottom right of the canvas, and the page remembers your choice. Add ?view=2d or ?view=3d to a link to open a particular view.
3 Simulate Mode
- Motor — a horseshoe magnet (N above, S below) and two rails. Close the switch: a constant-current supply drives I along the rod, which is pushed by F = BIL while it is between the poles and coasts to a stop (or to the end stop) once it leaves them. Drag the rod to a new start position while the switch is open.
- Generator — the supply is replaced by a centre-zero galvanometer. Push the rod moves it at speed v from one end to the other, or drag the rod yourself: the faster you move it, the bigger the EMF ε = BLv and the needle kick. The induced current’s own push (Lenz’s law) is shown against the motion.
- Angle — a wire on a turntable between two bar magnets. Set θ and switch the current on: the force F = BIL sin θ points up or down, out of or into the top view, and vanishes when the wire lies along the field.
- Conditions — Reverse the current, Turn the magnet over (or Swap the magnets) and Reverse the motion flip one direction at a time, so you can test the rule: one reversal flips the answer, two cancel.
In 3D, drag to turn the bench, Ctrl + scroll (or pinch) to zoom, and drag the rod along the rails. The hand floats beside the magnet with its thumb, first and second fingers along the three arrows; for the motor it is a left hand and for the generator a right hand. In 2D the rod is seen end-on, its current drawn as ⊙ (out of the page) or ⊗ (into the page), with the “catapult” field of the magnet and the rod added together; the rod’s own field is drawn far stronger than it really is so the shape can be seen.
4 The Explain Lesson
🎓 Explain builds a step-by-step lesson for the experiment and the conditions on screen: the field first, then the current (or the motion), then the finger that gives the answer, then the size from F = BIL or ε = BLv, and then what happens when you reverse the current, the field, the motion or change the angle. Each step sets the conditions it talks about, runs the apparatus, moves the 3D camera to the hand and annotates the canvas: the arrow or part being discussed pulses and its label lights up, while the others dim. Use ⏮ ⏭ or the arrow keys to step, the dots to jump, and Esc to close. Your own settings come back when the lesson ends.
5 Explore, Practice & Quiz
Explore has sixteen cards in four groups: The two rules, Formulas, Applications and Common mistakes. Practice mixes eight kinds of problem: four numerical ones (F = BIL sin θ, ε = BLv, I = BLv/R and B = F/IL) and four direction puzzles (left-hand rule, right-hand rule, finding the field, and electron flow), each with a small diagram and six direction buttons. Quiz asks six questions drawn at random from a pool of twenty, with the options shuffled, and scores you with up to three stars.
6 Key Concepts
F = BIL sin θ: 0.10 T × 5.0 A × 0.060 m × sin 90° = 30 mN (the Motor defaults). ε = BLv: 0.10 T × 0.060 m × 0.50 m/s = 3.0 mV, and through 0.50 Ω that drives 6.0 mA (the Generator defaults). The simulator works in SI units only, as electromagnetism is taught in SI on both sides of the Atlantic.
7 Tips & Other Features
Tick Electrons instead of current in Display Controls to see the electrons drifting against the conventional current — Fleming’s rules always use conventional current. Σ Calculations opens the working for the set-up on screen; PNG or a right-click (long-press) saves the view, copies the readings or starts the lesson. Clicks and a thump give sound feedback.
Fleming’s Left-Hand and Right-Hand Rules — an Interactive 3D Demonstrator
Fleming’s rules are two hand-shaped memory aids for the directions in electromagnetism. Stretch out the thumb, first finger and second finger so they are all at right angles. On the left hand they give the force on a current-carrying conductor in a magnetic field — the motor effect. On the right hand they give the current induced in a conductor moved through a field — the generator effect. This simulator puts a modelled hand next to real apparatus so you can see each finger line up with its arrow.
Fleming’s Left-Hand Rule (Motor Effect)
- First finger → Field, from the N pole to the S pole.
- SeCond finger → Current, conventional, from + to −.
- ThuMb → Motion: the direction of the force on the conductor.
In the rail experiment the N pole is above the rails, so the field points down. With the current flowing along the rod towards you (out of the page), the left-hand rule gives a force to the right, and the rod rolls right. The size of the force is F = BIL sin θ; with B = 0.10 T, I = 5.0 A and L = 6.0 cm at right angles it is 30 mN.
Fleming’s Right-Hand Rule (Generator Effect)
For a conductor that is moved through a field, use the right hand: the thumb along the motion, the first finger along the field, and the second finger then gives the induced current. Pushing the rod to the right through the downward field induces a current into the page. The EMF is ε = BLv: 0.10 T × 0.060 m × 0.50 m/s = 3.0 mV.
What Changes the Direction — Conditions at a Glance
| Condition (motor, starting from field down, current out of the page) | Field | Current | Force |
|---|---|---|---|
| As set up | down | out of the page | right |
| Reverse the current | down | into the page | left |
| Turn the magnet over | up | out of the page | left |
| Reverse both | up | into the page | right |
| Wire along the field (θ = 0°) | along the wire | along the field | none |
One reversal flips the force; two reversals cancel. Every row of this table is produced by the simulator’s own engine, and the Explain lesson walks through each one.
Why the Fingers Must Be at Right Angles
Both rules are pictures of a vector cross product. The force on a current is F = I L × B, and the push on the charges in a moving rod is along v × B. A cross product is perpendicular to both of the vectors it is made from, so the three digits must be mutually perpendicular. Swapping the order of a cross product reverses it, which is why the motor and generator rules need opposite hands. In the 3D view the hand is literally placed by these vectors: a left hand is a right hand reflected, the mirror image of a right-handed set of axes.
Lenz’s Law and Conventional Current
The current induced in the moving rod is itself a current in a field, so the left-hand rule acts on it, and the force always points against the motion. You have to keep pushing, and the work you do appears as electrical energy: F·v = ε·I. Fleming’s rules use conventional current; electrons in the copper drift the other way, and using them reverses the answer.
Who Uses This Simulator?
Students meeting the motor and generator effects in GCSE, IGCSE, A-level, IB, CBSE and introductory college physics; instructors who want to show the hand rule in three dimensions instead of drawing it on a board; and anyone revising for an exam question on the direction of a force or an induced current.
Frequently Asked Questions
What is Fleming’s left-hand rule?
Hold the thumb, first finger and second finger of your left hand at right angles to each other. Point the first finger along the magnetic field (N to S) and the second finger along the conventional current. The thumb then points along the force on the conductor. It is used for motors.
What is the difference between Fleming’s left-hand and right-hand rules?
The left-hand rule gives the force on a conductor that already carries a current (motor effect). The right-hand rule gives the direction of the current induced in a conductor that is moved through a field (generator effect): thumb along the motion, first finger along the field, second finger along the induced current.
Why is there no force when the wire is parallel to the field?
The force is F = BIL sin theta, where theta is the angle between the wire and the field. When the wire lies along the field, theta is 0 and sin 0 is 0, so the force is zero. Only the part of the current that crosses the field lines is pushed.
Explore Related Simulators
- DC Motor Simulator: the left-hand rule on both sides of a coil, turned into torque by a commutator.
- AC Generator Simulator: the right-hand rule on a spinning coil, with slip rings and a sine-wave output.
- Faraday’s Law Simulator: a magnet pushed through a coil, flux and Lenz’s law.
- Magnetic Playground: magnets, field lines, the motor effect and induction for younger students.
- Induction Motor Simulator: induced rotor currents pushed round by a rotating field.
- Transformer Simulator: induction with nothing moving, from a changing flux in a shared core.
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