When a current-carrying conductor sits inside a magnetic field, a force acts on it. Fleming's left-hand rule lets you predict the direction of that force: align your left hand so your First finger points with the Field and your seCond finger points with the Current — your thuMb then points in the direction of Motion.
Why does a current-carrying conductor experience a force?
A wire carrying an electric current has a magnetic field around it (this is the basis of electromagnets). When a current-carrying wire is placed inside an external magnetic field, the two magnetic fields interact: they add in some regions and cancel in others. This produces a non-uniform resultant field that exerts a net force on the wire — the motor effect.
The force exists because moving charges (the current) experience a force when they move through a magnetic field. This is the fundamental electromagnetic interaction described by the Lorentz force law.
The force on a current-carrying conductor is:
- Perpendicular to both the current direction and the magnetic field direction
- Zero when the conductor runs parallel to the magnetic field (the two fields do not interact)
- Maximum when the conductor runs at right angles to the magnetic field
How do you use Fleming's left-hand rule?
Fleming's left-hand rule gives the direction of the force (motion) on a conductor for a given current direction and field direction. Here is how to apply it:
- Hold your left hand out with your thumb and first two fingers at right angles to each other.
- Point your First finger (index finger) in the direction of the magnetic Field (from north to south pole, i.e. the direction of the field lines).
- Point your seCond finger (middle finger) in the direction of the conventional Current (from positive to negative, i.e. the direction positive charges would flow).
- Your thuMb then points in the direction of the Motion (the direction of the force on the conductor).
Memory aid: First = Field, Centre = Current, thuMb = Motion.
| Finger | Represents | Direction |
|---|---|---|
| First (index) | Magnetic Field | North → South (direction of B) |
| Second (middle) | Conventional Current | Positive terminal → negative terminal |
| Thumb | Motion / force | Direction the conductor moves |
Important: conventional current flows from positive to negative (opposite to electron flow). If a question gives you electron flow, reverse it to get conventional current before applying the rule.
How do you calculate the force on a conductor?
The magnitude of the force can be calculated using:
F = B I L
Where:
- F = force on the conductor (newtons, N)
- B = magnetic flux density (tesla, T) — the strength of the magnetic field
- I = current (amperes, A)
- L = length of conductor inside the magnetic field (metres, m)
This equation is only valid when the conductor is perpendicular to the magnetic field (the most common case in GCSE problems). If the conductor is at an angle θ to the field, F = BIL sin θ — but this extension is beyond standard GCSE.
Worked example:
A wire of length 0.25 m carries a current of 3.0 A. It is placed at right angles to a magnetic field of flux density 0.40 T. Calculate the force on the wire.
F = B × I × L = 0.40 × 3.0 × 0.25 = 0.30 N
How does a simple DC electric motor work?
A direct current (DC) electric motor uses the motor effect to convert electrical energy into rotational kinetic energy. The key components are:
- Rectangular coil of wire — carries the current and sits in the magnetic field
- Permanent magnet — provides the external magnetic field (B)
- Commutator (split-ring commutator) — reverses the direction of current through the coil every half-turn
- Brushes — maintain electrical contact between the fixed power supply and the rotating commutator
How it works:
- Current flows through the coil. Using Fleming's left-hand rule, the two sides of the coil (which carry current in opposite directions) experience forces in opposite directions — one side is pushed up and the other is pushed down.
- This creates a torque (turning effect) that rotates the coil.
- After half a turn, if the current direction stayed the same, the forces would now oppose the rotation (trying to push it back). The split-ring commutator automatically reverses the current direction every half-turn, so the forces always act to keep the coil rotating in the same direction.
- The brushes rub against the commutator, maintaining the electrical connection as it rotates.
What factors affect the force on a conductor?
From F = BIL, three factors directly control the force:
| Factor | Change | Effect on force |
|---|---|---|
| Magnetic flux density (B) | Increase (stronger magnet) | Force increases proportionally |
| Current (I) | Increase (higher voltage, lower resistance) | Force increases proportionally |
| Length (L) | Increase (longer conductor in field) | Force increases proportionally |
| Angle to field | Move from 90° to 0° (parallel to field) | Force decreases to zero |
To make a more powerful DC motor, use a stronger magnet, carry a higher current, and use more turns of wire (increasing the effective length).
Frequently asked questions
Why must you use your LEFT hand for the motor effect?
The left hand is used for the motor effect (a current-carrying conductor in a magnetic field, converting electrical energy to mechanical energy). The right hand would be used for generators (Fleming's right-hand rule — a conductor moving in a magnetic field induces a current, converting mechanical energy to electrical energy). The choice of hand reflects the physics: left-hand rule → motor → left hand for current in, right-hand rule → generator → right hand for current out. If you mix them up in an exam, you will predict the force or induced current in the wrong direction.
What is the difference between magnetic field strength and magnetic flux density?
Magnetic flux density (B) is the specific quantity used in F = BIL. It measures how many magnetic field lines pass through a given area — a strong field that is spread over a large area may have the same total flux as a weaker field concentrated into a small area. The units of B are teslas (T). A stronger permanent magnet or a larger current in an electromagnet increases B. At GCSE, the term "field strength" is often used loosely to mean B, but the formal SI quantity is magnetic flux density.
What happens to the force on the wire if it is parallel to the magnetic field?
If the conductor runs parallel to the magnetic field (F, B, and I are all in the same direction or the conductor is aligned along B), the cross-product of the velocity of charge carriers and the field direction is zero — there is no perpendicular component of force. Practically: the two magnetic fields (from the wire and the external magnet) run parallel and neither add nor cancel in a way that produces a net sideways force. The force on the conductor is exactly zero. This is why commutators in motors reverse the current at exactly the moment the coil passes through the position where it is parallel to the field (the "dead point").
How does increasing the number of coil turns improve a motor?
Each turn of wire in the coil is a separate conductor sitting in the magnetic field. The force F = BIL acts on each turn independently. With N turns, the total force contributing to the torque is N × BIL × (relevant geometry factor). More turns = greater total force = greater torque = more powerful rotation. Practical DC motors use many hundreds of turns of wire wound on a soft-iron core (the armature), and often use multiple coil sets offset at different angles so the torque is smoother and there is no dead point at any angle.
For predict-first GCSE physics with Professor Newton — predicting the direction of force before doing the calculation — visit aitutors.me.