Force on a current-carrying conductor in a magnetic field
A moving charge in a magnetic field feels a force. A current is just many moving charges, so a wire carrying current inside a magnetic field is pushed. This push is the magnetic force on a conductor.
What decides how big the force is?
- Current (I): more current, more force.
- Field strength (B): a stronger magnet gives more force.
- Length of wire in the field (L): longer wire, more force.
- Angle θ between wire and field: force is largest at 90° (perpendicular) and becomes zero when the wire is parallel to the field (0° or 180°).
In short, F ∝ I · B · L · sin θ. (At Class 10 you need the ideas; the formula F = BIL sin θ is used in higher classes.)
Which way is the push? Fleming's left-hand rule
Stretch the thumb, first finger and middle finger of your left hand so they are at right angles to one another. Point the first finger along the field (N to S) and the middle finger along the current. The thumb then shows the direction of the force (motion) on the conductor. Reverse either the current or the field and the force reverses; reverse both and it stays the same.
Electric motor (formative only in 2026-27)
Note: for CBSE 2026-27, the motor, electromagnetic induction and generator are assessed only formatively (class tests, activities), not in the board exam. Learn them anyway: they explain every fan and power station.
An electric motor changes electrical energy into mechanical energy. Its parts:
- Armature coil: a rectangular coil of insulated copper wire, often wound on a soft iron core, placed between the poles of a magnet.
- Split ring commutator: a ring cut into two halves joined to the ends of the coil. It turns with the coil.
- Brushes: two carbon or metal strips that press on the split ring and bring current from the battery.
How it works
Current flows one way in one long side of the coil and the opposite way in the other side, so by the left-hand rule one side is pushed up and the other down. The coil turns. After half a turn, the halves of the split ring swap brushes, the current in the coil reverses, and the forces again push the coil the same way round. So the coil keeps rotating in one direction. Commercial motors use electromagnets, many turns of wire and a soft iron core to make them stronger.
Electromagnetic induction and the generator
Michael Faraday found the reverse effect: a changing magnetic field through a coil makes a current in it. This is electromagnetic induction, and the current is called induced current.
- Push a magnet into a coil joined to a galvanometer: the needle swings (deflects).
- Pull it out: the needle swings the other way.
- Hold it still: no deflection, because the field is not changing.
- Move faster, use a stronger magnet or more turns: bigger deflection.
Fleming's right-hand rule
For a conductor moving in a field, stretch thumb, first finger and middle finger of the right hand at right angles. First finger = field, thumb = motion of conductor, middle finger = direction of induced current.
Electric generator
A generator changes mechanical energy into electrical energy. A coil is rotated between magnet poles; each side cuts the field and a current is induced. With slip rings the current reverses every half turn, giving AC (an AC generator). With a split ring commutator the output always flows one way, giving DC (a DC generator).
AC vs DC
Direct current (DC) always flows in one direction. Cells, batteries and solar panels give DC.
Alternating current (AC) reverses its direction again and again at regular intervals. In India the home supply is AC at about 220 V and 50 Hz: it changes direction 100 times each second (twice in every cycle).
| AC | DC |
|---|---|
| Direction reverses periodically | One direction only |
| From AC generators at power stations | From cells, batteries, DC generators |
| Can be sent over long distances with small energy loss (voltage changed by transformers) | Hard to step up or down easily; used in electronics |
Key formulas and definitions
- F ∝ I · B · L · sin θ (force on a conductor; F = BIL sin θ in higher classes)
- θ = 90° → maximum force; θ = 0° or 180° → zero force
- Fleming's left-hand rule (motor): First finger = Field, Middle finger = Current, Thumb = Force
- Fleming's right-hand rule (generator): First finger = Field, Thumb = Motion, Middle finger = Induced current
- Motor: electrical → mechanical energy; Generator: mechanical → electrical energy
- Indian mains: AC, 220 V, 50 Hz → direction reverses 100 times per second
Worked examples
1. A wire runs east to west (current towards west) in a magnetic field pointing vertically downward. Which way is the force?
First finger down (field), middle finger west (current). The left-hand thumb then points south. So the force is towards the south.
2. A current-carrying wire is placed parallel to the magnetic field lines. What force acts on it?
The angle between wire and field is 0°, so sin θ = 0 and the force is zero. The wire is not pushed at all.
3. In a rod-on-rails experiment the rod moves to the left. What happens if (a) the current is reversed, (b) both current and field are reversed?
(a) Reversing one of them reverses the force, so the rod moves right. (b) Reversing both gives two reversals, which cancel, so the rod still moves left.
4. The AC supply in India is 50 Hz. How many times does the current change direction in one second?
Each cycle has two reversals. 50 cycles × 2 = 100 reversals per second.
5. Why does a motor need a split ring commutator?
Without it, after half a turn the forces on the coil sides would push the coil back, and it would just rock. The split ring reverses the current in the coil every half turn, so the torque always acts the same way and the coil keeps turning.
Common mistakes
- Using the right hand for the force on a conductor. Force (motor effect) = LEFT hand; induced current (generator) = RIGHT hand.
- Thinking a still magnet inside a coil makes current. Only a CHANGING field (relative motion) induces current.
- Believing the force is the same at every angle. It is biggest at 90° and zero when the wire is parallel to the field.
- Mixing up the rings: a DC motor and DC generator use a split ring commutator; an AC generator uses slip rings.