The full, readable lecture — the magnetic field and its lines, the field wrapped around a current-carrying wire, the solenoid that becomes an electromagnet, the force a field exerts on a current (the motor effect) and on a moving charge, the torque that spins a current loop, the galvanometer that reads tiny currents, and where it all ends up: motors, loudspeakers and the MRI scanner. As you scroll, the panel on the right plays out each idea with an everyday object you already know — iron filings, a compass, a coil of nails, a spinning motor.
1 — Magnetism & the magnetic field
A magnetic field is the region around a magnet (or a current) in which a magnetic force can be felt. We picture it with magnetic field lines — the path a tiny free north pole would follow. Scatter iron filings on a card over a bar magnet, tap it, and the filings line up exactly along these lines; a small compass needle placed anywhere swings to point along the field.
- Magnetic field (B) — the region where a magnetic force acts; a vector quantity with both strength and direction.
- Field lines — drawn from N to S outside the magnet (and S to N inside); their direction is the direction of B, their crowding shows where B is strong.
- Poles — every magnet has a north (N) and a south (S) pole. Like poles repel, unlike poles attract.
- Magnetic flux density (B) — the strength of the field. Unit: the tesla (T); 1 T = 1 N A⁻¹ m⁻¹.
Exam point: field lines never cross and form closed loops — there is no single magnetic pole on its own (no "magnetic monopole"). Break a magnet in two and each piece grows a fresh N and S.
2 — Magnetic field of a current-carrying wire
In 1820 Oersted noticed a compass needle deflect near a current-carrying wire: a current makes a magnetic field. Around a long straight wire the field lines are concentric circles centred on the wire. Their direction is given by the right-hand grip rule: grip the wire with the right hand, thumb pointing along the current, and the curled fingers show the way the field circles round.
Field of a long straight wireB = μ₀ I / (2π r)
μ₀ = 4π × 10⁻⁷ T m A⁻¹ · r = distance from the wire
- The field circles the wire; it is strongest close to the wire and weakens as 1/r.
- Double the current → double B; double the distance → halve B.
- Reverse the current and every compass flips — the field reverses too.
Right-hand grip rule: thumb = current, curled fingers = field direction. (For conventional current, which flows from + to −.)
3 — Field of a solenoid / electromagnet
Wind a wire into a long coil — a solenoid — and the circular fields of all the turns add together. Inside it the field is strong, straight and uniform; outside it looks just like a bar magnet, with a north pole at one end and a south at the other. Put a soft-iron core inside and you have an electromagnet that switches on and off with the current and can lift a chain of iron nails.
Field inside a long solenoidB = μ₀ n I (n = turns per metre)
Uniform along the axis, independent of position inside
- More turns per metre (n), or more current (I) → stronger field.
- A soft-iron core multiplies the field hundreds of times (high permeability).
- Which end is N? Use the right-hand grip rule on the coil, or read the current direction at the end.
Why soft iron? Soft iron magnetises strongly but loses it the instant the current stops — perfect for a switchable electromagnet (scrapyard cranes, relays, doorbells). Steel would stay magnetised.
4 — Force on a current-carrying conductor
If a current already makes its own field, and it sits in another magnet's field, the two fields push on each other: the wire feels a force. Lay a wire between the poles of a horseshoe magnet, switch the current on, and the wire kicks sideways out of the gap. This is the motor effect — the force at the heart of every electric motor.
Force on a current in a fieldF = B I L sin θ
θ = angle between the current and B · max when θ = 90°, zero when θ = 0°
Fleming's left-hand rule gives the direction. Hold the thumb, first and second fingers of the left hand at right angles:
| Finger | Points along |
|---|
| First finger | Field (B), N → S |
| seCond finger | Current (I) |
| thuMb | Motion (force F) |
Exam point: the force is greatest when the wire is at 90° to the field and zero when the wire lies along the field (sin 0° = 0). Reverse either the current or the field and the force reverses.
5 — Force on a moving charge
A current is just moving charge, so a single moving charge in a magnetic field feels a force too. The force is always at right angles to the velocity, so it never changes the speed — it only bends the path. A charged bead fired across a field therefore curves round into a circle.
Force on a moving chargeF = q v B sin θ (maximum when v ⊥ B)
Circular path: q v B = m v² / r ⟹ r = m v / (q B)
- Force is perpendicular to v, so it does no work — speed and kinetic energy stay constant.
- The path is a circle (or a helix if v has a component along B) of radius r = mv/qB.
- A charge moving parallel to B feels no force (sin 0° = 0).
- Fleming's left-hand rule works here too — but for a negative charge, take the current opposite to its motion.
Real life: this is how a mass spectrometer sorts ions, how an old TV tube steered its electron beam, and how the Sun's particles spiral round Earth's field to light up the auroras.
6 — Torque on a current loop
Place a rectangular current loop in a field. By the motor effect, one side is pushed up and the opposite side down — equal and opposite forces a distance apart, which is a couple. That couple produces a torque that twists the coil round. Add a split-ring commutator to flip the current every half-turn and the coil keeps spinning the same way: a DC motor.
Torque on a current loopτ = B I A N sin α
A = area of the loop · N = number of turns · α = angle between the coil plane's normal and B
- Torque is maximum when the coil plane is parallel to the field and zero when it is perpendicular.
- More turns N, more current I, larger area A, stronger field B → larger torque.
- The commutator reverses the current twice per turn to keep the rotation continuous.
Exam point: the loop tends to rotate until its plane is at right angles to B (the position of zero torque) — the commutator's job is to never let it settle there.
7 — The moving-coil galvanometer
A moving-coil galvanometer turns a tiny current into a readable needle deflection. A coil hangs in the field of a curved (radial) magnet so that the field is always parallel to the coil's plane — then the torque (BIAN) is steady for any position. The coil turns against a hairspring until the spring's restoring torque balances the magnetic torque, and the needle settles at a steady angle.
At balanceB I A N = k θ ⟹ θ ∝ I
k = torsion constant of the spring · θ = deflection
- The deflection θ is directly proportional to the current I — so the scale is linear and even.
- The radial field (from concave pole faces + a soft-iron cylinder) keeps the torque constant.
- A galvanometer becomes an ammeter with a small parallel "shunt" resistor, or a voltmeter with a large series resistor.
Why the radial field? Without it the torque would vary as sin α and the scale would be cramped at the ends. The radial field makes sin α = 1 always, giving an evenly-spaced scale.
8 — Applications & recap
Every idea in this chapter is the same physics — a current and a field push on each other — reused in the machines around you:
- Electric motor — torque on a current loop spins a shaft (fans, drills, electric cars).
- Loudspeaker — a coil carrying the audio current sits in a magnet's field; F = BIL pushes the cone in and out, making sound.
- MRI scanner — a giant superconducting solenoid makes a powerful, uniform field (several teslas) that lines up the protons in your body to image it.
- Galvanometer / meters — current → deflection, the basis of analogue ammeters and voltmeters.
force on a wire
A 0.20 m wire carries 4.0 A at 90° to a 0.50 T field. Find the force.
F = B I L sin θ = 0.50 × 4.0 × 0.20 × sin 90°
F = 0.40 N
moving charge in a field
A proton (q = 1.6 × 10⁻¹⁹ C) moves at 2.0 × 10⁶ m/s across a 0.30 T field. Find the force.
F = q v B = 1.6 × 10⁻¹⁹ × 2.0 × 10⁶ × 0.30
F = 9.6 × 10⁻¹⁴ N — perpendicular to v, so the proton circles.
- Field lines: N → S outside, never cross, closed loops; B in teslas.
- Straight wire: B = μ₀I/2πr, circles by the right-hand grip rule.
- Solenoid: B = μ₀nI; acts like a bar magnet → the electromagnet.
- Force on a current: F = BIL sinθ; direction by Fleming's left hand (the motor effect).
- Force on a charge: F = qvB, perpendicular to v → circular path, r = mv/qB.
- Loop: τ = BIAN sinα → the DC motor; galvanometer: θ ∝ I.