§ 20.1 Concept of a magnetic field
Key ideas
- A magnetic field is produced by moving charges (currents) and by permanent magnets.
- Field lines run from N to S outside a magnet, never cross, and are closest where the field is strongest.
Watch out: a magnetic force acts only on a moving charge (or a current). A charge sitting still in a magnetic field feels no magnetic force at all.
§ 20.2 Force on a current-carrying conductor
Key ideas
- A current in a magnetic field feels a force F = BIL sin θ, greatest when the conductor is perpendicular to the field.
- Fleming's left-hand rule gives the direction: thumb = force (motion), first finger = field, second finger = current.
- This defines the magnetic flux density B (the tesla): the force per unit current per unit length on a perpendicular conductor.
Equations
F = B I L sin θforce on a current in a field; θ from the fieldN
Fig. 1 · The motor effect: with the field B running N to S and current I out of the page, Fleming's left-hand rule puts the force F upwards.
Watch out: θ is the angle between the conductor and the field. A wire parallel to the field (θ = 0) feels no force; the force is maximum when it is perpendicular (θ = 90°).
§ 20.3 Force on a moving charge
Key ideas
- A charge moving across a field feels F = BQv sin θ, perpendicular to its velocity, so it travels in a circle at constant speed.
- The Hall voltage appears across a current-carrying slab in a field; a Hall probe uses it to measure flux density.
- A velocity selector uses crossed E and B fields so only charges with v = E/B pass straight through.
Equations
F = B Q v sin θforce on a charge moving through a fieldN
V_H = B I / (n t q)Hall voltage across a slab of thickness tV
Watch out: the magnetic force is always perpendicular to the velocity, so it does no work and never changes the speed: it only bends the path. Kinetic energy stays constant in a pure magnetic field.
§ 20.4 Magnetic fields due to currents
Key ideas
- A straight wire is circled by concentric field lines; a flat coil and a solenoid give a field like a bar magnet's, uniform and strong inside the solenoid.
- A ferrous core greatly increases the flux density without changing the field's shape.
- Parallel currents in the same direction attract; in opposite directions they repel.
Fig. 2 · A solenoid's field: parallel and uniform along the inside, spreading into a bar-magnet pattern outside, with a north pole at the end the field lines leave.
Watch out: parallel currents in the same direction attract. This feels backwards next to charges (like charges repel), so do not carry the electrostatic intuition across.
§ 20.5 Electromagnetic induction
Key ideas
- Magnetic flux through a loop is Φ = BA (with B perpendicular to the area); flux linkage is NΦ for N turns.
- Faraday's law: the induced e.m.f. equals the rate of change of flux linkage.
- Lenz's law: the induced current opposes the change that causes it, which is energy conservation in action (hence the minus sign).
Equations
Φ = B Amagnetic flux through an areaWb
E = −d(NΦ)/dtFaraday's law with Lenz's minus signV
Fig. 3 · Lenz's law: as the magnet approaches, the coil's near face becomes a north pole to push back, so work is done against the motion and energy is conserved.
Watch out: it is the rate of change of flux linkage that induces an e.m.f., not the flux itself. A coil sitting still in a strong steady field, however large Φ, induces nothing.