磁与电磁

• Poles 磁极: where the magnetic force is strongest.

Like poles repel; unlike poles attract — a non-contact force.

• A permanent magnet 永磁体 produces its own field. An induced magnet 感磁体 becomes a magnet only while in a field — and induced magnetism always attracts (it loses its magnetism when removed).
• The magnetic field 磁场 is the region where a force acts on another magnet or magnetic material (iron, steel, cobalt, nickel). A magnet always attracts magnetic material.
• Field is strongest at the poles; direction = the force on a north pole at that point. Field lines run north → south.
• A compass is a small bar magnet; it points along the Earth's field — evidence the Earth has a magnetic field (its core behaves like a giant magnet).

Plotting a field: put a small plotting compass near the magnet, mark the needle's ends, move the compass so the tail sits on the last mark, repeat and join the dots. Iron filings show the whole pattern at once.

A current-carrying wire has a magnetic field around it (concentric circles; right hand grip — thumb with the current, fingers curl with the field). The field is stronger with more current and weaker further from the wire.

Bending the wire into a solenoid 螺线管:

• the fields of the loops add — the field inside is strong and uniform;
• outside, the shape matches a bar magnet's;
• adding an iron core increases the strength further — this is an electromagnet 电磁铁.

An electromagnet can be switched on and off and its strength changed with the current — that is why it beats a permanent magnet in scrapyards and relays.

A conductor carrying a current in a magnetic field feels a force (the motor effect — the field, the magnet and the conductor push on each other).

Fleming's left-hand rule: thumb = force, first finger = field (N→S), second finger = current — all three at right angles.

• $F$ force in N; $B$ magnetic flux density 磁感应强度 in tesla, T; $I$ current in A; $l$ length of conductor in the field, in m.
• Bigger force with: stronger field (larger $B$), larger current, longer conductor in the field. Maximum force when the conductor is at right angles to the field.

Electric motor: a current-carrying coil in a field rotates because the two sides feel forces in opposite directions.

A split-ring commutator reverses the current each half-turn so rotation continues.

Loudspeaker (physics only): an alternating current through a coil in a field makes the coil vibrate in and out; the cone pushes the air into pressure variations — sound waves whose frequency matches the signal's.

A transformer 变压器: primary and secondary coils wound on an iron core (easily magnetised; laminations not required).

An alternating current in the primary makes a changing magnetic field in the core; that changing field induces an alternating pd in the secondary.

• Step-up: $V_s > V_p$ (more secondary turns). Step-down: $V_s < V_p$.
• The second equation is power in = power out; use it to find the current drawn from the input supply.

Worked example. A transformer has 345 primary turns and 6000 secondary; the input is 230 V.

Worked example (power). That transformer supplies 50 mA at 4000 V.

• Power out: $P = V_sI_s = 4000 \times 0.050 = 200$ W.
• Input current: $I_p = P/V_p = 200/230 = 0.87$ A.

The National Grid story closes the loop: step-up before transmission (smaller current → $P = I^2R$ losses collapse), step-down for homes (see topic 2.7).