Electromagnetism and Electromagnetic Induction
FoundationCurrent creates magnetic fields; a field pushes current-carrying conductors to drive motors; changing flux induces an e.m.f. for generators; transformers scale a.c. voltages by turns ratio, and high-voltage transmission cuts line losses.
- A current is surrounded by a magnetic field; a straight wire's field forms circles, directed by the right-hand grip rule
- A solenoid with a soft-iron core makes an electromagnet, stronger with more current, more turns and a good core, and vanishing when switched off
- The force on a current-carrying conductor is F = BIL, directed by Fleming's left-hand rule; a d.c. motor keeps turning via its commutator
文體小知識：科學知識說明文——依「電生磁、磁生力、磁生電」的脈絡講解電磁現象，並以變壓器與高壓輸電收結。
§Text Passage
1Electricity and magnetism were long thought to be unrelated — until the Danish scientist Oersted noticed during a lecture demonstration that a compass needle near a current-carrying wire deflects. Current produces a magnetic field. The field of a straight wire forms concentric circles, its direction given by the right-hand grip rule: point the right thumb along the current and the curled fingers show the field. This simple discovery formally opened the door to electromagnetism.
2Wind the wire into a solenoid and the fields of all the turns add up, giving a pattern like a bar magnet with a north and a south pole that swap when the current reverses. Insert a soft-iron core and the field is greatly strengthened: an electromagnet. The larger the current and the more turns, the stronger the magnet, and it demagnetises almost completely when switched off. Electromagnets are everywhere — door bells, scrap-yard lifting magnets and maglev trains all rely on them, among the earliest practical fruits of combining electricity and magnetism.
3Conversely, a magnetic field exerts a force on a current-carrying conductor. When the conductor is perpendicular to the field, the force equals the product of field strength, current and wire length, its direction given by Fleming's left-hand rule: the first finger along the field, the second along the current, the thumb along the force. Place a coil in a field and switch on the current: opposite sides feel opposite forces and the coil turns — the principle of the electric motor, with a commutator reversing the current every half-turn to keep it spinning.
4In 1831 Faraday discovered that whenever the magnetic flux through a circuit changes, an induced e.m.f. appears — electromagnetic induction. A conductor cutting field lines, or a field changing in strength, both count as changing flux; the direction of the induced current follows Lenz's law, always opposing the change in flux. Generators exploit exactly this: a coil spinning in a field converts mechanical energy into electrical energy, the beating heart of the modern energy supply.
5A transformer steps a.c. voltages up or down at will: primary and secondary coils share one iron core, and the voltage ratio equals the turns ratio. It works only with alternating current, because a steady direct current gives an unchanging flux and no induced e.m.f. in the secondary. For long-distance transmission the voltage is first stepped up, the current falls, and the heating loss in the cables drops with the square of the current; near users the voltage is stepped back down in stages, ending at the safe 220 V of our homes — completing the journey of electric power.
1Summary 重點摘要
Current creates magnetic fields; a field pushes current-carrying conductors to drive motors; changing flux induces an e.m.f. for generators; transformers scale a.c. voltages by turns ratio, and high-voltage transmission cuts line losses.
2Vocabulary cards Vocabulary
The region around a magnet or current where magnetic forces act, represented by field lines running from the north pole to the south pole.
The phenomenon that a current produces a magnetic field around it, first discovered by Oersted.
The rule for finding the field direction around a current: the thumb points along the current and the curled fingers give the field direction.
A coil wound into a cylinder; when current flows, its field resembles that of a bar magnet.
A solenoid with a soft-iron core; its magnetism grows with current and turns, and disappears almost entirely when switched off.
The rule for the force on a current-carrying conductor in a field: first finger along the field, second along the current, thumb along the force.
The phenomenon, discovered by Faraday, that a changing magnetic flux through a circuit induces an e.m.f.
The e.m.f. produced in a circuit by a changing magnetic flux; an induced current flows only when the circuit is closed.
The induced current always opposes the change in flux that produces it — a consequence of energy conservation.
A device that changes a.c. voltages by electromagnetic induction, Vs/Vp = Ns/Np; it works only with alternating current.
3Step by step Steps
- Step 1: The magnetic effect of current and the right-hand grip ruleOersted found that a current-carrying wire deflects a nearby compass, proving that a current is surrounded by a magnetic field. The field lines of a straight wire are concentric circles centred on the wire, sparser further away; the direction follows the right-hand grip rule — thumb along the current, curled fingers along the field. For example, sprinkle iron filings on a horizontal card with a vertical wire through it; switch on the current and tap the card, and the filings line up in circles, revealing the field pattern. To find field directions, confirm the current direction first, then apply the rule — MC questions love converting between top and side views.
- Step 2: Solenoids and electromagnetsWinding the wire into a solenoid adds the fields of all turns: outside, the field resembles a bar magnet; inside, it is strong and uniform. Grip the solenoid with the right hand, fingers along the current, and the thumb points to the north pole. Add a soft-iron core and the field strengthens enormously — an electromagnet: larger current, more turns and a more easily magnetised core all increase the magnetism. For example, a scrap-yard electromagnet lifts tonnes of iron when switched on and drops them at a flick of the switch; door bells, relays and loudspeakers all contain electromagnets, showing how deeply this invention penetrates daily life.
- Step 3: The force on a current-carrying conductorA current-carrying conductor in a magnetic field experiences a force, largest when perpendicular to the field: F = BIL, where B is the field strength, I the current and L the length of wire in the field. The direction follows Fleming's left-hand rule: left-hand first finger along the field (north to south), second finger along the current, thumb along the force. For example, the voice coil of a loudspeaker carries a current that varies with the sound, vibrating back and forth in the field and driving the cone to produce sound. The three directions are mutually perpendicular; drawing a 3-D sketch with direction symbols is a scoring detail.
- Step 4: How a d.c. motor worksPlace a rectangular coil in a field and pass a current: the two sides carry currents in opposite directions, feel opposite forces, and the couple turns the coil. After half a turn the forces would reverse and swing it back, so a commutator (brushes and split rings) reverses the current in the coil every half-turn, keeping the torque in one direction and the rotation continuous. For example, the little motors in desk fans, toy cars and curtains are d.c. motors; open one up and you find the coil, the magnets and the commutator. Exams often ask the role of the commutator — answer 'it reverses the current so the torque keeps one direction'.
- Step 5: Electromagnetic induction and Lenz's lawFaraday discovered that when the magnetic flux through a circuit changes, an induced e.m.f. appears; a current flows only if the circuit is closed. A conductor cutting field lines, a magnet pushed into or pulled out of a coil, or a field changing in strength — all are flux changes, and the faster the change, the larger the induced e.m.f. The direction follows Lenz's law: the induced current always opposes the change producing it. For example, plunge a bar magnet quickly into a coil and the galvanometer swings sharply one way; withdrawing it swings the other way, and the faster the motion the larger the deflection — this experiment appears in practical questions almost every year. Fleming's right-hand rule gives the induced current direction for a wire cutting field lines.
- Step 6: Generators — mechanical energy into electricalA generator is structurally similar to a motor but reverses the energy conversion: an external force spins the coil in the field, the flux keeps changing, an induced e.m.f. drives the current, and mechanical energy becomes electrical. Slip rings output a.c.; a commutator outputs d.c. For example, a bicycle dynamo — a small a.c. generator — spins a magnet as the wheel turns: pedal faster and the lamp glows brighter, a perfect illustration that a faster change of flux gives a larger induced e.m.f. Power-station generators driven by water or steam turbines work on exactly the same principle, only vastly larger.
- Step 7: Transformers and high-voltage transmissionA transformer consists of primary and secondary coils wound on a shared soft-iron core: a.c. in the primary keeps the core's flux changing, inducing an e.m.f. in the secondary, with Vs/Vp = Ns/Np — the voltage ratio equals the turns ratio. It works only on alternating current; a steady direct current gives an unchanging flux and no output. For example, power stations step the voltage up to hundreds of thousands of volts for transmission: the cable current drops and the heating loss P = I²R falls with its square; near cities the voltage is stepped back down to the 220 V of our homes. Long questions often give turns and ask for the output voltage, or the reason for high-voltage transmission — write both the formula and the reason.
4Diagrams Diagrams
5Worked example Example
Example: an ideal transformer steps 220 V mains down to 11 V for a door bell. The secondary coil has 50 turns. Find (a) the number of turns in the primary coil; (b) the turns ratio of primary to secondary; (c) briefly explain why this transformer cannot be connected to a d.c. supply.
- Write the transformer equation: Vs/Vp = Ns/Np
- Substitute: 11 ÷ 220 = 50 ÷ Np, so Np = 50 × 220 ÷ 11 = 1000 turns
- Turns ratio Np : Ns = 1000 : 50 = 20 : 1; the secondary voltage is lower, so it is a step-down transformer
- Part (c): with a steady direct current the flux does not change with time, so no e.m.f. is induced in the secondary; since a transformer works by changing flux, it must be used with a.c.
- Answer: (a) The primary has 1000 turns. (b) The turns ratio is 20 : 1. (c) A direct current gives an unchanging flux, so no e.m.f. is induced in the secondary and the transformer fails — a.c. is required. Full-mark format: formula, substitution, answer, explanation.
6Common mistakes Mistakes
7Quick check Quick check
Q1How is the right-hand grip rule used?
Q2What do the three fingers represent in Fleming's left-hand rule?
Q3A transformer's primary coil has 500 turns and is connected to 220 V. How many turns must the secondary have to output 22 V?
Q4Why is electricity transmitted over long distances at high voltage?
Q5What is the difference between a generator and a motor?
8Recap Recap
- A current is surrounded by a magnetic field; a straight wire's field forms circles, directed by the right-hand grip rule
- A solenoid with a soft-iron core makes an electromagnet, stronger with more current, more turns and a good core, and vanishing when switched off
- The force on a current-carrying conductor is F = BIL, directed by Fleming's left-hand rule; a d.c. motor keeps turning via its commutator
- A changing magnetic flux induces an e.m.f. (electromagnetic induction), its direction given by Lenz's law; generators convert mechanical energy to electrical this way
- Transformers obey Vs/Vp = Ns/Np and work only on a.c.; high-voltage transmission cuts I²R line losses with a smaller current