IGCSE Physics · Unit 4: Electricity and Magnetism · Part 1 of 2 · Core + Extended

Electricity and Magnetism I: Magnetism & Electrical Quantities CoreExtended adds equations for I, E, V and I-V graphs

This is Part 1 of a two-part note on Electricity and Magnetism — the largest section in the syllabus. This part covers simple magnetism (poles, fields, magnetic materials) and the core electrical quantities: charge, current, e.m.f./p.d., resistance, and electrical energy and power. Part 2 covers circuits, safety, and electromagnetic effects.

Why this matters Every equation in this note — I = Q/t, V = W/Q, R = V/I, P = IV — describes a different “cost” of moving charge around a circuit. Once you see current as a flow of charge, and voltage as the energy carried per unit of that charge, most of circuit theory becomes bookkeeping rather than a pile of separate formulas.

1. Simple Phenomena of Magnetism

Every magnet has a north pole (N) and a south pole (S). Like poles repel; unlike poles attract. A magnet also attracts unmagnetised magnetic materials (like iron, nickel, cobalt), through a process called induced magnetism — the material temporarily becomes a magnet itself while in the field, which is why it’s attracted rather than repelled.

Temporary magnets (soft iron)Permanent magnets (steel)
magnetise and demagnetise easilyharder to magnetise, but keep their magnetism
used in electromagnetsused where a constant magnetic field is needed (e.g. compasses)

Magnetic materials (iron, nickel, cobalt, and their alloys) can be attracted by a magnet; non-magnetic materials (e.g. wood, plastic, copper, aluminium) are not.

Magnetic Fields

A magnetic field is a region in which a magnetic pole experiences a force. The direction of a field at any point is defined as the direction of the force on a north pole placed at that point. Field lines around a bar magnet always point from north to south outside the magnet, and are drawn closer together where the field is stronger (near the poles) — Extended: field line spacing represents relative field strength.

Plotting a magnetic field Field lines can be plotted either with iron filings (sprinkled on paper over a magnet; they line up along the field lines) or with a small plotting compass (moved step by step, marking the direction the needle points at each position, then joining the marks into a smooth line). A compass placed near a magnet points in the direction of the magnetic field at that point.
Uses of magnets Extended: forces from interacting fields Permanent magnets are used in compasses, fridge door seals, and loudspeakers. Electromagnets (temporary magnets, switched on/off with a current) are used in electric bells, relays, scrapyard cranes for lifting steel, and MRI scanners — anywhere a magnetic field needs to be turned on or off, or varied in strength. Extended: two magnetic fields close together (e.g. from two magnets, or a magnet and a current-carrying wire) interact with each other, and it is this interaction between the fields that produces the force felt as attraction or repulsion.
Try it — Magnetism
  1. Two bar magnets are brought close together, north pole to north pole. State what happens, and explain why.
  2. Explain why a paperclip is attracted to both poles of a magnet, even though the paperclip itself isn’t a permanent magnet.
  3. Explain why soft iron, rather than steel, is used in the core of an electromagnet.
Show answers
  1. The magnets repel each other, since like poles (north and north) always repel.
  2. The paperclip is made of a magnetic material. In the presence of the magnet’s field, it becomes an induced (temporary) magnet itself, with its near pole always induced to be opposite to the pole of the magnet it’s near — meaning it is always attracted, regardless of which pole of the permanent magnet is brought close.
  3. Soft iron magnetises and demagnetises very easily, meaning the electromagnet’s field can be switched on and off almost instantly (whenever the current is turned on/off). Steel would retain magnetism even when the current is switched off, so it isn’t suitable where the field needs to be turned off completely.

2. Electric Charge

Charge exists in two types: positive and negative. Like charges repel; unlike charges attract. Rubbing certain insulating materials together (e.g. a balloon on hair) can build up static electricity through friction — this charging process always involves only the transfer of negative charge (electrons) from one material to the other; the material that gains electrons becomes negatively charged, and the one that loses them becomes positively charged.

Conductors and insulators An electrical conductor (e.g. metals) allows charge to flow through it easily, because it contains many free (delocalised) electrons that are not bound to individual atoms and can move throughout the material. An insulator (e.g. plastic, rubber, glass) has electrons tightly bound to their atoms, with none free to move, so charge cannot flow through it. This can be tested experimentally by connecting different materials into a simple circuit with a battery and a lamp — the lamp lights only if the material is a conductor.
Electric fields Extended Charge is measured in coulombs (C). An electric field is a region in which an electric charge experiences a force; its direction at a point is defined as the direction of the force on a positive charge placed there. Standard field patterns: field lines point radially outward from a positive point charge (or a positively charged conducting sphere); field lines run straight and parallel, evenly spaced, between two oppositely charged parallel plates (from the positive plate to the negative plate).
Try it — Charge
  1. A plastic rod is rubbed with a cloth and becomes negatively charged. Explain, in terms of particles, how this charge was produced.
  2. Explain, using the idea of free electrons, why copper is a good electrical conductor but rubber is not.
  3. State the direction of an electric field at a point, in terms of the force on a charge placed there.
Show answers
  1. Friction between the rod and the cloth causes electrons to be transferred from the cloth onto the rod. Since the rod gains extra (negative) electrons, it becomes negatively charged overall, while the cloth becomes positively charged.
  2. Copper contains many free (delocalised) electrons that are not bound to individual atoms and can move freely through the material, allowing charge (current) to flow easily. Rubber’s electrons are all tightly bound to their atoms, with none free to move, so charge cannot flow through it.
  3. The direction of the field at a point is the direction of the force that would act on a positive charge placed at that point.

3. Electric Current

Electric current is related to the flow of charge, and is measured using an ammeter (connected in series, in the circuit itself). Electrical conduction in metals is due to the movement of free electrons through the metal.

I = Q / t Extended

Direct current (d.c.) flows in one direction only (e.g. from a battery); alternating current (a.c.) regularly reverses direction (e.g. mains electricity).

Extended: by convention, conventional current is defined as flowing from positive to negative around a circuit, even though the actual charge carriers in a wire (free electrons) flow from negative to positive — this is a historical convention that predates the discovery of the electron.

Worked example — I = Q/t A charge of 12 C flows past a point in a circuit in 4 s. Find the current.
I = Q / t = 12 / 4 = 3 A
Worked example — rearranging for charge A current of 0.5 A flows for 20 s. Find the total charge that has flowed.
Q = I × t = 0.5 × 20 = 10 C
Try it — Current
  1. A charge of 30 C passes a point in a circuit in 5 s. Calculate the current.
  2. A current of 2 A flows through a component for 3 minutes. Calculate the charge that flows.
  3. State the direction conventional current is defined to flow, and explain how this compares to the actual direction of electron flow in a metal wire.
Show answers
  1. I = Q/t = 30/5 = 6 A
  2. t = 3 minutes = 180 s. Q = I × t = 2 × 180 = 360 C
  3. Conventional current is defined to flow from positive to negative around a circuit. This is opposite to the actual direction electrons move in a metal wire, which is from negative to positive — conventional current direction is a historical convention, not the true direction of electron travel.

4. Electromotive Force and Potential Difference

Electromotive force (e.m.f.) is the electrical work done by a source (like a battery) in moving a unit charge around a complete circuit. Potential difference (p.d.), or voltage, is the work done by a unit charge passing through a single component. Both are measured in volts (V), using a voltmeter (connected in parallel across the component or source).

E = W / Q Extended
V = W / Q Extended
Worked example — potential difference 15 J of work is done moving 5 C of charge through a resistor. Find the potential difference across the resistor.
V = W / Q = 15 / 5 = 3 V
Worked example — e.m.f. A battery does 24 J of work moving 4 C of charge all the way around a complete circuit. Find its e.m.f.
E = W / Q = 24 / 4 = 6 V
Try it — E.m.f. and P.d.
  1. State the key difference between e.m.f. and potential difference.
  2. 10 C of charge passes through a lamp, and 25 J of work is done. Calculate the potential difference across the lamp.
  3. A cell has an e.m.f. of 1.5 V. Calculate the work done moving 6 C of charge around a complete circuit powered by this cell.
Show answers
  1. E.m.f. refers to the work done by the source moving charge around the WHOLE circuit, while p.d. refers to the work done as charge passes through just ONE component.
  2. V = W/Q = 25/10 = 2.5 V
  3. W = E × Q = 1.5 × 6 = 9 J

5. Resistance

R = V / I

Resistance, measured in ohms (Ω), can be found experimentally by connecting a component in a circuit with an ammeter (to measure current) and a voltmeter (to measure the p.d. across it), then applying R = V/I.

For a metallic wire: resistance is directly proportional to length (a longer wire has more resistance) and inversely proportional to cross-sectional area (a thicker wire has less resistance) — Extended: stated as formal proportionality relationships.

Worked example — calculating resistance A component has a potential difference of 12 V across it when a current of 3 A flows through it. Find its resistance.
R = V / I = 12 / 3 = 4 Ω
Current-voltage graphs Extended Resistor of constant resistance: a straight line through the origin — current is directly proportional to voltage (obeying R = V/I with a constant R).
Filament lamp: starts as a straight line, but curves and flattens (levels off) at higher currents — as the filament heats up, its resistance increases, so for each additional volt, current increases by progressively less.
Diode: allows almost no current to flow in the reverse direction (a flat line along the voltage axis), but once a small forward threshold voltage is exceeded, current rises steeply — a diode only conducts easily in one direction.
Try it — Resistance
  1. A resistor has a current of 0.4 A flowing through it when the p.d. across it is 8 V. Calculate its resistance.
  2. Two wires are made of the same material and have the same length, but one has twice the cross-sectional area of the other. State which wire has the greater resistance, and explain why.
  3. Describe how the shape of a filament lamp’s current-voltage graph differs from that of a resistor of constant resistance, and explain why.
Show answers
  1. R = V/I = 8/0.4 = 20 Ω
  2. The thinner wire (smaller cross-sectional area) has the greater resistance, since resistance is inversely proportional to cross-sectional area — a thinner wire offers a narrower path for charge to flow through, giving it more resistance.
  3. A constant-resistance resistor gives a straight line through the origin. A filament lamp’s graph starts similarly but curves and flattens at higher currents, because the filament heats up as more current flows, and its resistance increases with temperature — so equal increases in voltage produce smaller and smaller increases in current.

6. Electrical Energy and Power

An electric circuit transfers energy from a source (a cell, battery, or the mains supply) to the circuit’s components, and ultimately into the surroundings (often as heat and/or light).

P = IV
E = IVt

The kilowatt-hour (kWh) is a unit of energy (not power) commonly used for billing electricity usage: 1 kWh is the energy transferred by a 1 kW appliance running for 1 hour.

Worked example — electrical power A kettle draws a current of 10 A from a 230 V supply. Find its power.
P = IV = 10 × 230 = 2300 W (2.3 kW)
Worked example — energy transferred and cost A 2 kW heater runs for 3 hours. If electricity costs $0.20 per kWh, find the total energy used (in kWh) and the cost.
Energy = power × time = 2 kW × 3 h = 6 kWh
Cost = 6 × $0.20 = $1.20
Try it — Electrical Energy and Power
  1. A device draws a current of 5 A from a 12 V supply. Calculate its power.
  2. Calculate the energy transferred (in joules) by a 100 W lamp running for 60 s.
  3. A 3 kW oven runs for 2.5 hours. If electricity costs $0.25 per kWh, calculate the total cost of running the oven.
Show answers
  1. P = IV = 5 × 12 = 60 W
  2. E = IVt — or, since P = E/t, E = P × t = 100 × 60 = 6000 J
  3. Energy = 3 kW × 2.5 h = 7.5 kWh. Cost = 7.5 × $0.25 = $1.875 ≈ $1.88
Common mistakes to watch for
  • Mixing up e.m.f. (whole circuit) and p.d. (single component) — both are measured in volts, which makes them easy to confuse conceptually.
  • Forgetting to convert time into seconds for I = Q/t or E = IVt, or into hours when working with kWh.
  • Assuming a longer wire has less resistance — it’s the opposite: resistance is directly proportional to length.
  • Forgetting that conventional current direction (positive to negative) is the opposite of actual electron flow (negative to positive).
  • Believing a diode’s current-voltage graph is a straight line like a resistor’s — it only conducts easily above a threshold voltage, in one direction only.
  • Forgetting that kWh is a unit of energy, not power — don’t try to use it directly in P = IV.

7. Quick-Fire Challenge Round

True or False?
  1. Like magnetic poles attract each other.
  2. Charging by friction always involves the transfer of protons.
  3. Conventional current flows from negative to positive around a circuit.
  4. Resistance is inversely proportional to the cross-sectional area of a wire.
Show answers
  1. False — like poles repel; unlike poles attract.
  2. False — charging by friction only ever involves the transfer of electrons (negative charge); protons are fixed inside atomic nuclei and are not transferred.
  3. False — conventional current is defined to flow from positive to negative; it is the actual electrons that flow from negative to positive.
  4. True — a wire with a larger cross-sectional area has lower resistance, since it provides a wider path for current to flow through.
Spot the Error
  1. “A current of 4 A flows for 2 minutes, so the charge that flows is Q = 4 × 2 = 8 C.”
  2. “E.m.f. and potential difference are exactly the same thing and can be used interchangeably in any context.”
  3. “A wire is made twice as long, keeping the same material and cross-sectional area, so its resistance is halved.”
Show answers
  1. Time must be in seconds. 2 minutes = 120 s, so Q = I × t = 4 × 120 = 480 C, not 8 C.
  2. E.m.f. refers to work done by a source around the WHOLE circuit, while p.d. refers to work done across a single component — they describe different things, even though both are measured in volts.
  3. Resistance is directly proportional to length, so doubling the length DOUBLES the resistance, not halves it.

8. Mixed Practice — Bringing It All Together

  1. A charge of 18 C flows past a point in 6 s. Calculate the current.
  2. A resistor has 20 V across it when a current of 4 A flows. Calculate its resistance.
  3. A device draws 6 A from a 220 V supply. Calculate its power.
  4. Explain why a plastic comb, after being rubbed on a jumper, can pick up small pieces of paper.
  5. A 1.5 kW iron runs for 40 minutes. Calculate the energy transferred in kWh.
Show answers
  1. I = Q/t = 18/6 = 3 A
  2. R = V/I = 20/4 = 5 Ω
  3. P = IV = 6 × 220 = 1320 W
  4. Rubbing the comb on the jumper transfers electrons (charging it, typically negatively), giving the comb a net charge. This charged comb then induces an opposite charge on the surface of the paper nearest to it, resulting in an attractive force that lifts the small, light pieces of paper.
  5. Time = 40 minutes = 40/60 h = 2/3 h. Energy = 1.5 × 2/3 = 1 kWh

Practice at Home

Take this steadily — Part C onward includes Extended-only content.

Part A — Magnetism
  1. State the rule for how magnetic poles interact with each other.
  2. Describe how to plot the magnetic field pattern around a bar magnet using a plotting compass.
  3. Explain why an electromagnet, rather than a permanent magnet, is used in a scrapyard crane for lifting and releasing steel.
Part B — Charge and current
  1. Explain, in terms of electrons, how a balloon becomes negatively charged when rubbed on hair.
  2. State the difference between direct current and alternating current.
  3. A current of 1.5 A flows through a wire for 4 minutes. Calculate the charge that flows.
Part C — E.m.f., p.d. and resistance (Extended included)
  1. A battery does 30 J of work moving 5 C of charge around a complete circuit. Calculate its e.m.f.
  2. A resistor has a p.d. of 9 V across it and a current of 1.5 A flowing through it. Calculate its resistance.
  3. Sketch (in words) the current-voltage graph for a diode, and explain its shape.
Part D — Electrical energy and power
  1. A device draws a current of 8 A from a 230 V supply. Calculate its power.
  2. A 2.5 kW heater runs for 4 hours. If electricity costs $0.22 per kWh, calculate the total cost.
  3. Explain why kWh is described as a unit of energy rather than power.

Key Vocabulary Recap

Magnetic field — a region in which a magnetic pole experiences a force
Induced magnetism — a magnetic material temporarily becoming a magnet in the presence of a field
Current — the flow of charge, I = Q/t, measured in amperes
E.m.f. — work done by a source moving a unit charge around a complete circuit
Resistance — R = V/I; opposition to current flow, measured in ohms
Kilowatt-hour (kWh) — a unit of energy, used for billing electricity

Syllabus Reference

This note covers Cambridge IGCSE Physics (0625) section 4.1 (Simple phenomena of magnetism) and section 4.2 (Electrical quantities: 4.2.1 Electric charge, 4.2.2 Electric current, 4.2.3 Electromotive force and potential difference, 4.2.4 Resistance, 4.2.5 Electrical energy and electrical power). Core and Supplement content are both included, with Extended-only material (I=Q/t, conventional current vs. electron flow, E=W/Q, V=W/Q, current-voltage graphs, the length/area resistance relationships, electric fields, and field-line spacing) clearly flagged throughout. Part 2 of this note covers sections 4.3-4.5.

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