Current Electricity, Magnetism and Electromagnetic Induction
These three topics together supply the largest share of Physics marks in the paper, and they are connected by one thread: a moving charge is a current, a current makes a magnetic field, and a changing magnetic field drives a current back. Learning them as one story rather than three chapters saves a great deal of memorisation. The two places to be careful are both directional — the right-hand rules, where a sign error costs the whole mark, and Lenz's law, which is not a separate rule at all but energy conservation wearing a different hat.
Magnetic Fields and Forces
A charge moving in a magnetic field feels F⃗ = qv⃗ × B⃗, magnitude qvB sin θ, and a current-carrying wire feels F⃗ = IL⃗ × B⃗. Fields are produced by currents: the Biot–Savart law integrates to give B = μ₀I/2πr for a long straight wire, μ₀I/2R at the centre of a circular loop, and μ₀nI inside a long solenoid.
🎯 Why a magnetic force can never change a particle's speed
Because F⃗ = qv⃗ × B⃗ is a cross product, the force is always perpendicular to the velocity. A perpendicular force does no work, so the kinetic energy — and therefore the speed — cannot change. All a magnetic field can do is bend the path. That single fact answers a whole family of questions and gives you the geometry for free: a charge entering perpendicular to a uniform field moves in a circle of radius r = mv/qB, with period T = 2πm/qB that is independent of the speed. If it enters at an angle, the component along B is untouched and the result is a helix. Note the contrast with an electric field, which is parallel to the force and therefore does change the speed — that is precisely why accelerators use electric fields to speed particles up and magnetic fields to steer them.| Rule | Use |
|---|---|
| Right-hand thumb rule | Thumb along the current, fingers curl in the direction of B |
| Fleming's left-hand rule | Force on a current in a field — the motor rule |
| Fleming's right-hand rule | Direction of induced current — the generator rule |
| Lenz's law | The induced current opposes the change that caused it |
Induction, Lenz's Law and AC
Faraday's law gives the induced emf as ε = −dΦ/dt, where Φ = BA cos θ. The minus sign is Lenz's law. A rod of length L moving at v perpendicular to B develops a motional emf ε = BLv, which is the same law seen from a different angle.
🎯 Lenz's law is energy conservation, not an extra rule
Suppose the induced current helped the change instead of opposing it. Pushing a magnet towards a coil would then induce a current that pulled it in harder, accelerating it, inducing more current, and so on — free energy from nothing. So the minus sign is not an experimental curiosity; it is forced by conservation of energy. This gives you a reliable way to get any induction direction right without fumbling with hand rules: ask what the induced current would have to do to resist what you are doing, and that is its direction. Push a north pole towards a coil and the coil's near face must become a north pole to repel it; pull the magnet away and that face becomes a south pole to hold it back. The work you do against that opposition is exactly the electrical energy generated.| Element | Reactance | Phase of current relative to voltage |
|---|---|---|
| Resistor R | R, frequency-independent | In phase |
| Inductor L | X_L = ωL — rises with frequency | Current lags by 90° |
| Capacitor C | X_C = 1/ωC — falls with frequency | Current leads by 90° |
🧠 Resonance, and why a pure inductor or capacitor consumes no power
In a series LCR circuit the impedance is Z = √(R² + (X_L − X_C)²). At resonance X_L = X_C, so ω = 1/√(LC), the impedance falls to its minimum R, and the current is maximum and in phase with the voltage. Two further results are examined. Average power is P = V_rms I_rms cos φ, where cos φ = R/Z is the power factor — so at resonance cos φ = 1 and the circuit behaves purely resistively. And in a pure inductor or capacitor the phase difference is exactly 90°, so cos φ = 0 and the average power consumed is zero: energy flows into the element for a quarter cycle and back out the next, which is why these are called wattless components and why a choke coil dims a lamp without wasting energy as a resistor would.ℹ️ Transformers, and why power is transmitted at high voltage
A transformer works on mutual induction and obeys V_s/V_p = N_s/N_p, with an ideal device conserving power so that stepping voltage up steps current down in the same ratio. It works only on AC, because a steady current produces no changing flux — connect one to a battery and nothing appears at the secondary. The practical consequence shapes the whole grid: transmission loss is I²R, so carrying the same power at ten times the voltage means one tenth the current and one hundredth the loss. That is why long-distance lines run at hundreds of kilovolts and step down only near the consumer, and it is a favourite reasoning question.Key takeaways
- Drift velocity is under a mm/s, but the field is set up at nearly light speed — that is why a lamp lights instantly.
- In series use P = I²R (larger R glows brighter); in parallel use P = V²/R (smaller R glows brighter).
- Kirchhoff's junction rule is charge conservation; the loop rule is energy conservation.
- A magnetic force is always perpendicular to v, so it can never change speed — only bend the path.
- Circular radius r = mv/qB with period T = 2πm/qB, which is independent of speed.
- Lenz's law is energy conservation — the induced current always resists the change that caused it.
- X_L = ωL rises with frequency, X_C = 1/ωC falls; resonance at ω = 1/√(LC) with Z minimum.
- A pure L or C consumes zero average power (cos φ = 0); transformers need AC, and I²R is why the grid uses high voltage.
Practice questions (8)
Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.
A 100 W and a 60 W bulb, both rated for the same mains voltage, are connected in SERIES across the mains. Which glows brighter?
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Answer: B — The 60 W bulb
In series the current is common, so use P = I²R and the larger resistance dissipates more. Since R = V²/P, the 60 W bulb has the higher resistance and therefore glows brighter — the reverse of everyday expectation. In parallel the voltage is common instead, P = V²/R applies, and the 100 W bulb is brighter as usual.A charged particle enters a uniform magnetic field perpendicular to it. The field can change the particle's:
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Answer: B — Direction but not speed
F = qv × B is always perpendicular to the velocity, so it does no work and the kinetic energy — hence the speed — cannot change; only the direction does, bending the path into a circle of radius mv/qB. An electric field is the opposite case: being parallel to the force, it does change the speed, which is why accelerators use E to speed particles up and B to steer them.The north pole of a magnet is pushed towards a coil. The face of the coil nearer the magnet:
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Answer: B — Becomes a north pole, repelling the magnet
By Lenz's law the induced current opposes the change, so the near face becomes a north pole to repel the approaching magnet. If it attracted instead, the magnet would accelerate in, induce more current, and generate energy from nothing — so the minus sign in Faraday's law is required by energy conservation. Pulling the magnet away reverses the pole to south.In a series LCR circuit at resonance:
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Answer: B — The impedance equals R and the current is maximum
At resonance X_L = X_C, so those terms cancel in Z = √(R² + (X_L − X_C)²) and the impedance falls to its minimum value R. The current is therefore maximum and in phase with the voltage, giving a power factor cos φ = R/Z = 1 — the circuit behaves as if purely resistive.A transformer is connected to a battery. The output at the secondary is:
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Answer: B — Zero, apart from a momentary pulse when connected
A transformer works on mutual induction, which needs a changing flux. A battery supplies steady DC, so once the current settles there is no flux change and no induced emf — only a brief pulse at the instant of connection while the current is rising. This is why transformers work on AC only.Electric power is transmitted at high voltage mainly because:
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Answer: B — It reduces the current and so reduces I²R losses
For a given power P = VI, raising V by a factor of ten lowers I to a tenth, and since loss is I²R it falls to a hundredth. High voltage is emphatically less safe, which is exactly why it is stepped down near the consumer, and the resistance of the line is a property of the conductor and does not change with voltage.The average power consumed by a pure inductor in an AC circuit is:
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Answer: B — Zero
In a pure inductor the current lags the voltage by exactly 90°, so the power factor cos φ = cos 90° = 0 and the average power is zero. Energy flows into the magnetic field for a quarter cycle and returns in the next, which is why inductors and capacitors are called wattless components and why a choke can dim a lamp without wasting energy as a resistor would.The time period of a charged particle moving in a circle in a uniform magnetic field:
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Answer: B — Is independent of speed
T = 2πm/qB contains no v: a faster particle traces a proportionally larger circle (r = mv/qB) and so takes the same time to complete it. This speed-independence is exactly what makes the cyclotron possible, since a fixed-frequency alternating voltage stays in step with the particle as it gains energy.