Jupiter2U School
Chapter 16

Magnetism & Electromagnetism

High School
At a glance
Core ideaMoving charges make and feel magnetic fields; a changing flux induces an EMF (Faraday).
Key termLenz's law — the induced current always opposes the change that caused it.
You can…Find the force on a current-carrying wire and a transformer's turns/current ratio.
Watch outOnly a changing flux induces EMF — a magnet held still inside a coil does nothing.
Theory

Magnetic fields and forces

Moving charges create magnetic fields B (tesla, T) and feel forces in them. A charge q moving at velocity v experiences:

F = qvB sinθ Lorentz force, ⟂ to both v and B

A current-carrying wire of length L in field B feels F = BIL sinθ. The force direction follows Fleming's left-hand rule (thumb = force/motion, first finger = field, second = current).

Electromagnetic induction

Faraday's law: a changing magnetic flux Φ = BA through a loop induces an EMF:

ε = −N dΦ/dt N turns; minus = Lenz's law

Lenz's law (the minus sign) says the induced current opposes the change causing it — a direct consequence of energy conservation. Together these underpin generators, transformers and motors.

Explanation

One phenomenon: electromagnetism

Electricity and magnetism are two faces of one force. A current makes a magnet (Ørsted, 1820); a moving magnet makes a current (Faraday, 1831). Maxwell unified them in four equations and made a stunning prediction: changing electric and magnetic fields regenerate each other, propagating as a wave at speed c = 1/√(μ₀ε₀) = 3×10⁸ m·s⁻¹ — the speed of light. Light is an electromagnetic wave. Radio, microwaves, X-rays and light differ only in frequency. Chapter 21 revisits Maxwell's four equations in full differential form.

Motors and generators are the same device run in reverse. A motor uses the force on a current in a field to spin (electrical → mechanical). A generator spins a coil in a field to induce EMF (mechanical → electrical). Transformers use a changing flux shared between two coils to step voltage up or down — which is why power grids transmit at high voltage (low current, low I²R loss).

Lenz in action. Drop a magnet down a copper pipe and it falls in slow motion. Its motion induces eddy currents whose own field opposes the fall (Lenz's law), braking it — a beautiful demonstration of induction and energy conservation.
Practical

Worked example — force on a current-carrying wire & a transformer

Part A. A 0.25 m wire carries 4.0 A perpendicular to a 0.30 T field. Find the force.

  1. Perpendicular, so sinθ = 1. Use F = BIL.
  2. F = 0.30 × 4.0 × 0.25 = 0.30 N, directed ⟂ to both wire and field (left-hand rule).

Part B. A transformer steps 230 V down to 11.5 V. The primary has 2000 turns. Find the secondary turns and, if it's ideal and delivers 2.0 A out, the primary current.

  1. Turns ratio: Vs/Vp = Ns/Np, so Ns = 2000 × 11.5/230 = 100 turns.
  2. Ideal transformer conserves power: VpIp = VsIs.
  3. Ip = VsIs/Vp = 11.5 × 2.0 / 230 = 0.10 A.

Stepping voltage down steps current up (and vice versa): power in equals power out.

Q&A
Why do magnetic forces do no work on a moving charge?

The Lorentz magnetic force is always ⟂ to the velocity (F = qv×B). A perpendicular force changes direction but not speed, so it does zero work and never changes the charge's kinetic energy. It curves the path (e.g. into a circle) but can't speed the particle up.

State Lenz's law and why it must be true.

The induced current always opposes the change in flux that produces it. If it reinforced the change instead, the current would grow without limit and create energy from nothing — violating conservation of energy. The opposing direction ensures you must do work to generate electricity.

Why is electrical power transmitted at very high voltage?

Power loss in cables is I²R. For a fixed power P = VI, raising V lowers I proportionally, and since loss depends on I², a 10× higher voltage cuts transmission losses 100×. Transformers make this practical by stepping voltage up for transport and down for use.

A magnet is pushed into a coil connected to a meter. What is observed, and what happens if it's held still inside?

Pushing it in changes the flux, inducing a current (meter deflects). Held stationary inside, the flux is constant, dΦ/dt = 0, so no EMF and no current. Pulling it out induces current in the opposite direction. Only change induces EMF.

Concept mind map

How the ideas connect

Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.

Magnetic fieldF = B*I*LMotor effectInductionFaraday's lawTransformersMagnetism & EM
Infographic

The key facts, visualised

F = B*I*L
Force on a current-carrying wire in a field
F = q*v*B
Force on a moving charge in a field
EMF = -dPhi/dt
Faraday's law of induction
Vs/Vp = Ns/Np
Transformer turns ratio
Solved examples

Worked problems, step by step

Follow each solution line by line, then try to reproduce it on paper before moving on.

Example 1A 0.5 m wire carries 4.0 A across a 0.20 T field at right angles. Find the force.

  1. F = B*I*L
  2. F = 0.20 * 4.0 * 0.5

Example 2A transformer has 100 primary turns at 240 V and 25 secondary turns. Find the output voltage.

  1. Vs/Vp = Ns/Np
  2. Vs = 240 * 25/100
  3. = 240 * 0.25
Practice problem set

Now you try

Work each one out first, then tap to reveal the worked answer.

1Which way does a compass needle point near a bar magnet?
Along the field lines, its north end toward the magnet's south pole.
2What produces a magnetic field besides magnets?
A moving charge or an electric current.
3How do you induce a current in a coil?
Change the magnetic flux through it, for example by moving a magnet in or out.
4Why must transformers use alternating current?
Only a changing flux induces an EMF; steady DC gives no induction.
5A wire carries 2 A in a 0.5 T field over 0.3 m at 90 degrees. Force?
F = 0.5*2*0.3 = 0.30 N.
6What is electromagnetism in one idea?
Electricity and magnetism are two aspects of one force; changing one creates the other.