Magnetism and Electromagnetic Induction

What this unit covers

The topics below follow the published Physics 2 course framework for Unit 4. This unit is worth 12–15% of the exam, so budget your time against that rather than against how long the unit takes to teach.

Lessons in this unit

• Magnetic Fields & Their Sources12 min · 3 objectivesIdentify moving charges and currents as the source of all magnetic fields · Describe the geometry of magnetic field lines and use the right-hand rule for a wire · Relate the field near a long straight wire to the current and distance
• Magnetic Force on Charges & Currents14 min · 3 objectivesCalculate the magnetic force on a moving charge using F = qvB sinθ · Use the right-hand rule to find the direction of the magnetic force · Explain why the magnetic force does no work and produces circular motion
• Magnetic Flux & Faraday’s Law14 min · 3 objectivesDefine magnetic flux and identify the three ways to change it · Use Faraday’s law to calculate the magnitude of an induced EMF · Recognize that only a changing flux induces an EMF
• Lenz’s Law & the Direction of Induction12 min · 3 objectivesUse Lenz’s law to determine the direction of an induced current · Explain Lenz’s law as a consequence of energy conservation · Apply the induced-current-opposes-change idea to magnets and loops

Formulas in Unit 4

Every term in Unit 4

All 22 terms we publish for Magnetism and Electromagnetic Induction, with definitions. Reading them through is the fastest way to find the ones you cannot define — then drill those in cram mode until you can produce them without the prompt.

Magnetic field of a wire

B = μ₀I/2πr, circling the wire. Right hand: thumb along conventional current, fingers curl in the field direction.

Force on a moving charge

F = qvB sin θ, perpendicular to both velocity and field. A charge moving parallel to the field feels no force.

Magnetic force does no work

It is always perpendicular to velocity, so it changes direction but never speed — which is why it produces circular motion.

Charged particle in a magnetic field

Moves in a circle of radius r = mv/qB. Mass spectrometers use this to separate isotopes.

Force on a current-carrying wire

F = BIL sin θ. The basis of the electric motor, where the force on opposite sides of a loop produces torque.

Right-hand rule for force

Fingers point along v (or I), curl toward B, and the thumb gives the force on a positive charge. Reverse the result for a negative charge.

Magnetic flux

Φ = BA cos θ, the field passing through a surface. Changing B, A or the orientation all change flux.

Faraday's law

EMF = −ΔΦ/Δt. Only a CHANGING flux induces an EMF; a steady field through a stationary loop induces nothing.

Lenz's law

The induced current opposes the change producing it — the minus sign in Faraday's law, and a consequence of energy conservation.

Motional EMF

A rod of length L moving at speed v perpendicular to field B develops EMF = BLv across its ends.

Eddy currents

Circulating currents induced in a bulk conductor by changing flux. They oppose the motion, which is how magnetic braking works.

Transformers

Alternating current in the primary induces a changing flux in the secondary; V_s/V_p = N_s/N_p. Requires AC, since DC produces no flux change.

Why magnetic monopoles do not appear

Magnetic field lines always form closed loops, so the net flux through any closed surface is zero — Gauss's law for magnetism.

Domains and ferromagnetism

Regions of aligned atomic moments. An external field grows the aligned domains, which is how a permanent magnet is made and why heating demagnetises it.

Determining the field direction around a wire

Grip the wire with the right hand, thumb along conventional current; the curl of the fingers gives the field direction.

Two parallel wires

Currents in the same direction attract, opposite directions repel — the opposite of the intuition from electric charges.

Motor principle

Opposite sides of a current loop feel opposite forces, producing a torque. A commutator reverses the current each half turn to keep it rotating.

Generator principle

Rotating a loop in a field changes flux continuously, inducing a sinusoidal EMF. The mechanical work done against the opposing force becomes electrical energy.

Flux through a rotating loop

Φ = BA cos θ, so flux is maximum when the loop's plane is perpendicular to the field, and EMF is maximum where flux changes fastest — a quarter cycle later.

Applying Lenz's law to a falling magnet

A magnet dropped through a copper tube falls slowly, because induced currents create a field opposing its motion.

Transformer energy conservation

Power in equals power out for an ideal transformer, so stepping voltage up steps current down proportionally.

Why power is transmitted at high voltage

Losses are I²R, so raising voltage lowers current for the same power and cuts losses by the square of the reduction.

What examiners penalize here

• Two facts anchor this topic: magnetism comes from moving charge, and magnetic field lines are always closed loops (no monopoles). If a diagram shows field lines starting or stopping in mid-space, something is wrong.
• For any magnetic-force problem, first find the angle between v and B. Parallel → no force; perpendicular → maximum force qvB. The direction always comes from a right-hand rule, remembering to flip it for a negative charge.
• Faraday’s law depends on the *rate* of flux change, not the flux itself. A huge steady field induces nothing; a small field that changes quickly can induce a large EMF. Always compute ΔΦ/Δt, and multiply by N for a coil.
• To get an induced-current direction: (1) decide whether flux is increasing or decreasing, (2) the induced field opposes that change, (3) use the right-hand rule to find the current direction that makes that field. Then sanity-check with energy conservation — the loop should resist the motion.

Practice Physics 2

Our practice bank is drawn from across the whole course rather than filtered to one unit, which is closer to how the exam asks anyway — it will not tell you which unit a question is testing.

Questions about this unit

All 7 units of AP Physics 2: Algebra-Based

1. Unit 1 · Thermodynamics
2. Unit 2 · Electric Force, Field, and Potential
3. Unit 3 · Electric Circuits
4. Unit 4 · Magnetism and Electromagnetic Induction
5. Unit 5 · Geometric Optics
6. Unit 6 · Waves, Sound, and Physical Optics
7. Unit 7 · Modern Physics