Magnetism and Electromagnetism

Name: AP Physics 2: Algebra-Based Unit 4: Magnetism and Electromagnetism
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12–15% of the exam7 lessons · 96 min42 terms

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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.

Magnetic fieldsForces on chargesFaraday’s lawLenz’s law

Lessons in this unit

Formulas in Unit 4

Field of a long straight wire

B = μ₀ · I / (2π · r)

μ₀ = 4π × 10⁻⁷ T·m·A⁻¹ is the permeability of free space. B is measured in teslas (T). The field is proportional to the current and inversely proportional to the distance r from the wire.

Magnetic force on a charge and on a wire

F = q · v · B · sinθ · F = B · I · L

θ is the angle between v and B. Maximum force at θ = 90° (sinθ = 1); zero force at θ = 0°. For a wire, L is the length within the field and I the current.

Magnetic flux and Faraday’s law

Φ = B · A · cosθ · |EMF| = N · |ΔΦ / Δt|

ΔΦ/Δt is the rate of change of flux. N is the number of turns in the coil. The induced EMF depends on how fast the flux changes, not on the flux itself.

Lenz’s law (the minus sign)

EMF = − N · (ΔΦ / Δt)

The negative sign encodes Lenz’s law: the induced EMF (and current) opposes the change in flux. It is the mathematical statement that induction resists whatever is changing.

The two magnetic forces

on a charge: F = qvB sin θ · on a current-carrying wire: F = BIL sin θ

θ is the angle between v (or the current) and B. Both forces are ZERO when the motion is parallel to the field, which is a favorite exam case.

Circular motion in a magnetic field

qvB = mv²/r → r = mv/(qB)

Faster or heavier particles curve less; stronger fields or larger charges curve them more. This single relation drives the mass spectrometer.

Faraday and motional emf

ε = −ΔΦ/Δt with Φ = BA cos θ · for a rod of length L moving at speed v perpendicular to B: ε = BLv

The BLv form is the special case where the changing quantity is area, at rate Lv. The minus sign is Lenz's law.

The two stages

selector: v = E/B · separator: r = mv/(qB) → m/q = rB/v

Stage one fixes the speed; stage two sorts by mass-to-charge ratio. Combining them gives m/q = rBB'/E when the two magnetic fields differ.

Every term in Unit 4

All 42 terms we publish for Magnetism and Electromagnetism, 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: ε = BLv for a rod of length L moving at v perpendicular to B — the special case where the changing quantity is area, at rate Lv.
Eddy currents: Induced loops of current in bulk conductors. They oppose relative motion, which is how magnetic braking and induction cooktops work.
Transformers: V_s/V_p = N_s/N_p, and power is conserved in an ideal transformer so raising voltage lowers current. They work on AC only, since DC produces no changing flux.
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 reverse of the intuition built 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.
Two different right-hand rules: Force on a moving charge: fingers along v, curl toward B, thumb gives F. Field around a wire: thumb along the current, fingers curl as B loops.
Negative charges: solve then flip: Apply the rule for a positive charge, then reverse the answer. Never switch to your left hand mid-problem.
Zero force parallel to the field: F = qvB sin θ, so motion along the field lines gives no force at all. Check the angle before reaching for a rule.
Why magnetic force does no work: It is always perpendicular to the velocity, so it changes direction but never speed. Magnetic forces never enter energy conservation.
Radius of circular motion: qvB = mv²/r gives r = mv/(qB). Faster or heavier curves less; stronger field or larger charge curves more.
Flux, not field, induces emf: Φ = BA cos θ, and ε = −ΔΦ/Δt. A loop at rest in a strong steady field has large flux and ZERO induced emf.
Three ways to change flux: Change the field strength, the loop area, or the orientation. Any one produces an emf.
The rod-on-rails chain: ε = BLv → I = BLv/R → F = BIL = B²L²v/R, opposing the motion. Each link is a separate rubric point.
Lenz's law IS energy conservation: If the induced force assisted the motion, the system would accelerate without limit and generate energy from nothing.
The Fv against ε²/R check: Mechanical power supplied must equal electrical power dissipated. Agreement verifies the whole induction chain in one line.
Terminal velocity of a falling loop: The induced retarding force grows with speed until B²L²v/R equals mg. The reason a magnet falls slowly down a copper pipe.
Velocity selector: Crossed E and B with opposing forces: qE = qvB gives v = E/B. The charge CANCELS, so the same speed is selected for every particle.
Mass spectrometer: After the selector, r = mv/(qB) depends only on m/q. Heavier curves less, more highly charged curves more.
What a spectrometer actually measures: The mass-to-CHARGE ratio, not mass. Two ions with the same ratio land together, so the charge state must be known independently.
No magnetic monopoles: Field lines form closed loops with no beginning or end, unlike electric field lines which start and stop on charges.
Field of a long straight wire: B = μ₀I/2πr, looping around the wire. Falls as 1/r, more slowly than a point charge field.
Solenoid field: Nearly uniform inside and much weaker outside, with B = μ₀nI depending on turns per unit length, not total turns.
Why the force is zero along the field: F = qvB sin θ, so motion parallel to B gives zero force. Always check the angle before applying a right-hand rule.
Lenz's law as a direction rule: The induced current opposes the change in flux that produced it. It is energy conservation stated as a sign, not an independent law.
Generators and transformers: A rotating loop in a field produces AC by continuously changing flux orientation. Transformers work on AC only, since DC gives no changing flux.

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.
Say out loud which rule you are using and, for a negative charge, write "reversed for negative charge" in your working. Graders follow stated reasoning, and it also stops you from forgetting the flip.
Answer induction questions in the order emf → current → force → power. Each step feeds the next, they are usually separate rubric points, and the Fv against ε²/R check verifies the whole chain in one line.
Treat the two stages separately and in order. The selector fixes v with no reference to the particle; only then does the second field sort by m/q. Trying to combine them in one equation before establishing v is where these problems go wrong.

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.

97 practice questionsEvery one with a written explanation FRQ trainerWritten answers scored against the rubric Physics 2 study guideAll units, weights and score data in one place All 7 Physics 2 unitsThe full course

Questions about this unit

How much of the AP Physics 2: Algebra-Based exam is Unit 4?

Unit 4, Magnetism and Electromagnetism, is worth 12–15% of the Physics 2 multiple-choice section according to the published course framework. Across all 7 units that makes it a substantial share — heavier than an even split would give it.

What topics are covered in Physics 2 Unit 4?

Magnetism and Electromagnetism covers Magnetic fields, Forces on charges, Faraday’s law and Lenz’s law. We publish 42 terms with definitions for this unit, all of them on this page.

How should I study Physics 2 Unit 4?

Read the 7 lessons below first — about 95 minutes — then drill the 42 terms in cram mode until you can produce each definition from memory rather than just recognize it. Recognition is what makes a unit feel finished when it is not. Finish with practice questions and read the explanation for every one you get right by elimination as well as the ones you miss.

All 7 units of AP Physics 2: Algebra-Based

Unit names, topics and exam weights follow the published College Board course framework for AP Physics 2: Algebra-Based. AP® is a trademark registered by the College Board, which does not endorse this site.