AP Physics 2 Unit 12 ReviewMagnetism and Electromagnetism

AP Physics 2 Unit 12 covers magnetism and electromagnetism, the physics of how moving charges create magnetic fields and how those fields push back on other moving charges, currents, and loops of wire. The single biggest idea is the symmetry between electricity and magnetism. Moving charge makes a magnetic field, and a changing magnetic field makes an electric effect (an induced emf), which is the principle behind generators, transformers, and most of the electrical grid. This unit is 12-15% of the AP exam, and it leans heavily on vector reasoning and the right-hand rule.

What this unit covers

Magnetic fields and magnetic materials

• A magnetic field is a vector field. At every point in space it has a magnitude and direction, and you can map it with field lines just like you did with electric fields in Unit 10.
• The big structural difference from electric fields is that magnetic field lines always form closed loops. There are no magnetic monopoles. Every magnet is a dipole with a north and a south pole, and if you snap a bar magnet in half, you get two smaller dipoles, never an isolated pole.
• Magnetic dipoles come from circulating charge. In materials, that means the motion of electrons. Permanent magnetism and induced magnetism both happen when the dipoles inside a material line up in the same direction.
• Like poles repel, opposite poles attract. Field lines outside a bar magnet run from the north pole to the south pole.
• Magnetic permeability measures how much a material magnetizes in response to an external field. Free space has a fixed value, the vacuum permeability μ₀, which shows up in field equations. The permeability of actual matter depends on the material's composition and conditions, so it is not a single fixed constant.

Moving charges as sources and targets of magnetic force

• A single moving charge produces a magnetic field. The field at a point depends on the charge's speed and the distance to that point, and its direction is perpendicular to both the velocity and the line from the charge to the point. The right-hand rule gives you the direction.
• Flip it around and the same charge can feel a force from someone else's field. The magnitude is F = qvB sin θ, where θ is the angle between the velocity and the field. The force is always perpendicular to both v and B.
• Because the force is perpendicular to velocity, a magnetic force does no work on a charge. It changes direction, not speed. A charge moving perpendicular to a uniform field travels in a circle, with the magnetic force acting as the centripetal force.
• A charge moving parallel to the field, or a charge at rest, feels zero magnetic force. That sin θ factor matters.
• For negative charges, the force points opposite to what your right hand says. Either flip the result or use your left hand.

Current-carrying wires

• A long, straight, current-carrying wire produces a magnetic field whose vectors are tangent to concentric circles centered on the wire. The field has no component toward, away from, or along the wire. Point your right thumb along the current and your fingers curl in the field's direction.
• The field strength is proportional to the current and inversely proportional to the perpendicular distance from the wire, B = μ₀I / (2πr).
• A wire carrying current through an external magnetic field feels a force F = IℓB sin θ, where ℓ is the length of wire in the field and θ is the angle between the current direction and the field. Direction comes from the right-hand rule again, since a current is just a stream of moving charges.
• Two parallel wires interact through their fields. Currents in the same direction attract; currents in opposite directions repel. This is a classic exam setup.

Electromagnetic induction and Faraday's law

• Magnetic flux measures how much of a magnetic field passes perpendicularly through an area, Φ_B = BA cos θ. The area vector points perpendicular to the surface, and the sign of the flux tells you which way the field threads through.
• Faraday's law is the payoff of the whole unit. A changing magnetic flux through a loop induces an emf, and the faster the flux changes, the bigger the emf. The flux can change because B changes, because the area changes, or because the angle between them changes (a rotating coil, which is exactly how a generator works).
• Lenz's law gives the direction. The induced current flows so that its own magnetic field opposes the change in flux that created it. If flux through a loop is increasing into the page, the induced current circulates counterclockwise to push flux back out of the page.
• Lenz's law is energy conservation in disguise. If the induced current helped the change along instead of opposing it, you would get a runaway free-energy machine, which nature does not allow.
• These ideas power real technology. Generators rotate coils in magnetic fields to produce alternating emf, and transformers use a changing current in one coil to induce an emf in another.

Unit 12, Magnetism and Electromagnetism at a glance

Why Unit 12, Magnetism and Electromagnetism matters in AP Physics 2

This unit completes the electricity story you started in Units 10 and 11 by showing that electric and magnetic phenomena are two faces of the same interaction. It is also one of the most skill-dense units in the course, because almost every problem demands three-dimensional vector reasoning on top of the algebra.

• It develops the fields theme of the course. You already used vector fields for gravity and electric force; now you add a field whose force depends on velocity, which is genuinely new behavior.
• Conservation of energy shows up again through Lenz's law, reinforcing that conservation principles constrain what can physically happen.
• Induction explains the technology around you. Generators, transformers, induction stoves, and wireless chargers all run on Faraday's law, so this is the unit where circuit physics connects to the power grid.
• It builds the conceptual foundation for electromagnetic waves, which carry the course into optics and modern physics.

How this unit connects across the course

• Electric force, field, and potential (Unit 10) gives you the vocabulary of vector fields, field lines, and forces on charges. Unit 12 reuses all of it, then adds the twist that magnetic force depends on motion and acts perpendicular to velocity.
• Electric circuits (Unit 11) supplies the current, emf, and resistance concepts you need here. An induced emf from Faraday's law drives current through a circuit exactly like a battery does, so induction problems often turn into circuit problems halfway through.
• Geometric optics (Unit 13) and physical optics (Unit 14) deal with light, and light is an electromagnetic wave. The coupling between changing electric and magnetic fields you see in induction is the mechanism that lets light propagate through empty space.
• Modern physics (Unit 15) uses magnetic deflection of charged particles in contexts like mass spectrometry and historic experiments on the electron, so the circular motion of a charge in a field pays off again there.

Key equations and processes

• F_B = qvB sin θ gives the magnetic force on a moving charge, where θ is the angle between velocity and field. Use it with the right-hand rule for direction.
• F_B = IℓB sin θ gives the force on a length ℓ of current-carrying wire in a field. Same right-hand rule, with current playing the role of velocity.
• B = μ₀I / (2πr) gives the field a perpendicular distance r from a long, straight wire. Field strength falls off as 1/r, not 1/r².
• Φ_B = BA cos θ defines magnetic flux through an area, where θ is the angle between the field and the area vector (the normal to the surface).
• ε = −ΔΦ_B/Δt is Faraday's law. The induced emf equals the rate of change of flux, and the negative sign encodes Lenz's law.
• Circular motion of a charge in a uniform field combines qvB = mv²/r, letting you solve for the radius, speed, or charge-to-mass ratio of the particle.
• Lenz's law process: identify which way flux points and whether it is increasing or decreasing, then choose the induced current direction whose own field opposes that change.

Unit 12, Magnetism and Electromagnetism on the AP exam

This unit is 12-15% of the AP exam, one of the heavier weights in AP Physics 2. Multiple-choice questions love direction reasoning, asking which way a charge deflects, which way a field points around a wire, or which way an induced current flows, so you need the right-hand rule to be fast and reliable. Quantitative questions combine magnetic force with circular motion or stack a wire's field with the force on a second wire.

On the free-response side, expect induction scenarios. A loop slides into or out of a field region, a bar slides along rails, or the field through a coil ramps up over time, and you have to compute flux, find the induced emf, determine the current direction with Lenz's law, and explain your reasoning in words. Experimental design questions can ask you to plan a procedure to measure a field or an induced emf, and graph-based questions may give you flux versus time and ask for emf (the slope) or vice versa. Clear cause-and-effect explanations, not just equations, earn the points on the justification parts.

Essential questions

• How can a magnetic field exert a force on a charge only when the charge is moving?
• Why do magnetic field lines always form closed loops, and what does the absence of magnetic monopoles imply about magnets?
• What does it mean for electricity and magnetism to be symmetric, and how does that symmetry show up in induction?
• Why must an induced current oppose the change that creates it, and what would break if it did not?

Key terms to know

• Magnetic field: a vector field that exerts forces on moving charges, currents, and magnetic materials.
• Magnetic dipole: a north-south pole pair created by circulating charge; the only source of magnetic fields, since monopoles do not exist.
• Permanent magnetism: a lasting alignment of magnetic dipoles within a material.
• Induced magnetism: temporary dipole alignment in a material caused by an external magnetic field.
• Magnetic permeability: a measure of how much a material magnetizes in response to an external field; μ₀ is the value for free space.
• Right-hand rule: the hand tool for finding the direction of fields and forces involving moving positive charges and currents.
• Magnetic flux: the amount of magnetic field passing perpendicularly through an area, Φ_B = BA cos θ.
• Area vector: a vector perpendicular to a surface, used to define the angle in flux calculations.
• Electromagnetic induction: the creation of an emf by a changing magnetic flux.
• Faraday's law: the rule that induced emf equals the rate of change of magnetic flux through a loop.
• Lenz's law: the rule that an induced current's own field opposes the change in flux that produced it.
• Induced emf: the potential difference generated by changing flux, which drives current like a battery does.
• Motional emf: the emf produced when a conductor moves through a magnetic field, changing the flux through a circuit.

Common mix-ups

• Magnetic force is perpendicular to velocity, so it changes a charge's direction but never its speed and never does work on it. If a particle in a magnetic field speeds up, something else (like an electric field) is responsible.
• The field from a long, straight wire falls off as 1/r, not 1/r². Do not import the inverse-square habit from point charges in Unit 10.
• Flux depends on the perpendicular component of the field through the area. A strong field lying in the plane of a loop gives zero flux, because cos 90° = 0.
• Induction needs a changing flux, not just a big flux. A loop sitting still in a strong, steady field has zero induced emf. Constant flux means nothing happens.