Unit 12: Magnetism and Electromagnetism

What the CED requires across Unit 12

Unit 12 of AP Physics 2 is Magnetism and Electromagnetism. The course description weights it at 12 to 15% of the multiple-choice section and estimates about 10 to 14 class periods. That is the same band as Units 13, 14 and 15. The first three units are weighted 15 to 18% each: Thermodynamics, then Electric Force, Field, and Potential, then Electric Circuits.

Four topics and eight learning objectives, and the equations are not spread evenly across them:

Every one of those eight objectives opens with the same task verb, "describe". The CED says that verb "encompasses the range of possible graphical, mathematical, or verbal skill applications", so describing a magnetic field can mean drawing it, writing the algebra, or saying it in words, and the exam uses all three.

The CED frames the unit as building on electrostatic forces, fields, free charges and circuits by exploring the relationships between moving charges, the magnetic fields they generate, and the magnetic forces those fields exert on other moving charges. Its essential questions are everyday versions: how an induction stovetop heats a pan without heating the cooktop, why metal is dangerous inside an MRI machine, how an electric motor works.

One idea holds the whole unit together

Moving charge makes a magnetic field. A magnetic field pushes on moving charge. Change the magnetic flux through a loop and you drive a current around it. Every required statement in Unit 12 is a version of one of those three sentences, which is why the unit is magnetism and electromagnetism: it is what electricity looks like once things start moving.

The CED builds the first two in matched pairs, once for a single particle and once for a wire.

• Fields. 12.2.A.1 says a single moving charged object produces a magnetic field. 12.3.A.1 says a current-carrying wire produces one. A current is moving charge in bulk, so those are the same claim at two scales.
• Forces. 12.2.B.2 says a magnetic field may exert a force on a charged object moving in that field. 12.3.B.1 says a magnetic field may exert a force on a current-carrying wire. Same claim, same two scales.
• Induction. Topic 12.4 closes the circle: change the flux through a circuit and you get an induced emf, which drives a current, which is moving charge again.

Permanent magnets are not an exception. Essential knowledge 12.1.B.1 says magnetic dipoles result from the circular or rotational motion of electric charges, and that in magnetic materials this can be the motion of electrons. A bar magnet is not a different kind of object from a current loop; it is moving charge you cannot see.

One asymmetry with electrostatics is worth holding onto. Statement 12.1.A.1.i says magnetic fields can be produced by magnetic dipoles or combinations of dipoles, but never by monopoles. There is no magnetic equivalent of an isolated charge, which is why 12.1.A.2.i can say magnetic field lines form closed loops while an electric field line has to start or end on a charge.

How the four topics build

[12.1 Magnetic Fields](/ap-physics-2/unit-12-magnetism-and-electromagnetism/12-1-magnetic-fields) is the only topic in the unit whose required content names no equation. Its three objectives ask you to describe the properties of a magnetic field (12.1.A), the magnetic behavior of a material as a result of the configuration of its dipoles (12.1.B), and magnetic permeability (12.1.C). The content is qualitative and dense: field lines and poles, then a three-way sort of materials into ferromagnetic (iron, nickel, cobalt, which can be permanently magnetized), paramagnetic (aluminum, titanium, magnesium, which interact weakly and do not stay aligned), and diamagnetic, which the CED says applies to all materials. Vacuum permeability $\mu_0$ is introduced here too, with the caution that the permeability of matter is not a constant for a material and varies with temperature, orientation and field strength.

[12.2 Magnetism and Moving Charges](/ap-physics-2/unit-12-magnetism-and-electromagnetism/12-2-magnetism-and-moving-charges) turns the field into a force. It gives you the magnitude,

with $\theta$ the angle between the velocity and the magnetic field, and the direction rule: the force is perpendicular to both the field and the velocity, as defined by the right-hand rule. Two extras sit here that are easy to miss. Statement 12.2.B.3 says a moving charge in a region with both a magnetic and an electric field experiences independent forces from each, and 12.2.B.4 introduces the Hall effect as the potential difference created in a conductor by an external magnetic field with a component perpendicular to the direction the charges are moving.

[12.3 Magnetism and Current-Carrying Wires](/ap-physics-2/unit-12-magnetism-and-electromagnetism/12-3-magnetism-and-current-carrying-wires) does both jobs for wires. The field of a long straight wire is

and the CED is precise about its shape: the field vectors are tangent to concentric circles centered on the wire, with no component toward, away from, or parallel to it. The magnitude is proportional to the current and inversely proportional to the perpendicular distance from the wire's central axis, so it falls off as $1/r$, not $1/r^2$. Two more results live here: the field at the center of a current-carrying loop points along the loop's axis, and the field near several wires is found by vector addition. Then the force on a wire,

where $\ell$ is the length of the portion of the wire actually inside the field and $\theta$ is the angle between the current direction and the field direction.

[12.4 Electromagnetic Induction and Faraday's Law](/ap-physics-2/unit-12-magnetism-and-electromagnetism/12-4-electromagnetic-induction-and-faradays-law) is the payoff. Magnetic flux is the amount of the component of a magnetic field perpendicular to a cross-sectional area,

with the area vector defined perpendicular to the plane of the surface. Faraday's law relates changing flux to induced emf, Lenz's law fixes the direction, and the rod-on-rails case gives motional emf $\mathcal{E} = B\ell v$. One learning objective, four equations: the only topic in the unit with that shape.

The seven magnetism equations on the sheet

The Magnetism section of the AP Physics 2 equation sheet prints seven equations. Counted off the sheet, not recalled:

Vacuum permeability is not in that block; it sits in Constants and Conversion Factors:

Two things you might expect are missing.

The signed form of Faraday's law is not printed. The sheet gives the absolute-value form only. The version carrying the minus sign, $\mathcal{E} = -\Delta \Phi_B / \Delta t$, appears in the framework under 12.4.A.4 as the statement of Lenz's law, but it is not what you are handed in May. So the direction of an induced current is always something you argue for, never something you read off.

There is no radius formula for a charge circling in a magnetic field. Nothing in the Magnetism block gives one and Topic 12.2 does not list one. The situation is still fair game: the CED's optional sample activities for this unit include a graphing task on radius versus speed for a circling charge. You get there by setting the magnetic force equal to the centripetal force the circular motion requires, a Physics 1 move applied to a Physics 2 force.

The CED says outright that the framework and the sheet are different lists: some equations are printed in the framework only to show the end result of a derivation students are expected to be able to do, which it labels Derived Equations. Motional emf is the interesting case. Statement 12.4.A.5 calls $\mathcal{E} = B\ell v$ a derived equation, and it is also printed on the sheet, so you may quote it but should still be able to get it from $\Phi_B = BA\cos\theta$ with a changing area. The full sheet is at the AP Physics 2 formula sheet.

Directions are the whole difficulty

Six of Unit 12's essential-knowledge statements name the right-hand rule: 12.2.A.1.ii, 12.2.B.2.ii, 12.3.A.1.iii, 12.3.A.1.iv, 12.3.B.1.ii and 12.4.A.4.ii, spread across three of the four topics. The magnitudes here are one-line arithmetic. The direction is where the difficulty sits.

The CED is blunt about this in its Preparing for the AP Exam notes for Unit 12: when you write or identify a justification, simply referencing an equation, law or physical principle is not sufficient, and the example it chooses is a right-hand-rule answer. Saying the force on a charged particle is to the right "because of the 'right-hand rule'" is not complete enough to earn free-response points. Lay out the steps from the principle to the claim: which vectors you put where, and which quantity you read off your thumb.

Four things make directions go wrong.

1. Current means conventional current. The exam conventions printed with the Table of Information state it outright, unless a question says otherwise. Point your thumb the way positive charge would flow, not the way electrons drift.
2. A negative charge reverses the answer. The CED states the direction rule without spelling out the sign case, so this one is on you. The force depends on the sign of $q$, so an electron feels a force opposite to the one the right-hand rule gives for a proton with the same velocity in the same field. Work the rule for a positive charge, then flip it.
3. Three equations, three different angles. In $F_B = qvB\sin\theta$, $\theta$ is between the velocity and the field. In $F_B = I\ell B\sin\theta$, $\theta$ is between the current direction in the wire and the field. In $\Phi_B = BA\cos\theta$, $\theta$ is measured from the area vector, which the CED defines as perpendicular to the plane of the surface and directed outward from a closed surface. That last one is where the cosine comes from, and it is why a loop lying flat with the field pointing straight through it has maximum flux rather than zero.
4. Draw the field before you use the rule. Statement 12.1.A.2 says a magnetic field is a vector quantity representable with vector field maps, and suggested skill 1.A for Topics 12.1 and 12.2 is creating diagrams. The page notation is a dot for a field pointing out at you and a cross for one going in. Sketch it, then put your hand on the sketch.

Algebra-based: where the CED draws the line

AP Physics 2 is an algebra-based introductory college-level course, equivalent to the second course in an introductory college sequence in algebra-based physics. Its prerequisites say students should have completed AP Physics 1 or a comparable introductory course and should have taken or be concurrently taking precalculus. That is the reason Unit 12 stops where it does, and knowing the stopping point saves study time.

Unit 12 carries exactly one boundary statement across its four topics, and it sits under Topic 12.2. It says that quantitative treatment of the magnitude of the magnetic force exerted by a magnetic field on a moving charge is limited to angles of 0, 90 and 180 degrees between the velocity and the magnetic field. It then adds that qualitative analysis of other angles is permitted.

Both halves are load-bearing. You will not be asked to compute $qvB\sin 37^\circ$, but you can absolutely be asked whether the force grows or shrinks as the angle moves away from 90 degrees, or to rank three scenarios, and that is routine. At the three permitted angles the sine is 1 at 90 degrees and 0 at 0 and 180 degrees, so the arithmetic collapses to either $qvB$ or zero. Note also that the statement is attached to Topic 12.2 and to the force on a moving charge; the CED prints no equivalent restriction on the wire equation in Topic 12.3.

What the Physics 2 course description does not contain is just as useful. The Biot-Savart law and Ampere's law appear nowhere in it. Those belong to AP Physics C: Electricity and Magnetism, whose own Unit 12, titled Magnetic Fields and Electromagnetism, runs 12.1 Magnetic Fields, 12.2 Magnetism and Moving Charges, 12.3 Magnetic Fields of Current-Carrying Wires and the Biot-Savart Law, and 12.4 Ampere's Law. Physics 2 keeps the first two topic names, replaces the calculus-based pair with one algebra-based topic on wires, and adds a separate topic on induction. The Physics 2 CED makes the same point from its side, saying its Unit 12 concepts are "greatly expanded upon" in AP Physics C: Electricity and Magnetism.

So if a textbook chapter hands you an integral over a current element or a closed line integral of the field, you are reading Physics C material. Not wrong physics, just not on your exam, and $B = \mu_0 I / (2\pi r)$ is the printed result you use instead.

Traps that span more than one topic

No change, no emf. A loop parked in an enormous steady magnetic field has enormous flux and exactly zero induced emf. Faraday's law is about $\Delta \Phi_B / \Delta t$, and since $\Phi_B = BA\cos\theta$ there are three ways to change it: change $B$, change the area $A$ of the circuit inside the field, or change the orientation $\theta$. Rotating coils, expanding loops and rods sliding on rails are the three standard setups, one per variable.

Lenz's law opposes the change, not the field. Statement 12.4.A.4.i says an induced emf generates a current that creates a magnetic field opposing the change in magnetic flux. If the flux is increasing, the induced field inside the loop points against the applied field. If the flux is decreasing, the induced field points with it, propping it up. Memorizing "opposes the field" gets every decreasing-flux case backwards.

A magnetic force does no work on a point charge. The CED does not state this as required content, but it follows from one that is: 12.2.B.2.ii says the force is perpendicular to the velocity. A force perpendicular to the displacement does no work, so a magnetic field alone changes a particle's direction, never its speed. Any question with a magnetic field speeding a particle up needs an electric field somewhere.

Electric and magnetic forces add independently. Statement 12.2.B.3 makes this explicit. The electric force acts on a charge whether or not it is moving; the magnetic force needs motion and depends on the angle. In a velocity-selector setup they can cancel, but as two separate vectors, not as one combined law.

A wire's field falls as $1/r$; a point charge's field falls as $1/r^2$. Doubling the distance from a long straight wire halves the field, but doubling the distance from a point charge quarters the electric field. Carrying the Coulomb's law instinct into Topic 12.3 loses functional-dependence questions, and functional dependence, skill 2.D, is suggested for Topics 12.3 and 12.4.

Breaking a magnet gives you two magnets. Statement 12.1.B.1.ii gives the example directly: break a bar magnet in half and both halves are dipoles. No north pole is ever found in isolation from a south pole.

How Unit 12 is assessed

The AP Physics 2 exam is 3 hours long and splits evenly. Section I is 42 multiple-choice questions in 85 minutes for 50% of the score. Section II is 4 free-response questions in 95 minutes for the other 50%, and the four are always one of each type: Mathematical Routines, Translation Between Representations, Experimental Design and Analysis, and Qualitative/Quantitative Translation. A four-function, scientific or graphing calculator is allowed on both sections.

With four free-response questions and seven units, a Unit 12 free-response question is not guaranteed in any given year. The reliable number is the multiple-choice weighting, 12 to 15%. The unit's AP Classroom Progress Check is about 18 multiple-choice questions and 4 free-response questions covering all four types.

The suggested skills the CED lists per topic are teaching suggestions rather than a promise about the exam, but they line up with the question styles worth rehearsing:

Read down that table and the unit's shape shows. Topic 12.3 carries five suggested skills where the others carry four, and it alone lists 3.A, creating experimental procedures, and 1.B, quantitative graphs with scales and units, which fits a topic whose field you can measure against current and distance with a compass. Topic 12.4 is the only one listing 1.C, qualitative graph sketches, and 2.B, calculating an unknown quantity with units. So rehearse lab design and graph-plotting on wires, and sketching how flux and emf behave over time on induction.