AP Physics 2: Magnetism and Electromagnetic Induction

Magnetism in AP Physics 2 is not a separate chapter that sits beside electricity. It is electricity in motion. When charges move, they create magnetic fields, and when magnetic fields change, they can drive charges to move. That two-way relationship is the backbone of motors, generators, transformers, magnetic braking, and many modern sensing technologies. This unit focuses on how magnetic fields exert forces on moving charges and currents, and how changing magnetic environments induce electric effects through Faraday’s law and Lenz’s law.

Magnetic Fields: What They Are and How We Describe Them

A magnetic field is a vector field, written as B, that describes the magnetic influence of currents and magnets in space. Unlike electric field lines, which begin and end on charges, magnetic field lines form closed loops. That visual rule is consistent with the fact that isolated magnetic “charges” (magnetic monopoles) are not part of standard AP Physics 2 models.

Sources of Magnetic Fields

In the AP course framework, magnetic fields are primarily produced by:

• Moving charges (a current is an organized motion of charge)
• Permanent magnets (modeled as microscopic current loops)

A long, straight current-carrying wire creates circular magnetic field lines around the wire, with direction given by the right-hand rule. A solenoid (a long coil of wire) produces a magnetic field that is approximately uniform inside, resembling the field of a bar magnet but with a direction set by the current direction.

Magnetic Force on Moving Charges

A defining feature of magnetism is that magnetic forces act on charges only when they move. The magnetic force on a charge $q$ moving with velocity v in a magnetic field B has magnitude

$F=|q|vB\sin \theta$

where $\theta$ is the angle between v and B. The direction is perpendicular to both v and B, found using the right-hand rule for a positive charge, and reversed for a negative charge.

Key Consequences You Should Know

• If a particle moves parallel or antiparallel to B, then $\sin \theta =0$ and the magnetic force is zero.
• Because the force is perpendicular to velocity, the magnetic field does no work on the particle. It can change direction of motion, not speed.
• Circular motion is a common result. If a charged particle enters a uniform magnetic field perpendicular to its velocity, it undergoes uniform circular motion where magnetic force provides centripetal force:

$$|q|vB=\frac{m{v}^2}{r}$$

This leads to $r=\frac{mv}{|q|B}$, a relationship used in mass spectrometers and particle detectors to relate curvature to momentum and charge.

Magnetic Force on Current-Carrying Wires

A current in a magnetic field experiences a force because the moving charges within the conductor experience magnetic forces. For a straight wire segment of length $L$ carrying current $I$ in a uniform field B, the force magnitude is

$F=ILB\sin \theta$

where $\theta$ is the angle between the current direction and B. Direction again follows a right-hand rule, using current direction (conventional current) instead of charge velocity.

Practical Interpretation: Why Motors Work

In a motor, current runs through loops of wire placed in a magnetic field. Forces on opposite sides of the loop point in opposite directions, producing a torque that rotates the coil. That torque increases with stronger magnetic fields, larger current, more turns of wire, and loop geometry that maximizes $\sin \theta$.

Magnetic Flux: Measuring “How Much Field” Passes Through an Area

Electromagnetic induction is built on magnetic flux, which is a measure of how much magnetic field passes through a surface. For a uniform magnetic field passing through a flat area $A$,

${\Phi }_B=BA\cos \theta$

where $\theta$ is the angle between B and the surface’s area vector (a vector perpendicular to the surface). Flux increases if:

• The field strength $B$ increases
• The area $A$ increases
• The surface rotates so it becomes more “face-on” to the field (increasing $\cos \theta$)

Flux is central because induced emf depends on how flux changes, not simply on the presence of a magnetic field.

Faraday’s Law: Changing Flux Creates Induced emf

Faraday’s law states that a changing magnetic flux through a loop induces an electromotive force (emf) around that loop:

$$\mathcal{E}=-\frac{d{\Phi }_B}{dt}$$

For a coil with $N$ turns, the induced emf is multiplied:

$$\mathcal{E}=-N\frac{d{\Phi }_B}{dt}$$

This equation explains a wide range of phenomena that look different on the surface but share the same cause: the flux through a circuit is changing.

How Flux Can Change in Real Situations

1. Changing __MATH_INLINE_22__: Move a magnet toward a coil or vary current in a nearby electromagnet.
2. Changing area: A sliding conducting bar on rails changes the enclosed area.
3. Changing angle: Rotating a loop in a uniform magnetic field, the basis of AC generators.

In a rotating loop generator, $\theta$ changes with time, making ${\Phi }_B$ vary sinusoidally, so the induced emf alternates. This is the essential mechanism behind most electrical power generation.

Lenz’s Law: The Minus Sign Has Physical Meaning

The negative sign in Faraday’s law is not a mathematical nuisance. It encodes Lenz’s law: the induced current creates a magnetic field that opposes the change in flux that produced it.

This is a conservation of energy principle in disguise. If induced currents reinforced the change instead of opposing it, you could create self-amplifying energy from nothing.

Example: Magnet and Coil

• Push a magnet into a coil: flux through the coil increases. The induced current produces a magnetic field opposing the increase, effectively resisting the magnet’s motion.
• Pull the magnet out: flux decreases. The induced current produces a magnetic field that tries to keep flux from decreasing, again resisting the motion.

That “magnetic resistance” is why you feel a drag force when moving magnets near conductors, and it is the basis of eddy current braking used in some trains and exercise equipment.

Inductance: When Circuits Resist Changes in Current

Inductance is the circuit property that links changing current to induced emf. When current in a coil changes, the magnetic field produced by that current changes, changing flux through the coil itself. That self-induced emf opposes the change in current.

For an inductor of inductance $L$,

$$\mathcal{E}=-L\frac{dI}{dt}$$

The larger the inductance, the more strongly the inductor resists rapid changes in current. In circuits, inductors behave like “inertia” for current.

Energy Stored in an Inductor

Inductors store energy in their magnetic fields. The energy increases with current and inductance:

$$U=\frac{1}{2}L{I}^2$$

This is especially relevant in transient behavior, such as when a switch is opened or closed in an RL circuit. The inductor can briefly maintain current by inducing an emf, which is why coils can generate voltage spikes when circuits are interrupted.

Connecting the Ideas: From Physics to Applications

Magnetism and electromagnetic induction show up repeatedly in AP Physics 2 free-response and multiple-choice questions because they blend fields, forces, energy, and circuit reasoning.

• Motors rely on magnetic forces on current-carrying conductors to create torque.
• Generators rely on Faraday’s law: changing magnetic flux induces emf.
• Transformers (in the AP framework) are explained by changing magnetic flux in a shared core inducing emf in a secondary coil, with coil turns playing a central role.
• Eddy currents are induced currents in bulk conductors that oppose motion and dissipate energy as thermal energy, consistent with Lenz’s law.

What to Emphasize for AP Physics 2 Mastery

Focus on three habits:

1. Track direction carefully using right-hand rules and sign conventions.
2. Translate physical motion or changing conditions into “flux is changing,” then apply Faraday’s law.
3. Use Lenz’s law as a reality check: induced effects oppose the change, and that opposition is tied to energy conservation.

Magnetism and induction can feel abstract until you recognize the consistent pattern: motion of charge creates magnetic effects, and changing magnetic environments drive electrical effects. Once that loop is clear, most problems become an exercise in identifying what is changing and how the system responds.