Physics 2 · Unit 5: Magnetism and Electromagnetic Induction · 14 min read · Updated 2026-05-11
Magnetic Flux, Induced EMF, Faraday's and Lenz's Law — AP Physics 2
AP Physics 2 · Unit 5: Magnetism and Electromagnetic Induction · 14 min read
1. Magnetic Flux★★☆☆☆⏱ 4 min
Magnetic flux ($\Phi_B$) is a scalar quantity that measures the total magnetic field passing through a defined surface area, analogous to electric flux from Gauss's Law. For induction problems, we almost always work with flat open surfaces bounded by a closed loop of wire.
\Phi_B = B A \cos\theta
Where $B$ is magnetic field magnitude, $A$ is surface area, and $\theta$ is the angle between the magnetic field vector and the *normal (perpendicular) vector* to the surface. Flux can change for three reasons, all of which produce induced EMF: $B$ changes, $A$ changes, or $\theta$ changes.
Exam tip: Always confirm you are using the angle between the magnetic field and the normal to the loop, not the plane of the loop. This is the most common mistake on introductory flux calculation MCQs.
2. Faraday's Law of Induction★★★☆☆⏱ 5 min
Faraday's Law of Induction formalizes the relationship between changing magnetic flux and induced EMF. It states that the induced electromotive force around a closed loop is equal to the negative rate of change of magnetic flux through the loop, multiplied by the number of turns in the coil.
\varepsilon = -N \frac{d\Phi_B}{dt}
For a finite change in flux over a time interval $\Delta t$, we use the average induced EMF form:
Each turn of the coil experiences the same flux change, so EMF adds in series, hence multiplication by $N$. The negative sign encodes direction information, which we handle separately with Lenz's Law, so we almost always just calculate the magnitude of EMF first. A common special case is motional EMF, which simplifies to $\varepsilon = BLv$ when speed $v$ is perpendicular to $B$ and rod length $L$.
Exam tip: Write $N$ explicitly into your Faraday's Law equation at the start of every problem, even if $N=1$. This eliminates the common mistake of forgetting to multiply by $N$ for multi-turn coils on FRQs.
3. Lenz's Law★★★☆☆⏱ 3 min
Lenz's Law gives the direction of induced EMF and induced current in a closed conducting loop. It states: *The induced current flows in a direction that creates a magnetic field that opposes the change in magnetic flux that produced the induction*. A critical point: Lenz's Law opposes the change in flux, not the flux itself — this is the most common point of confusion for students.
Find the direction of the original magnetic field through the loop.
Determine if the total flux through the loop is increasing or decreasing.
If flux is increasing, the induced magnetic field points opposite the original field; if flux is decreasing, the induced magnetic field points in the same direction as the original field.
Use the right-hand rule for current loops to find the direction of induced current from the direction of the induced magnetic field.
Exam tip: Always explicitly note whether flux is increasing or decreasing before finding the direction of induced $B$. This step prevents the common mistake of always making induced $B$ opposite the original field.
4. Common AP Problem Types★★★★☆⏱ 5 min
Common Pitfalls
Why: Problems often give the angle between the plane and $B$ directly, leading students to confuse the definition of $\theta$.
Why: Students treat a coil the same as a single loop, forgetting each turn adds EMF in series.
Why: Students misremember Lenz's Law as 'opposes the magnetic field' instead of 'opposes the change in flux'.
Why: Students confuse flux with change in flux, especially for rotation problems that take a loop from maximum to zero flux.
Why: Students memorize $\varepsilon = BLv$ without remembering the restriction that $v$ must be the perpendicular component.