Inductor in AP Physics C: Electricity and Magnetism

In AP Physics C: E&M, an inductor is a circuit element (usually a coil of wire) that opposes changes in current by inducing an emf, ε = −L(dI/dt), and stores energy in its magnetic field, U = ½LI².

What is Inductor?

An inductor is a coil of wire, sometimes wrapped around an iron or ferrite core, that pushes back whenever the current through it tries to change. When current flows, the coil builds a magnetic field and magnetic flux through its own turns. If the current changes, that flux changes too. Faraday's law says a changing flux induces an emf, and Lenz's law says that emf opposes the change. So the inductor's back emf is ε = −L(dI/dt), where L is the inductance in henries (H).

Think of an inductor as inertia for current. A heavy object resists changes in velocity. An inductor resists changes in current. It doesn't care how big the current is, only how fast it's changing. While current flows, the inductor stores energy in its magnetic field, U = ½LI², and it can hand that energy back to the circuit when the current drops. An ideal inductor has no resistance, so in steady DC it acts just like a plain wire.

Why Inductor matters in AP® Physics C: E&M

Inductors live in Unit 13: Electromagnetic Induction, across three topics. In 13.4 Inductance you define L, use ε = −L(dI/dt), and calculate stored energy. In 13.5 LR Circuits the inductor's resistance to change produces exponential current growth and decay with time constant τ = L/R. In 13.6 LC Circuits it trades energy back and forth with a capacitor and oscillates at ω = 1/√(LC).

The inductor is where Faraday's law stops being abstract flux-through-a-loop math and becomes a real circuit component you analyze with Kirchhoff's rules. That makes it one of the main bridges between Unit 11 (circuits) and Unit 13 (induction), and it shows up regularly in both MCQs and lab-style FRQs.

How Inductor connects across the course

Faraday's Law and Self-Inductance (Unit 13)

An inductor is Faraday's law turned back on itself. The coil's own changing current changes its own flux, which induces an emf in that same coil. That's self-inductance, and ε = −L(dI/dt) is just Faraday's law with the flux written as LI.

Magnetic Field of a Solenoid (Unit 12)

Most AP inductors are solenoids. The Unit 12 result B = μ₀nI tells you the field inside, and multiplying flux by the number of turns gives L = μ₀N²A/ℓ. More turns, a wider coil, or a shorter coil all mean more inductance.

Capacitors and RC Circuits (Units 10-11)

The LR circuit is the RC circuit's mirror image. A capacitor resists sudden changes in voltage, and an inductor resists sudden changes in current. Both give exponential curves, with τ = RC for one and τ = L/R for the other, so the same graph-reading skills carry over.

LC Circuits and Oscillations (Unit 13)

Hook a charged capacitor to an inductor and energy sloshes back and forth, like a mass on a spring. The capacitor's electric energy plays the role of spring potential energy, and the inductor's ½LI² plays the role of kinetic energy, giving ω = 1/√(LC).

Is Inductor on the AP® Physics C: E&M exam?

Inductor questions usually ask you to do one of four things.

• Apply ε = −L(dI/dt). If I(t) = I₀sin(ωt), the emf is proportional to cos(ωt). So the maximum emf is LI₀ω, and it happens when the current is zero, not at its peak. For example, L = 30 mH with I = (2.0 A)sin(120πt) gives a max emf of about 23 V.
• Use U = ½LI² for scaling. Cut the current to I/3 and raise the inductance to 9L, and the energy is unchanged, because 9 × (1/9) = 1.
• Analyze LR circuits. Right after the switch closes, the inductor keeps the current at zero, so it acts like a break in the circuit. After a long time it acts like a wire, and the current settles at ε/R. You'll find the current or stored energy at specific times using τ = L/R.
• Design and linearize experiments. On the 2026 FRQ Q3, students collect data to graph and determine an inductor's inductance using several capacitors, which points to LC oscillation (T = 2π√(LC), so T² vs. C is linear). The 2024 FRQ Q2 puts an inductor of known L in series with a battery and resistors, and the goal is to find R. That's a classic time-constant setup. The 2019 FRQ Q2 also builds on a multi-battery resistor circuit. Expect to sketch I vs. t, justify behavior at t = 0 and t → ∞, and pull L or R from a slope.

Inductor vs Capacitor

A capacitor stores energy in an electric field (U = ½CV²) and resists sudden changes in voltage. An inductor stores energy in a magnetic field (U = ½LI²) and resists sudden changes in current. Their switch behavior is opposite. Right after a switch closes, an uncharged capacitor acts like a wire and an inductor acts like an open circuit. After a long time, the capacitor acts like an open circuit and the inductor acts like a wire.

Key things to remember about Inductor

• An inductor opposes changes in current by inducing a back emf given by ε = −L(dI/dt), so it reacts to how fast current changes, not to how big the current is.

• The energy stored in an inductor's magnetic field is U = ½LI², so doubling the current quadruples the stored energy.

• In an LR circuit, the inductor acts like an open circuit right after the switch closes and like an ordinary wire after a long time.

• The time constant of an LR circuit is τ = L/R, and the current approaches its final value of ε/R exponentially.

• In an LC circuit, energy oscillates between the capacitor and the inductor with angular frequency ω = 1/√(LC), just like a mass-spring system.

• When current is sinusoidal, the inductor's emf is greatest when the current is zero, because that's when the current is changing fastest.

Frequently asked questions about Inductor

What is an inductor in AP Physics C E&M?

An inductor is a coil that opposes changes in current by inducing an emf ε = −L(dI/dt) and stores energy in its magnetic field as U = ½LI². It's covered in Unit 13, Topics 13.4 through 13.6.

Does an inductor block current?

No. An ideal inductor only resists changes in current. In steady DC it behaves like a plain wire with zero resistance. It only looks like a break in the circuit at the instant a switch closes, when it stops the current from jumping up suddenly.

Is the induced emf in an inductor biggest when the current is biggest?

No. The emf depends on dI/dt, not I. For I = I₀sin(ωt), the emf is maximum (LI₀ω) when the current passes through zero, at t = 0, T/2, and T in the first cycle.

How is an inductor different from a capacitor?

A capacitor stores electric field energy (½CV²) and resists sudden voltage changes. An inductor stores magnetic field energy (½LI²) and resists sudden current changes. Their time constants are RC and L/R, and their behavior at t = 0 and t → ∞ is exactly opposite.

Are inductors on the AP Physics C E&M exam?

Yes. Recent FRQs feature them directly. The 2024 FRQ Q2 uses an inductor of known L in a battery-resistor circuit to find R, and the 2026 FRQ Q3 asks students to determine an inductance from graphed data. MCQs regularly test U = ½LI² scaling and ε = −L(dI/dt).