Induced current in AP Physics 2

Induced current is the electric current that flows in a conducting loop or circuit when the magnetic flux through it changes; you find it by first getting the induced EMF from Faraday's law, then applying I = ε/R, where R is the circuit's resistance.

Verified for the 2027 AP Physics 2 examLast updated June 2026

What is Induced current?

An induced current is what you get when electromagnetic induction meets a closed circuit. Change the magnetic flux through a conducting loop (by changing the field strength, the loop's area, or the angle between them, since Φ_B = BA cos θ) and Faraday's law says an EMF appears. If the loop is a complete circuit with resistance R, that EMF pushes charge around it, and the resulting current is I = ε/R.

The key idea is the chain of cause and effect. Changing flux creates an induced EMF, and the EMF drives the induced current. No change in flux means no EMF and no current, no matter how strong the magnetic field is. A loop sitting still in a huge constant field has zero induced current. The direction of the induced current comes from Lenz's law, so the current always flows in the direction that opposes the change in flux that created it.

Why Induced current matters in AP® Physics 2

Induced current lives in Topic 12.4 (Electromagnetic Induction and Faraday's Law) in Unit 12: Magnetism and Electromagnetism, supporting learning objective 12.4.A, which asks you to describe the induced electric potential difference resulting from a change in magnetic flux. It's also the payoff of the whole unit. Earlier topics build up magnetic fields and flux; induced current is where that machinery produces something measurable in a circuit. It's the physics behind generators, transformers, and induction stoves, and it's one of the most reliable calculation setups on the AP Physics 2 exam because it chains together flux, Faraday's law, and Ohm's law in one problem.

How Induced current connects across the course

Induced EMF (Unit 12)

Induced EMF is the cause, induced current is the effect. Faraday's law gives you the EMF from the changing flux, and the current only shows up if there's a closed conducting path. An open loop still has an induced EMF but carries zero current.

Ohm's Law and Resistance (Unit 11)

Every induced current calculation ends with circuit physics from Unit 11. The induced EMF acts like a battery, so I = ε/R, and you can go further to find power dissipated in the loop with P = I²R. Induction problems are secretly circuit problems with a flux-powered battery.

Magnetic Force on Current-Carrying Conductors (Unit 12)

Once a rod or loop carries an induced current inside a magnetic field, the field exerts a force F = BIL on it. By Lenz's law that force opposes the motion, which is why the classic rod-on-rails problem needs an applied force just to keep the rod moving at constant velocity.

Mutual Inductance (Unit 12)

Mutual inductance is induced current between circuits. A changing current in one coil (like a solenoid) changes the flux through a nearby loop, inducing a current there even though the two circuits never touch. This is how transformers work.

Is Induced current on the AP® Physics 2 exam?

Induced current shows up in a handful of repeatable setups. The conducting rod sliding on rails gives motional EMF (ε = BLv), then I = BLv/R. A loop in a time-varying field like B = B₀ sin(ωt) asks you to recognize that current is biggest when the flux is changing fastest, not when B is biggest. A loop being pulled out of a field region only has an induced current while the flux is actually changing, so watch for the moment the loop is fully in or fully out. A small loop inside a solenoid with changing current tests whether you can chain the solenoid's field into the loop's flux. Released FRQs, including 2025 FRQ Q1 on current-carrying wires, expect you to combine field, flux, and induction reasoning in one problem. For full credit you usually need three moves in order. Compute the rate of change of flux, apply Faraday's law to get ε, then apply I = ε/R, and use Lenz's law to justify the current's direction in words.

Induced current vs Induced EMF

Induced EMF is the voltage created by changing flux; induced current is the charge flow that EMF drives if a closed circuit exists. Faraday's law always gives you an EMF when flux changes, but you only get a current when there's a complete conducting path with finite resistance. On the exam, ε = ΔΦ/Δt is the Faraday step and I = ε/R is the separate Ohm's law step. Mixing them up (or forgetting to divide by R) is one of the most common point-losers on induction problems.

Key things to remember about Induced current

  • Induced current is found in two steps. Use Faraday's law to get the induced EMF from the changing magnetic flux, then use I = ε/R to get the current.

  • Only a changing flux induces current. A strong but constant magnetic field through a stationary loop induces nothing.

  • Flux can change three ways, through the field magnitude B, the area A, or the angle θ in Φ_B = BA cos θ, and the exam tests all three.

  • Lenz's law gives the direction. The induced current always flows so that its own magnetic field opposes the change in flux that created it.

  • For a rod sliding on rails, the motional EMF is ε = BLv, so the induced current is I = BLv/R.

  • When the field varies like B₀ sin(ωt), the induced current is largest when the flux is changing fastest, which is when B passes through zero, not at its peak.

Frequently asked questions about Induced current

What is induced current in AP Physics 2?

It's the current that flows in a closed conducting loop when the magnetic flux through the loop changes. You calculate it with I = ε/R, where ε is the induced EMF from Faraday's law and R is the circuit's resistance. It's tested in Topic 12.4 of Unit 12.

How is induced current different from induced EMF?

Induced EMF is the voltage produced by changing flux, and it exists even in an open loop. Induced current is the charge flow that EMF drives, and it only exists in a complete circuit. Get the EMF first with Faraday's law, then divide by resistance to get current.

Does a constant magnetic field induce a current?

No. A loop sitting still in a constant, uniform field has constant flux, so the induced EMF and induced current are both zero. Current is only induced while the flux is actively changing, like when the loop moves, rotates, or the field strength varies.

How do you find the direction of an induced current?

Use Lenz's law. The induced current flows in whichever direction makes a magnetic field that opposes the change in flux. If flux into the page is increasing, the induced current flows counterclockwise to push flux back out of the page.

What's the formula for induced current in the rod-on-rails problem?

A rod of length L moving at speed v perpendicular to field B generates a motional EMF of ε = BLv, so the induced current is I = BLv/R. This setup is one of the most common induction problems on the AP Physics 2 exam, and it often pairs with a force question since the field pushes back on the current-carrying rod with F = BIL.

Induced Current — AP Physics 2 Definition & Exam Guide | Fiveable