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Premium experiment • changing magnetic flux

PHYSICS • ELECTROMAGNETISM

Faraday’s Law & Electromagnetic Induction

Change field strength, rate of change, coil area, orientation and turn count to generate magnetic flux and induced current.

● CHANGING FLUXFaraday + Lenz
Flux linkage
Induced emf
Current
Power

Reasoning inspector

live model state
Coil turns N—
Coil area A—
Magnetic field B—
cos θ—
Flux Φ—
Flux linkage NΦ—
dB/dt—
Induced emf—
Induced current—
Resistive power—
Lenz direction—

Changing magnetic flux creates emf

The induced voltage scales with how rapidly total magnetic flux linkage changes. The minus sign encodes Lenz’s law: induction opposes the change that creates it.

LEARN WITH THE SIMULATION

Understand Faraday’s Law & Electromagnetic Induction by experimenting.

START HERE

Faraday’s law links induced voltage to change in magnetic flux rather than to magnetic field strength by itself. This laboratory separates static flux Φ = BA cosθ from flux linkage NΦ and the changing-field term that produces emf. By varying turns, area, coil orientation, dB/dt and circuit resistance, learners can distinguish what controls induced voltage from what only changes the instantaneous amount of flux.

BUILD THE IDEA

What you should understand first

  • Calculate magnetic flux Φ = BA cosθ and flux linkage NΦ.
  • Apply ℰ = −N dΦ/dt for a field changing at fixed area and orientation.
  • Use the sign of emf to interpret Lenz’s-law current direction.
  • Separate factors controlling induced emf from resistance, which changes induced current but not the emf source.

TRY IT YOURSELF

Can the magnetic flux change while the induced emf stays the same, or the static flux change while emf stays zero?

  1. Set a nonzero dB/dt and record emf, then change static B without changing the rate.
  2. Set dB/dt to zero and vary B; compare large static flux with zero emf.
  3. Restore dB/dt and rotate the coil toward 90°.
  4. Increase turn count and compare flux linkage, induced emf and current.
Read the visual:

In this simplified case emf depends on N, A, cosθ and dB/dt, not on the current value of B itself. Static B changes instantaneous flux, while dB/dt determines how fast that flux changes. Resistance changes current through I=ℰ/R after the emf is generated.

WHY IT WORKS 01

Flux and flux change are different quantities

Magnetic flux Φ=BA cosθ describes how much magnetic field passes through the oriented loop at an instant. Faraday’s law depends on dΦ/dt. A coil can have a large static Φ with dΦ/dt=0 and therefore no induced emf, which is why the inspector shows flux and induced voltage separately.

WHY IT WORKS 02

Turns multiply linkage and induced voltage

For N tightly coupled identical turns, each turn experiences approximately the same flux, so the total flux linkage is NΦ. Differentiating that linkage gives ℰ=−N dΦ/dt. Doubling N therefore doubles induced emf under the model assumptions without changing the per-turn magnetic flux.

WHY IT WORKS 03

Resistance belongs to the circuit response, not Faraday’s source law

Faraday’s law determines the induced emf. Once a resistive loop is specified, Ohm’s law gives I=ℰ/R and dissipation P=I²R. Increasing resistance reduces current and power for the same induced emf, but it does not change the emf created by the prescribed flux-change rate in this idealized model.

DO NOT MIX THESE UP

Common misconception

A strong magnetic field does not automatically induce a voltage; magnetic flux must change with time. Flux can change because B, area or orientation changes, although this simulator varies only dB/dt while treating area and angle as fixed during each instantaneous calculation. The minus sign represents Lenz’s law, not a loss of voltage magnitude.

PRACTICE CHALLENGE

Can you hit a target induced voltage and then prove that changing static B alone does not change that voltage?

  • Choose a target |emf| and reach it using turns, area, angle or dB/dt.
  • Record static B, flux and emf.
  • Change only static B while holding dB/dt fixed.
  • Explain why flux changes but induced emf remains the same in the modeled scenario.
Reveal the reasoning

With fixed area and orientation, ℰ=−NA cosθ·dB/dt. Static B determines Φ=BA cosθ but does not appear in the derivative when dB/dt is independently prescribed. Therefore changing B alone changes instantaneous flux while leaving the modeled induced emf unchanged.

MODEL BOUNDARIES

What this simulation assumes

Every simulation simplifies reality or a mathematical system. These are the assumptions and limits to keep in mind while interpreting the results.

Model assumptions

  • Magnetic field is uniform across the coil area and changes linearly at the selected dB/dt.
  • Flux uses Φ = BA cosθ and total flux linkage is NΦ.
  • Induced current follows Ohm's law using one lumped resistance.

Model limitations

  • Self-inductance, coil impedance, nonuniform fields, eddy currents and transient circuit dynamics are omitted.
  • Current direction is reported from the emf sign in a simplified loop convention.

CONNECT IT

Where this matters

  • Electrical generators
  • Transformers and induction coils
  • Inductive sensors
  • Wireless power and magnetic pickup systems

WORDS THAT MATTER

Key vocabulary

Magnetic flux
Oriented magnetic-field passage through a surface, Φ = BA cosθ for a uniform field.
Flux linkage
Total linked flux NΦ for a coil with N equivalent turns.
Electromotive force
Induced circuit voltage generated by changing magnetic flux.
Lenz’s law
Direction rule encoded by the minus sign: induced effects oppose the flux change that produces them.
dB/dt
Rate of magnetic-field change with time, one possible cause of changing magnetic flux.