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Concept module

Faraday's Law and Lenz's Law

Track one magnet passing one coil and see how changing magnetic flux linkage creates induced emf while Lenz's law fixes the response direction, with the stage, galvanometer, and graphs all driven by the same bounded motion.

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Starter track

Step 2 of 30 / 3 complete

Magnetism

Earlier steps still set up Faraday's Law and Lenz's Law.

1. Magnetic Fields2. Faraday's Law and Lenz's Law3. Magnetic Force on Moving Charges and Currents

Previous step: Magnetic Fields.

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Why it behaves this way

Explanation

Faraday's law is the bridge moment where magnetism stops being just a field pattern and starts becoming a source of electrical response. A magnetic field through a loop is not enough by itself. The loop only develops an emf when the magnetic flux through that loop changes, and Lenz's law fixes the sign so the induced effect opposes the change that produced it.

This module keeps one compact moving-magnet-and-coil picture in charge. One bar magnet passes one coil on one shared axis. The same magnet position, speed, pole orientation, coil turns, and coil area determine the stage, the galvanometer, the current arrows, the flux graph, the induced-response graph, the worked examples, the prediction prompts, the checkpoint challenge, and the quick test, so the Faraday/Lenz story stays tied to one honest changing setup instead of turning into a detached formula rule.

Key ideas

01Induced emf depends on changing flux linkage $\Lambda = N\Phi$, not on the mere presence of a magnetic field.

02Relative change matters. A strong magnetic field can exist through the coil while the induced emf is still zero if the flux is not changing at that instant.

03More turns, larger coil area, stronger magnetic coupling, or faster relative motion can all increase the induction signal because they increase how much linked flux changes.

04Reversing the motion direction or flipping which pole faces the coil reverses the sign of the induced emf and current. Lenz's law says that sign always opposes the change in flux.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Work directly from the live moving-magnet state on screen. The same magnet pass, coil geometry, and polarity now driving the stage also set the flux linkage, emf, and current below.

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Frozen valuesUsing frozen parameters

For the current magnet pass, what flux linkage, induced emf, and loop current does the coil have right now?

B_{0}

Magnet strength

1.4 T

N

Coil turns

120 turns

A

Coil area

1 m^2

v

Magnet speed

1.2 m/s

x_{m}

Magnet position

-2.6 m

1. Read the live magnet pass

The magnet is at

x_{m} = - 2.6 m

with

v = 1.2 m/s

, so it is approaching the coil.

2. Evaluate the signed field through the coil

With pole sign

s = + 1

, the bounded field model gives

B_{coil} = 0.24 T

3. Build the linked flux

Using

N = 120

and

A = 1 m^{2}

, the coil links

Λ = N A B_{coil} = 0.52 Wb \cdot turn

in this bounded setup.

4. Turn changing flux into emf and current

Faraday's law gives

E = - d Λ/ d t = - 0.4 V

, so the loop current is

I = - 0.17 A

Induction state

Λ = 0.52 Wb \cdot turn, E = - 0.4 V, I = - 0.17 A

The linked flux is changing enough to drive a clockwise current in the stage convention, which is the model's Lenz-law response to the present change.

Flux-change checkpoint

Suppose the magnet is centered in the coil and the coil is linking a strong field at that instant. Should the galvanometer necessarily show a large deflection? Answer from flux-change logic, not from field-size intuition.

Make a prediction before you reveal the next step.

Predict what the induced-response graph should do at the instant the flux curve reaches a maximum or minimum.

Check your reasoning against the live bench.

No. The galvanometer can read zero even at a strong-field moment if the flux linkage is not changing right then.

Faraday's law cares about

d Λ/ d t

, not just

Λ

. At the top or bottom of the flux curve, the slope is zero, so the induced emf and current cross through zero even though the field and linked flux can still be large.

Common misconception

If the magnetic field through the coil is large, the induced emf must also be large.

A large field can produce a large flux, but induction depends on the rate of change of flux. A flat flux curve gives zero emf even at a strong-field moment.

That is why the induced-response graph crosses zero when the magnet is centered in a symmetric pass: the flux is momentarily at an extremum, so its slope is zero there.

Quick test

Reasoning

Question 1 of 4

Answer from flux-change reasoning, not from isolated formulas or memorized slogans.

A coil sits in a steady magnetic field that is not changing through time. Which statement is best?

Use the live bench to test the result before moving on.

Accessibility

The simulation shows one circular coil fixed at the center of the stage and one bar magnet sliding horizontally past it. A field band marks the signed magnetic field through the coil, a galvanometer card reports induced emf and current, and optional arrows show the loop-current direction when the response is not zero.

A live readout lists time, magnet position, field through the coil, flux-change rate, induced emf, and current. The same shared pass also drives the graphs, so hovering the time-based plots previews the corresponding moment on the stage.

Graph summary

The first graph compares the field through the coil with the linked flux. The second graph compares induced emf with loop current over the same time axis.

The key accessibility takeaway is that the response graph depends on how quickly the linked flux changes, not on whether the field or flux itself is merely large at one instant.

Keep the electricity-magnetism story moving

Keep this idea moving

Open the next concept, route, or track only when you want the current model to widen into a larger branch.

Tie the four laws togetherElectromagnetism