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Grade 10-11 (age 15-17)

high school physics Magnetic Field & Induction

A coil develops an emf only while the magnetic flux Φ through it is changing; if the flux stays constant, no current flows, however strong the magnet beside it. The size of the emf is set by how fast the flux changes, that is, the slope ΔΦ/Δt of the Φ-t graph multiplied by the number of turns N. Pushing a magnet toward the coil faster, or spinning the coil faster, makes the slope steeper, and generators and transformers run on this same principle. As the slider changes the flux change rate, the slope of the graph and the emf of a 100-turn coil change together.

An EMF Appears Only While the Flux Changes

2 Wb/s
👀 Reading the Graph
①The blue line is the flux Φ growing with time, and its slope is the flux change rate ΔΦ/Δt
②In the dashed orange triangle, the horizontal side runs from 0.1 s to 0.3 s, so Δt = 0.2 s, and the vertical side is the flux gained in that time, ΔΦ
③Doubling the slope doubles the induced emf V = N × ΔΦ/Δt
④With the rate set to 0 the line lies flat on the time axis; the flux does not change, so the emf is 0 too

Flux and Faraday's Law

Magnetic flux
Φ = B A
The product of the field B perpendicular to the coil and the coil's area A: the amount of field passing straight through the coil (unit Wb)
Faraday's law
V = N ΔΦΔt
The induced emf equals the number of turns N times the flux change rate ΔΦ/Δt. What sets the value is how fast the flux changes, not how large it is

Lenz's Law: Direction of the Current

🧲 Against the Change
①The induced current flows in the direction that opposes the change in flux (Lenz's law)
②If the flux is growing, the current sets up a field that holds the growth back; if it is shrinking, a field that makes up for the loss
③When the N pole of a magnet is pushed into a coil, the near end of the coil becomes an N pole and pushes the magnet back; when it is pulled out, that end becomes an S pole and pulls on the magnet
④If the current ran the other way, the change would feed itself and energy would appear from nothing, so Lenz's law goes hand in hand with energy conservation

Examples

Example 1
In 0.2 s, the flux through a single-turn coil changes from 0.1 Wb to 0.5 Wb. Find the magnitude of the induced emf.
1
The change in flux is ΔΦ = 0.5 − 0.1 = 0.4 Wb.
2
Put N = 1 and Δt = 0.2 s into V = N·ΔΦ/Δt.
V = 1 × 0.40.2 = 2 V
▸ 2 V
Dividing the initial flux 0.1 Wb or the final flux 0.5 Wb by the time is wrong; what sets the emf is the change, 0.4 Wb.
Example 2
The flux through a 100-turn coil takes 0.01 s to change by 0.02 Wb. Find the magnitude of the induced emf.
1
The coil has 100 turns, so multiply by N = 100.
V = N ΔΦΔt
2
The flux change rate is ΔΦ/Δt = 0.02/0.01 = 2 Wb/s.
V = 100 × 2 = 200 V
▸ 200 V
Leaving out the turns N gives 2 V, only 1/100 of the right answer.

Wrap-up

Key result
Φ = B A, V = N ΔΦΔt
Flux is B × A, the induced emf is the number of turns times the flux change rate, and the induced current flows in the direction that opposes the change
2021 CSAT Science (Physics I) type, adapted
The flux through a 200-turn coil takes 0.1 s to change uniformly by 0.3 Wb. What is the magnitude of the induced emf?
①60 V
②200 V
③300 V
④600 V
⑤900 V
▸ ④ 600 V
1
Put N = 200, ΔΦ = 0.3 Wb and Δt = 0.1 s into V = N·ΔΦ/Δt.
V = 200 × 0.30.1
2
The flux change rate is 3 Wb/s; multiply it by the 200 turns.
V = 200 × 3 = 600 V
🎯 Exam Points
①Flux is Φ = BA, measured in Wb
②In Faraday's law V = N·ΔΦ/Δt, do not leave out the turns N
③The slope of a Φ-t graph is the flux change rate, so a steeper slope means a larger emf
④A large but constant flux has slope 0 and induces no current
⑤By Lenz's law, the induced current flows in the direction that opposes the change in flux
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Current and Resistance
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Uniform Circular Motion

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