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Grade 11-12 (age 16-18)

high school physics Electromagnetic Induction

Moving a magnet near a coil makes a current flow in the coil, and when the magnet stops, the current soon disappears. What produces the current is not the strength of the field itself but a change in the magnetic flux Φ through the coil, and the faster the flux changes, the larger the induced emf. Faraday's law writes this as ε = −N dΦ/dt, and the minus sign stands for Lenz's law: the induced current flows in the direction that opposes the change in flux. In the picture, changing the rate of flux change dΦ/dt changes both the size of the emf and the direction of the induced current in the loop.

Moving a Magnet Drives a Current

🧲 Faraday's Discovery
①When a magnet moves near a coil, the needle of a galvanometer connected to the coil moves
②When the magnet stops, the needle returns to 0, and when the magnet moves the other way, the needle swings the other way too
③The condition for a current is not that a magnet is present but that the flux through the coil is changing

Changing Flux and Induced Current

5 Wb/s
💡 Reading the Picture
①When dΦ/dt is positive, the flux into the screen is increasing, so the induced current flows counterclockwise and makes a field out of the screen (⊙)
②When dΦ/dt is negative, the flux is decreasing, so the induced current flows clockwise and adds field into the screen (⊗)
③Either way the induced current opposes the change in flux, and the larger the rate, the larger the emf and current
④With dΦ/dt at 0, no current is induced even though the field is still there

Faraday's Law

Faraday's Law of Induction
ε = −dΦdt
The induced emf is the time rate of change of the flux with a minus sign
Coil with N Turns
ε = −NdΦdt
The more turns N, the larger the induced emf for the same change in flux
Magnetic Flux
Φ = BA cosθ
Φ: flux (Wb), B: magnetic field (T), A: area (m²), θ: angle between the field and the normal to the surface

Lenz's Law

🔄 Lenz's Law: Opposing the Change
①The induced current flows in the direction that opposes the change in flux
②When the flux increases, the induced current makes a field opposite to the original field
③When the flux decreases, the induced current makes a field in the same direction as the original field, making up for the loss
④The minus sign in Faraday's law expresses exactly this direction
⑤The motional emf ε = Bℓv of a wire moving through a field, a generator that turns a coil to change θ, and a transformer that changes voltage by the turns ratio ε₁/ε₂ = N₁/N₂ all rest on the same principle

Worked Examples

Example 1
In a 200-turn coil, the magnetic flux takes 0.5 s to change by 0.01 Wb. What is the magnitude of the induced emf?
1
Use the magnitude form of Faraday's law, ε = N ΔΦ/Δt.
ε = NΔΦΔt
2
Substitute N = 200, ΔΦ = 0.01 Wb and Δt = 0.5 s.
ε = 200 × 0.010.5 = 4 V
▸ 4 V
The size of the emf is turns × rate of flux change. The minus sign indicates direction, so use the absolute value when finding the size.
Example 2
A single loop of area 0.5 m² sits in a perpendicular magnetic field that, over 0.2 s, rises from 0.1 T to 0.3 T. What is the induced emf?
1
The surface is perpendicular to the field, so θ = 0 and Φ = BA; the change in flux is ΔΦ = ΔB × A.
ΔΦ = ΔB·A = (0.3 − 0.1) × 0.5 = 0.1 Wb
2
Substitute into ε = ΔΦ/Δt.
ε = 0.10.2 = 0.5 V
▸ 0.5 V
Even with the area and angle unchanged, a changing field alone changes the flux and produces an emf. If the field had stayed at 0.1 T, the emf would be 0.

Summary

Faraday's Law
ε = −NdΦdt
The size of the induced emf is turns × rate of flux change, and the sign marks the direction that opposes the change
CSAT-style problem, adapted
A coil has induced EMF ε. If the number of turns is doubled and the rate of flux change is also doubled, what is the induced EMF?
①2ε
②3ε
③4ε
④ε2
⑤6ε
▸ ③ 4ε
1
Since ε = N dΦ/dt, the emf is proportional to both N and dΦ/dt.
ε = NdΦdt
2
N doubles and dΦ/dt doubles, so the emf becomes 2 × 2 = 4 times as large.
(2N)(2dΦdt) = 4NdΦdt = 4ε
🎯 Exam Points
①Since ε = −N dΦ/dt, the emf is larger when the flux changes faster and when there are more turns
②Lenz's law: the induced current flows in the direction that opposes the change in flux
③In Φ = BA cosθ, a change in any one of B, A or θ causes induction
④A generator turns a coil to change θ, which changes Φ and produces an emf
⑤A transformer follows ε₁/ε₂ = N₁/N₂, changing voltage by the turns ratio
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