Electromagnetic induction is the phenomenon in which changes in magnetic flux produce voltage. Faraday’s law and Lenz’s law determine its direction and magnitude.
Basic Knowledge
Magnetic flux Φ [Wb = T·m²]: The amount of magnetic field passing through area S in the perpendicular direction:Φ = BS cosθ（θ: the angle between the magnetic field and the normal to the surface）
Faraday’s law of electromagnetic induction:ε = −N dΦ/dt
（ε: induced electromotive force, N: number of turns in the coil, dΦ/dt: rate of change of magnetic flux with time）
Lenz’s law: The induced current flows in the direction that opposes the change in magnetic flux that produced it.
Electromotive force of a conducting rod（a rod of length L moving at speed v in a magnetic field）:ε = BLv（when the rod is perpendicular to both the magnetic field and its velocity）
Magnetic flux Φ (magnetic flux)（the amount of magnetic field passing through a surface. Unit: Wb = T·m²）
Faraday’s law（induced electromotive force is proportional to the rate of change of magnetic flux）
Lenz’s law（induced current flows in the direction that opposes the change in magnetic flux）
Induced electromotive force ε（electromotive force produced by electromagnetic induction. ε = BLv）
Self-induction and mutual induction（phenomena in which changes in the current of the same/nearby coil produce electromotive force）
Further Exploration (Background and Significance)
The principle of every generator is electromagnetic induction. When a coil rotates in a magnetic field, its magnetic flux changes sinusoidally, producing an alternating electromotive force ε = NBAω sinωt.
Self-induction produces the property that opposes changes in current (inductance L): ε = −L dI/dt. An inductor has impedance X_L = ωL for alternating current.
A transformer uses mutual induction and converts voltage according to V₁/V₂ = N₁/N₂. It is essential for reducing power loss in long-distance transmission by stepping up the voltage (power loss P = I²R → increase voltage and reduce current).
- Magnetic flux Φ = BS cosθ
- Faraday: ε = −N dΦ/dt
- Lenz: direction that opposes the change in magnetic flux
- Electromotive force of a conducting rod: ε = BLv
- Self-induction: ε = −L dI/dt
- Transformer: V₁/V₂ = N₁/N₂
- The principles of generators and transformers are electromagnetic induction
Notes (Easily Confused Points)
① The minus sign in Faraday’s law mathematically expresses Lenz’s law. ② A change in magnetic flux produces electromotive force (not magnetic flux itself). ③ When determining the direction using Lenz’s law, first check whether the magnetic flux is increasing or decreasing. ④ ε = BLv applies only when the conducting rod is perpendicular to both the magnetic field and its velocity.
Practice
- Find the induced electromotive force when the magnetic flux through a 100-turn coil changes by 0.10 Wb in 0.02 s.
- Find the electromotive force produced when a conducting rod of length L = 0.30 m moves at v = 2.0 m/s in a magnetic field with flux density B = 0.50 T.
- An induced current is produced when a magnet is brought near a coil. Explain the direction of the induced current using Lenz’s law when the magnet is brought even closer.