Lesson 10 of 10 · 15 min
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Faraday, Lenz and inductance, full chapter
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Must-know facts
17 facts
- 01An emf is induced only while the magnetic flux through a circuit is changing.
- 02ΦB = B·A = BA cos θ, θ between B and the normal; unit weber, 1 Wb = 1 T m².
- 03Faraday's law: ε = −N dΦB/dt for a coil of N turns.
- 04Flux changes if B, the area or the angle between B and the normal changes.
- 05Lenz's law: the induced current opposes the change in flux that causes it; this follows from energy conservation.
- 06An N pole approaching a coil makes the near face an N pole (repulsion); receding, an S pole (attraction).
- 07Motional emf across a rod moving at right angles to B: ε = Blv.
- 08Rod of length R rotating about one end with angular speed ω: ε = ½BωR².
- 09A time-varying magnetic field produces an electric field.
- 10Flux linkage NΦ = LI (self) or N₁Φ₁ = MI₂ (mutual); unit henry, dimensions [M L² T⁻² A⁻²].
- 11Long coaxial solenoids: M = μ₀n₁n₂πr₁²l; M₁₂ = M₂₁.
- 12Long solenoid: L = μ₀n²Al, or μrμ₀n²Al with a core.
- 13Self-induced emf ε = −L dI/dt opposes both rise and fall of current.
- 14Energy stored in an inductor: ½LI²; magnetic energy density B²/2μ₀.
- 15AC generator: ε = NBAω sin ωt, peak ε₀ = NBAω.
- 16Generator emf is maximum when the coil's plane is parallel to B and zero when it faces B.
- 17Supply frequency: 50 Hz in India, 60 Hz in the USA.
Common traps
Where marks are lost
Formulas
10 to know
Magnetic flux
ΦB = B·A = BA cos θ
θ between B and the normal; unit Wb = T m².
Faraday's law
ε = −N dΦB/dt
Minus sign is Lenz's law.
Motional emf
ε = Blv
Rod, velocity and field mutually perpendicular.
Rotating rod
ε = ½BωR²
Between pivot and free end; field along the axis.
Mutual inductance, coaxial solenoids
M = μ₀n₁n₂πr₁²l
r₁ is the inner radius; multiply by μr for a core.
Mutually induced emf
ε₁ = −M dI₂/dt
M₁₂ = M₂₁.
Self-inductance of a solenoid
L = μrμ₀n²Al
μr = 1 for air.
Self-induced emf
ε = −L dI/dt
Back emf.
Energy in an inductor
U = ½LI², u = B²/2μ₀
u is energy per unit volume.
AC generator emf
ε = NBAω sin ωt, ε₀ = NBAω
ω = 2πν; θ = 0 at t = 0.
Key terms
16 terms
- Electromagnetic induction
- Producing an emf, and a current in a closed circuit, by changing the magnetic flux through it.
- Magnetic flux (ΦB)
- B·A summed over a surface; a scalar measured in webers.
- Weber (Wb)
- SI unit of magnetic flux, 1 T m².
- Faraday's law
- Induced emf equals minus the rate of change of flux linkage.
- Lenz's law
- The induced current flows so as to oppose the change in flux that produced it.
- Motional emf
- The emf Blv across a conductor moving through a magnetic field.
- Flux linkage
- NΦB for a closely wound coil of N turns.
- Inductance
- Flux linkage per unit current; depends on geometry and core material.
- Henry (H)
- SI unit of inductance, 1 Wb/A.
- Mutual inductance (M)
- Flux linkage in one coil per unit current in another; the same either way round.
- Self-inductance (L)
- A coil's own flux linkage per unit current in it; electrical inertia.
- Back emf
- The self-induced emf −L dI/dt that opposes changes in current.
- Magnetic energy density
- Energy stored per unit volume in a magnetic field, B²/2μ₀.
- AC generator
- A machine that turns a coil (or magnets) to make an alternating emf NBAω sin ωt.
- Armature
- The rotating coil of a generator.
- Slip rings and brushes
- Sliding contacts that carry the generator coil's current to the outside circuit.