Faraday Induction

• Animation – Faraday induction• Magnetism and Induction Roadmap• Magnetic Flux / Induced emf• Lenz’s Law• Examples of Lenz’s Law• Examples of Induced emf• Generators• Transformers

Induction animation

https://phet.colorado.edu/en/simulation/faradays-law

faradays-law_en.jar

Magnetism and Induction Flowchart

law change field Current force direct examples

Force Law 1 B → qv → F = qv x B RHR 1 charge deflection picture tube

Force Law 2 B → il → F = il x B RHR 1 2 wires, motor, loudspeaker

Ampere’s Law

B = μoi/2πr ← i RHR 2 electromagnet solenoid

Faraday Induction

d/dt → Φ = B*A → ε = dΦ/dt i = ε/R

Lentz generator transformer

Changing magnetic field creates current

Magnetic flux and induced emf• Magnetic Flux

– Area “vector” perpendicular to Area

– If area “vector” inline with field, area perpendicular to field

– Flux units weber of T-m2

• Induced emf

• Units

Direction of Induced Current• Lenz’s Law

– Induced current will create magnetic field to oppose **change** that produced it

– Natural logic – things are not going to reinforce change that produces them – perpetual motion!

• Flux can change in 3 ways – Area– Orientation– Magnetic Field

Examples of Lenz’s Law – Fig 21-6

• Fig 21-6

Flux down -> flux less down, change up, oppose change down, current CW

• Fig 21-7

Examples of Lenz’s Law – Fig 21-9

a) Flux up -> flux less up, change down, oppose change up, current CCW

b) Flux down -> flux less down, change up, oppose change down, current CW

c) Flux down -> flux more down, change down, oppose change up, current CCW

d) Magnetic field parallel to plane, no flux, no change in flux, no induced emf

e) Flux zero, flux increasing to left, change to left, oppose change right, current CW

Examples of Lenz’s Law – Fig 21-11

a) Flux down -> flux more down, change down, oppose change up, current CCW

b) Flus down -> flux less down, change up, oppose change down, current CW

c) No changing flux, no induced current.

d) Flux down -> flux more down, change down, oppose change up, current CCW

Calculation of induced emf (1)

• Know– B = 0.6 T– Width 5 cm– 100 turns– Time 0.1 s– R = 100 ohms

• Find– Emf, current (1.5 v 15 mA)– Force required (.045 N)– Work done by that force (2.25 mJ)– Power, Work (22.5 mW, 2.25 mJ)

Calculation of induced emf (2)• Emf for single loop

• Emf for 100 loops

• Current

clockwise by Lentz’s Law

i

Calculation of induced emf (3)• Mechanical force to pull loop out

to left

• Mechanical work to pull loop out

• Electrical power dissipated during pulling • Electrical energy lost to pull loop out

Other examples

1. Change in B

Other examples2. Change in A

Other examples2. Change in A

• EMF from Flux (0.168V)• EMF from qvB• Current (0.168V/27.5 ohm = 6.1 ma)• Force (0.64 mN)

Other examples

3. Change in θ

Generator

Generator

• Φ = BA cos(ωt)• ε = N dφ/dt• ε = NBωA sin(ωt)• Lentz’s Law• Problems 20-25– Prob 20 (42 loops)

Generator

• Φ = BA cos(ωt)• ε = N dφ/dt• ε = NBωA sin(ωt)• Lentz’s Law• Problems 20-25– Prob 20 (42 loops)

Generator and Transformer• Transformer– On Primary• Vp = Np ΔΦ /Δt

– On Secondary• Vs = Ns ΔΦ /Δt

– Since changing flux is same• Vs/Vp = Ns/Np

– Power is conserved• Is/Ip = Np/Ns

– Problems 30-

Applications

– Electric generators – Car alternators– Transformers (why our power is AC)– Hard drives, magnetic tapes– Credit-card readers (why you always “swipe”)