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

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

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 il → F = il x B 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 Φ 𝐵 = 𝐵 ┴ 𝐴=𝐵𝐴 𝑐𝑜𝑠𝜃 Area “vector” perpendicular to Area If area “vector” inline with field, area perpendicular to field Flux units weber of T-m2 Induced emf ℰ=− ∆ Φ 𝐵 ∆𝑡 (𝑠𝑖𝑛𝑔𝑙𝑒 𝑙𝑜𝑜𝑝) ℰ=−𝑁 ∆ Φ 𝐵 ∆𝑡 (𝑁 𝑙𝑜𝑜𝑝𝑠) Units 𝑤𝑒𝑏𝑒𝑟 𝑠 = 𝑇∙ 𝑚 2 𝑠 = 𝑁 𝐴∙𝑚 ∙𝑚 2 𝑠 = 𝐽 𝐴 𝑠 = 𝐽 𝐶=𝑉𝑜𝑙𝑡𝑠

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 Φ 𝐵 = 𝐵 ┴ 𝐴=𝐵𝐴 𝑐𝑜𝑠𝜃 Area Orientation Magnetic Field

Examples of Lenz’s Law – 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 Flux up -> flux less up, change down, oppose change up, current CCW Flux down -> flux less down, change up, oppose change down, current CW Flux down -> flux more down, change down, oppose change up, current CCW Magnetic field parallel to plane, no flux, no change in flux, no induced emf Flux zero, flux increasing to left, change to left, oppose change right, current CW

Examples of Lenz’s Law – Fig 21-11 Flux down -> flux more down, change down, oppose change up, current CCW Flus down -> flux less down, change up, oppose change down, current CW No changing flux, no induced current.

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 ℇ= ∆ Φ 𝐵 ∆𝑡 = 0− 0.6 𝑇 2.5∙ 10 −3 𝑚 2 0.1 𝑠 =− 1.5∙ 10 −3 𝑁 𝐴∙𝑚 𝑚 2 0.1 𝑠 =−0.015 𝐽 𝐶 Emf for 100 loops ℇ=100 ∆ Φ 𝐵 ∆𝑡 =−1.5 𝑉 Current 𝑖= ℇ 𝑅 = 1.5 𝑉 100 Ω =15 𝑚𝐴 clockwise by Lentz’s Law i

Calculation of induced emf (3) Mechanical force to pull loop out F=𝐼𝐿𝐵 = .015𝐴 (0.05 𝑚)(0.6 𝑁 𝐴 𝑚 ) =0.045 𝑁 to left Mechanical work to pull loop out 𝑊=𝐹∙𝑑= 0.045 𝑁 0.05 𝑚 =2.25∙ 10 −3 𝐽 Electrical power dissipated during pulling 𝑃= 𝐼 2 𝑅= 0.015 𝐴 2 100 Ω =0.025 𝑊 Electrical energy lost to pull loop out ∆𝐸=𝑝𝑜𝑤𝑒𝑟∙𝑡𝑖𝑚𝑒= 0.025 𝑊 0.1s =2.25∙ 10 −3 𝐽

Other examples Φ 𝐵 =𝐵𝐴𝑐𝑜𝑠𝜃 ℇ=− ∆ Φ 𝐵 ∆𝑡 Change in B ××××××× Φ 𝐵 =𝐵𝐴𝑐𝑜𝑠𝜃 ℇ=− ∆ Φ 𝐵 ∆𝑡 Change in B ××××××× °°°°°°°°°°°°°

Other examples Φ 𝐵 =𝐵𝐴𝑐𝑜𝑠𝜃 ℇ=− ∆ Φ 𝐵 ∆𝑡 Change in A ×××××××

Other examples Φ 𝐵 =𝐵𝐴𝑐𝑜𝑠𝜃 ℇ=− ∆ Φ 𝐵 ∆𝑡 Change in A Φ 𝐵 =𝐵𝐴𝑐𝑜𝑠𝜃 ℇ=− ∆ Φ 𝐵 ∆𝑡 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 Φ 𝐵 =𝐵𝐴𝑐𝑜𝑠𝜃 ℇ=− ∆ Φ 𝐵 ∆𝑡 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 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”)