1. 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

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

3. 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

4. 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

5. 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

6. Examples of Lenz’s Law – Fig 21-6
Flux down -> flux less down, change up, oppose change down, current CW
Fig 21-7

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

8. 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.

9. 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)

10. Calculation of induced emf (2)
Emf for single loop
ℇ= ∆ Φ 𝐵 ∆𝑡
= 0− 0.6 𝑇 2.5∙ 10 −3 𝑚 𝑠
=− 1.5∙ 10 −3 𝑁 𝐴∙𝑚 𝑚 𝑠
=− 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

11. 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= 𝑁 𝑚
=2.25∙ 10 −3 𝐽
Electrical power dissipated during pulling
𝑃= 𝐼 2 𝑅= 𝐴 Ω =0.025 𝑊
Electrical energy lost to pull loop out
∆𝐸=𝑝𝑜𝑤𝑒𝑟∙𝑡𝑖𝑚𝑒= 𝑊 0.1s =2.25∙ 10 −3 𝐽

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

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

14. 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)

15. Other examples
Φ 𝐵 =𝐵𝐴𝑐𝑜𝑠𝜃 ℇ=− ∆ Φ 𝐵 ∆𝑡
Change in θ
Generator

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

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

18. 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-

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