1. Faraday’s Law of Induction
Review
Faraday’s Law of Induction

2. Faraday’s Law The fourth Maxwell Equation
Calculates induced emf due to changing magnetic flux

3. Magnetic Flux ΦB = BA ΦB= BAcos(θ) ΦB: magnetic flux (Wb)
B: magnetic field (T)
A: area (m2)
θ : angle between the magnetic field and a vector which is normal to the area

4. Unit of Magnetic Flux
Weber (Wb)
1 Wb = 1 Tm2

5. E = -dΦB/dt Faraday’s Law E : induced potential (V)
ΦB: magnetic flux (Wb)
t: time (s)

6. Ways to Change Flux
ΦB = BAcos(θ)
a) Change B
b) Change A
c) Change θ

7. E = B L v Motional emf L: length of bar or wire
E : induced potential
L: length of bar or wire
V: speed of bar or wire

8. Lenz’s Law
When the magnetic flux is changing, current will flow so as to oppose the change in flux.

9. Induced E-Field Caused by changing magnetic flux
Does not arise from charge
Causes induced potential
Circular; loopy
Non-conservative

10. Faraday’s Law
E = -dΦB/dt
E = ∫ Eds
∫ Eds= -dΦB/dt

11. Betatron: accelerates electrons by changing magnetic flux

12. Gauss’ Law of Electricity

13. Gauss’ Law of Magnetism

14. Faraday’s Law of Induction

15. Ampere’s Law

16. Ampere-Maxwell Law

17. Inductor A coil in a circuit.
Resists change in current with an induced potential.
Stores energy in a magnetic field.

18. Inductor, L L
When switch is closed, EL opposes emf of cell. EL i E

19. Inductor, L L e i
When switch is opened, EL supports emf of cell. EL

20. Inductance EL = -L di/dt EL: potential across inductor
L: inductance in Henrys
i: current in amperes
t: time in seconds

21. Inductance, in general EL = -Nd ΦB/dt Ldi = NdΦB Li = NΦB
EL = -Ldi/dt
EL = -Nd ΦB/dt
Ldi = NdΦB
Li = NΦB
true for all inductors

22. Inductance, in solenoids
Li = NΦB
N = nl
ΦB = BA = n μo i
Li = n l (n μo i) A
L = n2 l μoA

23. Inductance, in solenoids with paramagnetic filings
L = n2 l μoA κB

24. The LR Circuit E - EL - VR = 0 E - Ldi/dt - iR i = imax(1 - e-t/τ)

25. The LR Circuit-continuedV
0 = EL + V
0 = -Ldi/dt + iR
i = imax(e-t/τ)
τ = L/R t i

26. Energy stored in Inductor
UB = ½ L i2
UB : energy stored in magnetic field
L: inductance in Henrys
i: current in amperes

27. Radius of loop: 16 cm
resistance: 8.5 Ω
1.0
B (T)
0.5 2 4
t (s) 6 8