1. Chapter 7 Electrodynamics
7.0 Introduction
7.1 Electromotive Force
7.2 Electromagnetic Induction
7.3 Maxwell’s Equations

2. 7.0 Introduction electrostatic static magnetostatic =
magnetostatic =
conservation of charge

3. 7.0 (2)
Maxwell’s equations:

4. 7.0 (3) =
Magnetic flux
Induced electric field (force)
induce

5. 7.0 (4)
e.g. , ~
E,B fields propagate in vacuum
wave

6. 7.0 (5) A.C. current can generate electromagnetic wave antenna
cyclotron mass
free electron laser
…..

7. 7.1 Electromotive Force 7.1.1 Ohm’s Law 7.1.2 Electromotive Force
7.1.3 Motional emf

8. 7.1.1 Ohm’s Law Current density conductivity force per unit charge
of the medium
for perfect conductors
resistivity
( a formula based on experience)
usually true
but not in plasma; especially, hot.
Ohm’s Law

9. 7.1.1 (2) Total current flowing from one electrode to the other
V=I R
Ohm’s Law (based on experience)
Potential current resistance [ in ohm (Ω) ]
Note : for steady current and uniform conductivity

10. 7.1.1 (3)
I=?
R=?
uniform V
Ex. 7.1
sol:

11. 7.1.1 (4) A=const Ex. 7.3 Prove the field is uniform V=V0 V=0 =const

12. 7.1.1 (5)
Ex. 7.2 V

13. 7.1.1 (6) The physics of Ohm’s Law and estimation of microscopic s
the charge will be accelerated by before a collision
time interval of the acceleration is
mean free path
typical case
for very strong field and
long mean free path

14. 7.1.1 (7)
The net drift velocity caused by the directional acceleration is =
mass of the molecule
e charge
molecule density
free electrons per molecule
Power is dissipated by collision
Joule heating law

15. 7.1.2 Electromotive Force electrostatic force electromotive force
The current is the same all the way around
the loop.
Produced by
the charge accumulation
due to Iin > Iout
electrostatic
force
electromotive force
outside the source

16. 7.1.3 motional emf

17. 7.1.3 (2) =
Work is done by the pull force, not .

18. 7.1.3 (3)
magnetic flux
for the loop
flux rule for motional emf

19. 7.1.3 (4)
a general proof

20. 7.1.3 (5)
Ex. 7.4 =?

21. 7.2 Electromagnetic Induction
7.2.1 Faraday’s Law
7.2.2 The Induced Electric Field
7.2.3 Inductance
7.2.4 Energy in Magnetic Fields

22. 7.2.1 Faraday’s Law M. Faraday’s experiments Induce induce induce
loop moves
B moves
Induce
induce
induce
Faraday’s Law (integral form)
Faraday’s Law (differential form)

23. 7.2.1 (2) A changing magnetic field induces an electric field.
(b) & (c) induce that causes
drive
Lenz’s law : Nature abhors a change in flux
( the induced current will flow in such a direction that
the flux it produces tends to cancel the change. )

24. 7.2.1 (3)
Ex. 7.5
Induced ?
sol:
at center , spread
out near the ends

25. 7.2.1 (4)
Ex. 7.6
Plug in, induces
Plug in, why ring jump?
ring jump.

26. 7.2.2 The Induced Electric Field

27. 7.2.2 (2)
Ex. 7.7
induced = ?
sol: =

28. 7.2.2 (3) Ex. 7.8. The charge ring is at rest sol: What happens?
torque on
the angular momentum on the wheel

29. 7.2.2 (4)
Induced
sol:
quasistatic

30. 7.2.2 (5) =
Constant K( s , t )
s << c t
t = I / (dI/dt)

31. 7.2.3 Inductance
mutual inductance

32. 7.2.3 (2)
Neumann formula
The mutual inductance is a purely geometrical quantity
M21 = M12 = M
F1 = M12 I2
F1 = F2 if I1 = I2

33. 7.2.3 (3) Ex. 7.10 1 2 sol: B1 is too complicated… 2 = ?
n2 turns per unit length
Ex. 7.10 1
n1 turns per
unit length
I given 2
sol:
assume I too.
B1 is too complicated… 2 = ?
Instead, assume I running through solenoid 2

34. 7.2.3 (4) changing current in loop1, induces current in loop2
self inductance
self-inductance (or inductance )
[ unit: henries (H) ]
back emf

35. 7.2.3 (5)
Ex. 7.11
L(self-inductance)=? b a
N turns
sol:

36. 7.2.3 (6)
Ex. 7.12
sol:
general solution
particular solution

37. 7.2.4 Energy in Magnetic Fields
In E.S.
test charge
From the work done, we find the energy
in ,
But, does no work.
WB = ?
In back emf

38. 7.2.4 (2)
In volume

39. 7.2.4 (3)
Ex. 7.13
sol: ＜

40. 7.3 Maxwell’s Equations 7.3.1 Electrodynamics before Maxwell
7.3.2 How to fix Ampere’s Law
7.3.3 Maxwell’s Equations
7.3.4 Magnetic Charge
7.3.5 Maxwell’s Equation in Matter
7.3.6 Boundary Conditions

41. 7.3.1 Electrodynamics before Maxwell
(Gauss Law)
(no name)
(Faraday’s Law)
(Ampere’s Law)
but =0
Ampere’s Law fails because

42. 7.3.1 an other way to see that Ampere’s Law fails for nonsteady
current
loop 1 2
For loop 1, Ienc = 0
For loop 2, Ienc = I
they are not the same.

43. 7.3.2 How to fix Ampere’s Law
continuity equations, charge conservation
such that, Ampere’s law shall be changed to
Jd displacement current
A changing electric field induces a magnetic field.

44. 7.3.2 =
loop 1 2
for the problem in 7.3.1
between capacitors

45. 7.3.3 Maxwell’s equations Gauss’s law Faraday’s law
Ampere’s law with Maxwell’s correction
Force law
continuity equation
( the continuity equation can be obtained from
Maxwell’s equation )

46. 7.3.3
Since , produce ,

47. 7.3.4 Magnetic Charge Maxwell equations in free space ( i.e., , )
symmetric
With and , the symmetry is broken.
If there were ,and
symmetric
and
So far, there is no experimental evidence of magnetic monopole.

48. 7.3.5 Maxwell’s Equation in Matter
bound charge
bound current Q
surface charge

49. 7.3.5 (2)
Ampere’s law ( with Maxwell’s term )

50. 7.3.5 (3) In terms of free charges and currents, Maxwell’s equations
become
displacement current
one needs constitutive relations:

51. 7.3.5 (4)
for linear dielectric. or

52. 7.3.6 Boundary Condition Maxwell’s equations in integral form
Over any closed surface S
for any surface
bounded by the S
closed loop L

53. 7.3.6 = = =