1. Maxwell’s Equations
Electromagnetic
In the electric field E, and the magnetic field B, a charge q will experience a force: the Lorentz force:
F = q{E + v × B}.
Static Charges produces E fields and Moving charges produces B fields

2. Maxwell’s Equations
Electromagnetic
The effects may be summarized in the expressions for the divergence and the curl of E and B:
divE = /,
curlE = 0 ,
divB = 0 ,
curlB = µ0J

3. Maxwell’s Equations
Electromagnetic
Equations without divergence and curl express passive aspects, while with curl and divergence express active aspects.
A field with a curl but no divergence is
called a solenoidal field, while one with a divergence but no curl is called an irrotational field.

4. Electrostatic Field Potential Distribution.

5. Equipotentials and Electric Field Vectors of
Electrostatic Field
Equipotentials and Electric Field Vectors of
Electrostatic Field.

7. Electric Field Vectors
Equipotentials and Electric Field Vectors of a Microstrip Line.

8. Potential Distribution
Potential Distribution associated with a Corner
Resistor.

9. Electric Field Magnitude
Logarithmic scaled Electric Field Magnitude

10. Electrodynamics F = eE A Charged Particle
If a charged particle is set free in an electric field, it is accelerated by a force proportional to the field and charged particle
F = eE
Where F is Force
e is a charge, and
E is electric Field Intensity

11. Electrodynamics d(mv) dv dm F = = m + v dt dt dt Newton’s Second Law
Where m = mass of particle, kg
V = velocity of particle, m-1

12. Electrodynamics F = m dv = ma dt ma = eE
Newton’s Second Law
F = m dv
= ma dt
ma = eE
Velocity is very small as compared to velocity of light
Mass is essentially constant

13. Electrodynamics W = m  a •dL = e E • dL W = m v •dv = eV
Energy
Integrating the force over the distance traveled by charged particle is 2 2
W = m  a •dL = e E • dL 1 1
While the Integral of E between points of 1 and 2 is a potential difference V 2
W = m v •dv = eV 1
W = ½ m( v22 – v12) = eV

14. Electrodynamics W = eV = ½ mv2 Particle Energy where
W = energy acquired by particle, J
v2 = velocity of particle at point 2, or final velocity, ms-1
V1 = velocity of particle at point 1, or initial velocity, ms-1
e = charge on particle, C
m = mass of particle, kg
V = magnitude of potential difference between points 1 & 2, V

15. Electrodynamics  =  2eV/m
Final velocity
Considering a charged particle e starting from rest and passing through a potential of V, will attain the final velocity of :-
 =  2eV/m

16. m = mass of 0.91 x 10-30kg, will attain Velocity = v = 5.9 x 105 V
Electrodynamics
Final velocity
While
e = 1.6 x 10-19C falling through
V = 1 volt
Energy = 1.6 x Joules
m = mass of 0.91 x 10-30kg, will attain Velocity = v = 5.9 x 105 V
at 1 volt the charge attains 590 kms-1

17. Electrodynamics ay = eVd eVdL ; vy = ayt = md mvxd vy ;  = tan-1 vx LEd  vx d

18. Electrodynamics Problem:- A CRT with Va = 1500V,
Deflecting space d = 10mm,
Deflecting plate length = 10mm,
Distance x = 300mm,
Find Vd to deflection of 10mm:-
Deflection y = VdLx/2Vad
Vd = 2Vady/Lx= 100 V

19. Electrodynamics dF = (I x B)dL (N) …Motor equation I = q/t
Moving particle in static magnetic field
Force on a current element dL in a magnetic field is given by:
dF = (I x B)dL (N) …Motor equation
I = q/t
IL = qL/t = qv
IdL = dqv
dF = dq(v x B)
F = e(v x B) Lorentz force

20. Moving conductor in a magnetic field
Electrodynamics
Moving conductor in a magnetic field
E = F/e = v x B
V12 =  E • dL =  (v x B) • dL 2 2 1 1 1
Generating Equation B    dL   v          2
E = v x B

21. Electrodynamics
Magnetic Brake

22. Electrodynamics Magnetic Brake
I, B, & PUSH
Therefore F due to I is opposing to PUSH
Conductive Plate
Magnet Assembly

23. Electrodynamics
Magnetic Levitation

24. How does the LEVITRON¨ work?
When the top is spinning, the torque acts gyroscopically and the axis does not overturn but rotates about the (nearly vertical) direction of the magnetic field.

25. How does the LEVITRON¨ work?
levitionta

26. Electrodynamics
levitation

27. Electrodynamics
levitation
"We may perhaps learn to deprive large masses of their gravity and give them absolute levity, for the sake of easy transport."
- Benjamin Franklin

28. Electrodynamics
Maglev Trains

29. Electrodynamics Maglev Train
A maglev train floats about 10mm above the guidway on a magnetic field. It is propelled by the guidway itself rather than an onboard engine by changing magnetic fields (see right). Once the train is pulled into the next section the magnetism switches so that the train is pulled on again. The Electro-magnets run the length of the guideway

30. Electrodynamics
Maglev Train Track

31. Maglev Train
Aerodynamics Brakes

32. Electrodynamics no components that would wear out
Advantages:
no components that would wear out
there is no friction. Note that there will still be air resistance.
less noise
The final advantage is speed