1. ELEC 3105 Basic EM and Power Engineering
Magnetostatics The Basics

2. Magnetostatics Stationary charge: vq = 0 E  0 B = 0 Moving charge:
vq  0 and vq = constant
E  0 B  0
Accelerating charge:
vq  0 and aq  0
Radiating field
A stationary charge produces an electric field only.
A uniformly moving charge produces an electric and magnetic field.
A accelerating charge produces an electric and magnetic field and a radiating electromagnetic field.

3. Magnetostatics Units and definitions Magnetic field vector
Magnetic induction
Magnetic flux density
Magnetic field strength
Tesla
Gauss
SI unit
Weber

4. Magnetostatics Permeability Exact constant Permeability of free space
Relative permeability for a medium
Permeability of the medium
Exact constant

6. Ferromagnetic materials WHY?
What happens when we cycle the applied magnetic field.

8. Permittivity and Permeability

9. ELEC 3105 Basic EM and Power Engineering
Magnetostatics 1st Postulate

10. Magnetostatics
POSTULATE 1 FOR THE MAGNETIC FIELD
A current element immersed in a magnetic field will experience a force given by:
Units of Newtons {N}

11. Magnetostatics
POSTULATE 1 FOR THE MAGNETIC FIELD
A current element experiences a force which is at right angles to the plane formed by the current element and magnetic field direction magnitude:

12. Magnetostatics vs Electrostatics

13. Magnetostatics Consider a straight segment
postulate 1 for the magnetic field
Consider a straight segment
Net force on the segment
Right hand rule for direction

14. Magnetic force on a moving charge
postulate 1 for the magnetic field
Current density:
Volume charge density
Current through cross section dA:
Where is an element of volume enclosing charge q

15. Magnetic force on a moving charge
postulate 1 for the magnetic field
Modify force equation:
Net force on charge q

16. Magnetic force on a moving charge
postulate 1 for the magnetic field
Lorentz force
Often used to define the magnetic field. Force, charge, and charge velocity are measurable.

17. Magnetic force on a moving charge

18. Magnetic Electric Force at right angle to v and B vectors
Force proportional to v
Can do no work on a charge
Force along electric field lines
Force independent of v
Can do work
0 always

19. Electric AND Magnetic

22. ELEC 3105 Basic EM and Power Engineering
Hall effect

23. Hall effect

24. Hall Effect
3-D view of block q
When a conductor that carries a current is placed in a uniform magnetic field, an electrostatic field appears whose direction is perpendicular both to the magnetic field and to the current. The electric field here is known as the Hall field and reaches equilibrium in the order of s. The electric field is characterized also by the Hall voltage across the faces of the conductor.

25. Hall Effect
3-D view of block z q y x

26. Hall Effect Negative charge build up on this surface
Look onto this surface
from above
Top view of block z q y x
Positive charge build up on this surface

27. Hall Effect Top view of block
Accumulation of charge continues until induced electric force equals magnetic force. q
Voltage difference across charge distribution

28. Hall Effect Current density 3-D view of block w q t get v Current
with N density of carriers in the material.

29. Hall Effect Velocity of the moving charge 3-D view of block w
Magnetic force q t
Simplified magnetic force on the charge moving at velocity v

30. Hall Effect
Accumulation of charge continues until induced electric force equals magnetic force.
Top view of block q w
with
and
Voltage difference across charge distribution

31. Hall Effect In the steady state - - - - - - - - - - - - then q w
then q w

32. ELEC 3105 Basic EM and Power Engineering
Magnetostatics 2nd Postulate

33. Magnetostatics
POSTULATE 2 FOR THE MAGNETIC FIELD
A current element produces a magnetic field which at a distance R is given by:
Units of {T, G, Wb/m2}

34. Magnetostatics
POSTULATE 2 FOR THE MAGNETIC FIELD
Postulate 2 implies that the magnetic field is everywhere normal to the element of length

35. Magnetostatics Magnitude of the magnetic field Similar to:
Conceptually similar to a magnetic charge.
Magnetic charges have not yet been found.

36. Magnetostatics For a closed path made up of current elements
Biot-Savard Law

37. Magnetostatics
Magnetic field produced by extended conductor

38. Magnetostatics
Magnetic field produced by single moving charge conductor

39. Magnetostatics
POSTULATE 1 and 2 FOR THE MAGNETIC FIELD
Magnetic field lines are continuous and close on themselves. There are no magnetic charges for the lines to start or end on. Magnetic forces and magnetic fields are at 90 degrees to their sources.

40. Consequence of postulates 1 and 2
From postulate 2: A moving charge produces a magnetic field.
From postulate 1: A magnetic field produces a force on a moving charge.
Is it possible then that a moving charge generate a magnetic force on a second moving charge?

41. Consequence of postulates 1 and 2
Is it possible then that a moving charge generate a magnetic force on a second moving charge?
Answer “YES”

42. Consequence of postulates 1 and 2
Recall for a moving charge that the following substitution is possible:
THEN
BECOMES

43. Compare magnitude of magnetic and electric force between two moving charges

44. Compare magnitude of magnetic and electric force between two moving charges
The magnetic force on these two moving charges can be obtained from the elctric force and the velocity of the two charges. Concepts of relativity come into play.
maximum

45. Magnetic induction charging

46. Induction Stove