1. Electrical and Computer Engineering Dept.
Magnetism
INEL 4151
Dr. Sandra Cruz-Pol
Electrical and Computer Engineering Dept.
UPRM ch 7

2. http://videos. howstuffworks

3. Applications Motors Transformers MRI More…

4. H= magnetic field intensity [A/m] B= magnetic field density [Teslas]
In free space the permeability is:

5. Magnetic Field Biot-Savart Law
States that:

6. Example For an infinite line filament with current Iaf a1 r
For an infinite line filament with current I
(a1=180o and a2=0o):

7. PE. 7.1 Find H at (0,0,5) Due to current in (figure): where a1=90o andz
Due to current in (figure):
where a1=90o and
(0,0,5) y
10A 1 x

8. Circular loop Defined by Apply Biot-Savart:dl R z y
dHz
dHr x
Defined by
Apply Biot-Savart:
Only z-component of H survives due to symmetry:

9. Ampere’s Law Simpler Analogous to Gauss Law for Coulombs
For symmetrical current distributions

10. Ampere’s Law
We define an Amperian path where H is constant.

11. Infinitely long coaxial cablez
Four cases:
1) For r<a

12. Infinitely long coaxial cablez
Four cases:
2) For a<r<b

13. Infinitely long coaxial cable
Four cases:
3) For b<r<b+c z

14. Infinitely long coaxial cable
Four cases:
4) For r>b+c

15. Sheet of current distributionz
Cross section is a Line! 4 b a
The H field is given by: 1 y
K [A/m] 3 2
The H field on the Amperian path is given by: x

16. PE. 7.5 Sheet of current
Plane y=1 carries a current K=50 az mA/m. Find H at (0,0,0). y
K =50 mA/m z -x

17. A toroid
A circular ring-shaped magnetic core of iron powder, ferrite, or other material around which wire [N- loops] is coiled to make an inductor. Toroidal coils are used in a broad range of applications, such as high-frequency coils and transformers.
Toroidal inductors can have higher Q factors and higher inductance than similarly constructed solenoid coils. This is due largely to the smaller number of turns required when the core provides a closed magnetic path. The magnetic flux in a toroid is largely confined to the core, preventing its energy from being absorbed by nearby objects, making toroidal cores essentially self-shielding.
Fields stay inside core, no interference.

18. Magnetic Flux Density, B
The magnetic flux is defined as:
which flows through a surface S.
The total flux thru a closed surface in a magnetic field is:
Monopole doesn’t exist.

19. Maxwell’s Equations for Static Fields
Differential form
Integral Form
Gauss’s Law for E field.
Gauss’s Law for H field. Nonexistence of monopole
Faraday’s Law; E field is conserved.
Ampere’s Law

20. Magnetic Scalar and Vector Potentials, Vm & A
When J=0, the curl of H is =0, then recalling the vector identity:
We can define a Magnetic Scalar Potential as:
The magnetic Vector Potential A is defined:

21. The magnetic vector potential, A, is
It can be shown that:
The magnetic vector potential A is used in antenna theory.
Substituting into equation for Magnetic Flux:
This is another way of finding magnetic flux.

22. P.E. 7.7 A current distribution causes a magnetic vector potential of:
Find :
B at (-1,2,5)
Answer:
Flux thru surface z=1, 0≤x≤1, -1≤y ≤4
Answer :