1. -Magnetic Flux -Gauss’s Law for Magnetism -“Ampere-Maxwell” Law
AP Physics C
Mrs. Coyle

2. Magnetic Flux θ

3. Magnetic Flux, F: The number of magnetic (flux) field lines which pass through a given cross-sectional area A
Units:
F webers
B Tesla
A area m2
angle formed between B and the normal to the loop (area vector A)
The area vector A is perpendicular to the surface A and has a magnitude equal to the area A.

4. When B is perpendicular to the loop?
= BA
Why?

5. Which has the largest magnetic flux?
Answer: A

7. When B is along the plane of the loop?
Hint: q is the angle formed between B and the normal to the loop.

9. Gauss’ Law in Magnetism
Magnetic fields do not begin or end at any point
The number of lines entering a surface equals the number of lines leaving the surface
Gauss’ law in magnetism says:

10. Ampere’s Law – General Form
Also known as the Ampere-Maxwell law
Where is the electric flux.
The second term Id is called displacement current and is caused by electric fields that vary with time as in a capacitor.

11. Example: Capacitor Consider surfaces S 1 and S2 .
The current through S1 is I.
There is no conducting current through S2
The electric flux through
S2 is EA
A is the area of the capacitor plates
E is the electric field between the plates
If q is the charge on the plate at any time, FE = EA = q/eo

12. Example: Capacitor cont’d
The displacement current is
The displacement current is the same as the conduction current through S1
The displacement current on S2 is the source of the magnetic field on the surface boundary

13. Magnetic fields are produced both by conduction currents and by time-varying electric fields

14. Classification of Magnetic Substances
Paramagnetic and ferromagnetic materials are made of atoms that have permanent magnetic moments
Diamagnetic materials are those made of atoms that do not have permanent magnetic moments

15. Classifying Materials by Permeability
Materials can be classified by how their permeability compares with the permeability of free space (mo)
Paramagnetic: mm > mo
Diamagnetic: mm < mo

16. Examples of Ferromagnetic Materials
iron
cobalt
nickel
gadolinium
dysprosium

17. Domains
The domain is an area in a material within which all magnetic moments are aligned

18. Domains, Unmagnetized Material
The magnetic moments in the domains are randomly aligned
The net magnetic moment is zero

19. Domains, External Field Applied

20. Meissner Effect
Certain types of superconductors also exhibit perfect diamagnetism
This is called the Meissner effect
If a permanent magnet is brought near a superconductor, the two objects repel each other

21. Earth’s Magnetic Field
Like a bar magnet
The Earth’s south magnetic pole is located near the north geographic pole
The Earth’s north magnetic pole is located near the south geographic pole
Magnetic Declination

22. Dip Angle of Earth’s Magnetic Field
If a compass is free to rotate vertically as well as horizontally, it points to the Earth’s surface
The angle between the horizontal and the direction of the magnetic field is called the dip angle
The farther north the device is moved, the farther from horizontal the compass needle would be
The compass needle would be horizontal at the equator and the dip angle would be 0°
The compass needle would point straight down at the south magnetic pole and the dip angle would be 90°

23. Reversals of the Earth’s Magnetic Field
The direction of the Earth’s magnetic field reverses every few million years
Evidence of these reversals are found in basalts resulting from volcanic activity
The origin of the reversals is not understood