1. Magnetic field around a straight wire

2. Magnetic Field of Two Wires
Field at points on the x-axis
to the right of point (3)
Magnetic field outside of a conductor pair falls off more rapidly

3. Magnetic field of a circular arc

4. Falls off just as the electric field of the electric dipole
Magnetic Field of a Circular Current Loop
Falls off just as the electric field of the electric dipole
Magnetic Field on the Axis of a Coil

5. The magnetic field of a (small) loop behaves “on the outside” like the electric field of the electric dipole of the same orientation – that’s why “magnetic dipole”.

6. Magnetic force between two parallel conductors with currents

7. Example: Two straight, parallel, superconducting wires 4
Example: Two straight, parallel, superconducting wires 4.5 mm apart carry 15,000 A current each in opposite directions
Should we carry about the mechanical strength of the wires?

8. Ampere’s Law

9. General Statement
Magnetic fields add as vectors, currents – as scalars

10. Just as with the integral form of Gauss’s law, the integral form of Ampere’s law is powerful to use in symmetric situations

11. Magnetic Field of a Solenoid

12. Field of a toroidal solenoid

13. Magnetic Field of a Sheet of Current
The field of a magnetic “capacitor”

14. Magnetic materials
When materials are placed in a magnetic field, they get magnetized.
In majority of materials, the magnetic effects are small. Some however show strong responses.
The small magnetism is of two kinds:
Diamagnetics are repelled from magnetic fields
Paramagnetics are attracted towards magnetic fields
This is unlike the electric effect in matter, which always causes dielectrics to be attracted.

15. The Bohr Magnetron

16. Magnetization

17. Diamagnetism occurs in substances where magnetic moments inside atoms all cancel out, the net magnetic moment of the atom is zero. The induced magnetic moment is directed opposite to the applied field. Diamagnetism is weakly dependent on T.
Diamagnetic (induced atomic moment) effect is overcome in paramagnetic materials, whose atoms have uncompensated magnetic moments. These moments align with the applied field to enhance the latter. Temperature T wants to destroy alignment, hence a strong (1/T) dependence.
Magnetic effects are a completely quantum-mechanical phenomenon, although some classical physics arguments can be made.

18. Example: Magnetic dipoles in a paramagnetic material
Nitric oxide (NO) is a paramagnetic compound. Its molecules have maximum magnetic
moment of ~ mB . In a magnetic field B=1.5 Tesla, compare the interaction energy of the
magnetic moments with the field to the average translational kinetic energy of the molecules
at T=300 K.

19. Alignment of magnetic domains in applied field
Ferromagnetism
Alignment of magnetic domains in applied field
In ferromagnetic materials, in addition to atoms having uncompensated magnetic moments, these moments strongly interact between themselves.
Strongly nonlinear behavior with remnant magnetization left when the applied field is lifted.
Permeability Km is much
larger, ~1,000 to 100,000