Magnetic field around a straight wire

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

Magnetic field of a circular arc

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

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”.

Magnetic force between two parallel conductors with currents

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?

Ampere’s Law

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

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

Magnetic Field of a Solenoid

Field of a toroidal solenoid

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

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.

The Bohr Magnetron

Magnetization

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.

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.

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