5. Magnetostatics The force is generated by the magnetic field B.

Early evidence for the magnetic field.

Magnetic Field Bar magnetMagnetic field lines

Magnetic Field of the Earth Direction measured by a compass.

Oersted, in 1820What he saw.

Qersted’s experiment, modern version

Biot and Savert found that the force on a compass encircles a wire. Formulated the Biot-Savert law.

Ampere stated that all magnetic field are generated by currents. The elementary magnetic dipoles are current loops.

The force is generated by the magnetic field B. How does the field act on the moving charge? How is the field generated by the moving charges?

Total force on a charge: Lorentz’s law: Right – hand rule Magnetic force on a moving charge:

Example 5.2 – Cyclotron Motion

Cloud Chamber 1.6 MeV proton 7 MeV alpha

The Cylcotron O. E. Lawrence M. S. Livingston 1934

Magnetic Bottle

Van Allen Belts Protons and electrons from the solar wind are trapped by the earth’s magnetic field.

Currents Line current I 1 A = 1 C/s

Magnetic forces do not work!

Example 5.3 B points into the page.

Surface current density

Volume current density continuity equation:

Example 5.4

Biot-Savart Law Magnetostatics: Steady currents Magnetic field of a steady line current Permeability of free space – defines the unit Ampere

Example 5.5

Example 5.6 ?

Superposition principle for the magnetic field gives the different versions of the Biot-Savart law. line current surface current volume current Moving point charge