Magnetic Field and Currents
Empirically, we know that moving charges produce a magnetic field. We also know that the field B is perpendicular to the direction of current flow and the vector connecting the current source and the location at which we want to know the field. We also know that the field falls off like 1/r2.  These lead to the Biot-Savart Law, the magnetic equivalent of Coulomb’s Law. 
The magnetism equivalent of Gauss’ Law is called Ampere’s law., Symmetry considerations often allow us to use Ampere’s Law to calculate B as a function of the current sources.
In this lab, we will be measuring various fields: that due to a single coil, that due to 2 coils, and that due to a toroidal coil arrangement. In every case, B is linearly proportional to I and the proportionality constant just depends on the coil geometry. The next few slides contain examples of coil geometries very commonly used to produce magnetic fields for experiments. The examples are:
• Helmholtz coils: two coils with spacing = coil radius. This makes a very uniform field in a small region of space.
• Solenoid: makes a very uniform and long field
• Toroid: very useful when azimuthal symmetry is required. Toroidal fields are also used in tokomaks for plasma fusion experiments.