Lab 9
Measure B-field

Two current carrying coils of wire, axially centered and fixed in position, with their center-to-center separation equal to their radius are called a pair of Helmholtz Coils. When current is passed through each coil in the same direction a magnetic field is generated which falls off rapidly with distance from the coils.

The goal, today, is to use a magnetometer to measure the magnetic field strength as a function of distance from the coils. See Figure 1.

Figure 1. Measure a Magnetic Field

Review Theory

Consider a current, I, that flows through a coil of wire of radius, R. Suppose the origin of a coordinate system is centered on the axis of the coil at a distance, R/2, from its center. Then the axial component of the magnetic field strength, B, is given by:

where, µ0 = 4π x 10-7 henry/m, is called the permeability of free space, N, is the number of turns of wire in the coil and, x, is the distance from the origin. 

Consider two identical coils, parallel to each other and separated by a coil radius. If the current in each coil is identical (and flows in the same direction) the axial components of the magnetic field will add together. This configuration is called a pair of Helmholtz Coils where:

Notice that the field strength will increase linearly with current. If the current is reversed the direction of the magnetic field will reverse.