Lab 10
Helmholtz Coils

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 very uniform magnetic field is generated over a fairly large volume between the coils. Outside the coils the field falls off rapidly with distance.

The goal, today, is to examine a pair of Helmholtz Coils and to use a magnetometer to measure the magnetic field strength at the center of the coils. See Figure 1.

Figure 1. Helmholtz Coils

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:

At the center of the coils (x = 0) the axial magnetic field strength becomes:

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