Aim :

To study the magnetic field produced by current carrying coils.

Theory :

The magnetic induction of a circular coil of radius R, carrying a current I, at a distance z from the center of the loop along the axis (see Fig. 7.1) is given by

(7.1)

where μ0 is the permeability of free space. At z = 0, B(0) = μoI/(2R) ~= B10. If there are two such parallel coils at a distance S such that the current flows in the same direction in both the coils (see Fig. 7.2), then magnetic field adds in the space between them. Then we have

where, st = S/R, zt = z/R and B10 = μoI/(2R).

At the midpoint @~B/@z is zero. Further d2B/dz2 is also equal to zero at z = 0 if S = R. Because of these properties, the axial magnetic field is fairly constant over certain region in the middle of the pair of coils. This arrangement is very popular in producing uniform axial fields in regions easily accessible to experimental situations needing such uniformity.

In this experiment we will study the magnetic field variations for such a pair of Helmholtz coils. The magnetic field is measured using a Hall probe connected to a gaussmeter.

Construction of Helmholtz coils

The two coils are made of copper wire windings in 14 layers, each of 11 turns, such that the total number of turns (n) = 154. The sockets of the coil winding are cast into the plastic foot of the coil and the connecting leads can be used to connect the coils in parallel or series as required. The sockets are numbered (1, 2) to make it easier to wire the coils. See Fig. 7.3. In the Helmholtz arrangement, the coils are positioned by three spacer rails so

Figure 7.3: Experimental setup of Helmholtz coil.

that their axial spacing is equal to the average coil radius. The rails can be removed after undoing knurled screws, allowing coils to be used individually or with variable spacing.

The coil of the diameter 400 mm

No of turns per coil 154

Coil resistance 2.1