Ampere balance – measurement of μ_o

This apparatus can be used to determine the value of μ_o,the permeability of free space. The apparatus used is known as an ampere balance and one can easily be constructed since it is not available from apparatus suppliers at present. Two views of the Ampere balance are shown in Figure 1.

The small coil (of area A) is pivoted on a horizontal axis which passes through the centre of the large coil (radius R).

The apparatus should be set up with the two coils connected in series. The balance screws and the rider on the small coil should be adjusted until the pointer fixed to it is perfectly horizontal as shown by the vertical scale. The two coils are connected in series and a known current I should then be passed through them. The position of the rider is then adjusted to bring the pointer back to the horizontal once more.

The field (B) at the centre of the large coil (N turns) is given by:   B = μ_oNI/2R

and due to this the small coil (n turns) will experience a torque BAnI, which may be balanced by an opposing torque mgd, where d is the distance that the rider has to be moved to rebalance the pointer.

Therefore:      mgd = [μ_oNI/2R]AnI = μ_onNAI²/2R

and hence μ_o may be found.