Magnetic effect of an electric current

An electric current will produce a magnetic field, a fact discovered by Oersted in 1820. The intensity and shape of this field depends on the strength of the current and the arrangement of the wires carrying it. In 1820 Sturgeon also showed that the strength of the field in a coil could be increased considerably by placing an iron core in the coil.

Magnetic fields have a large number of uses in the modern world in, for instance, particle accelerators, plasma bottles, lifting magnets, linear induction motors, tape recording heads and many other applications. Knowledge of those fields has also helped in the studies of the Physics of the van Allen radiation belts, quasars and aurorae.

You will have seen some magnetic field arrangements in your foundation level course and we will be considering these and other field arrangements in detail.
The shapes of the magnetic fields for some simple arrangements are shown in Figure 1-3. You can see that these fields are not uniform and it is found that the strength of the field depends on the closeness of the lines of magnetic flux.
The direction of the magnetic force can be found by Maxwell's corkscrew rule. If we imagine ourselves driving a corkscrew in the direction of the current, then the direction of rotation of the corkscrew is the direction of the lines of force.
The polarity of a coil of wire can be found by Fleming's right-hand grip rule, where the fingers of the right hand indicate the current direction and the thumb the north pole of the solenoid.
A single wire connected to a cell and doubled back on itself has no net magnetic field - the field produced by the current in one direction cancels that produced by the current in the other. This is known as non-inductive winding; it is used in resistance boxes and in the platinum resistance thermometer.

Equations for electromagnetic fields

Consider a wire carrying a current I (Figure 5). The flux density B at a point P due to a length of wire dL is given by:

dB = moIdLsinq/4px2

This is known as the Biot-Savart rule, after two French physicists. The constant of proportionality in this formula is known as the permeability of the medium and is denoted by m.

The unit of permeability is the henry per metre (H m-1).

The permeability of free space (a vacuum) is written as mo and is 4px10-7 H m-1.

In a vacuum the field for a short current element is given by:

dB = moIdLsinq /4px2

Using this formula the fields due to various arrangements of currents in a vacuum can be found.

For the present we will quote them without deriving them.

(a) At distance r from a long straight wire carrying a current I (Figure 6).

B = moI/2pr

(b) At the centre of a plane circular coil, radius r, of N turns and carrying
a current I (Figure 7):
B = moNI/2r

(c) At the centre of a long solenoid of n turns per metre carrying
a current I (Figure 8):
B = monI = moNI/L

where N is the total number of turns on the solenoid of length L

(d) At the end of a long solenoid n turns per metre carrying
a current I:

B = monI/2 = moNI/2L

where N is the total number of turns on the solenoid of length L (Figure 9).

(e) Helmholtz coils - two coils of radius r, each of N turns, carrying a current I and placed as shown in Figure 10 so that the centres of the coils are separated by a distance equal to the radius of the coil:

B = moNI/5[(5)1/2r]

This arrangement gives a fairly uniform field in the space between the two coils.