Elliptically polarised fields

When there is just a single source of magnetic field, the field oscillates backwards and forwards along a straight line. But where there is more than one source of field at the same frequency, the magnetic field traces out an ellipse in space. The orientation and shape of the ellipse depend on the details of the sources.

Defining the size of the field

The red ellipse in this diagram shows the ellipse traced out by the magnetic field over the course of one cycle.

The largest value obtained by the field is along the major axis (or long axis) of the ellipse.

Arrow 1 shows the root-mean-square (rms) of the field along this direction. This is defined as the maximum field.

Arrow 2 has a particular property: because of the geometry of ellipses, the length of arrow 2 gives the rms of the magnetic field, known as the resultant field. This is the normal way of describing an elliptically polarised field.

Measuring elliptically polarised fields

If you take a single-axis meter (eg a single coil) and rotate it until it gives the maximum reading, it will be measuring the field along the direction of arrow 1. Assuming the meter is calibrated to give the rms, it will measure arrow 1: the maximum field.

If you take a three axis meter (ie three coils at right angles to each other), you don’t need to rotate it. Whatever orientation it is in relative to the field, it will give arrow 2: the resultant field. (Most meters do this by recording the rms of the field in each of the three directions, then adding these by root-sum-of-squares. This gives the same answer as measuring the rms directly.)

More on measuring fields.

The extreme cases

As the ellipse gets more and more squashed, arrows 1 and 2 become more and more similar. In the limit of a linearly polarised field, they are the same.

The other extreme is when the ellipse becomes a circle. For circularly polarised field, the resultant (arrow 2) is bigger than the maximum field (arrow 1) by a factor of the square root of 2, about 1.4 times.

Electric fields

Electric fields can also be elliptically polarised. But under power lines, close to the ground, they tend to be vertical and nearly linearly polarised.

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