### What direction do the magnetic field lines produced by a power line point in?

Firstly, the field lines always lie in a vertical plane perpendicular to the power line itself. This would be exactly true if the power line were a perfect straight line. In that case there would be no component of the field along the direction of the line at all. In practice, power lines sag and change direction, so this statement is not exactly true. But the axial components of field - the components along the power line - are rarely more than a few percent of the total field. So it's a pretty good approximation to say that the field lines lie in a vertical plane perpendicular to the power line.

Secondly, we can plot the field lines at an instant of time, as shown in the picture on the left. This gives the impression that the field has a specific direction at each point in space. But with alternating currents, as the current reverses direction during each cycle, the field lines change direction. At each point, rather than just oscillate back and forwards, the magnetic field vector traces out an ellipse. This is called elliptical polarisation and we describe it in more detail here. This means we can't just give a single direction for the field, the best way of describing the direction is actually to plot out these ellipses.

We illustrate here the ellipses traced out by the magnetic field for a series of progressively more complicated power lines. In each case the calculation is for 1 m above ground level and the clearance of the lowest conductor is 12 m.

## Single current

This would never occur in practice but it's conceptually the simplest possible case so it's a good starting point. The field lines would form concentric circles and as we move under the line we intersect those circles at varying angles. Because there is only one current, in this case, the field is in fact linearly polarised not elliptically polarised and the magnetic field vector at any point oscillates backwards and forwards along a single direction.

## Horizontal array

In practice, most power lines consist of at least one three-phase circuit. Consider the three phases arranged in a horizontal array. This produces a dipole pattern of field. This calculation is for the phases spaced 5 m apart. Different combinations of the phase spacing and the height above ground would mean our calculations intersected the dipole pattern at different places and the details of the field direction would change, but it would still be a dipole. At larger distances, the dipole field again tends to linear polarisation, but at closer distances (too close for the dipole approximation to be good), the field is noticeably elliptical.

## Vertical array

Now consider the same single three-phase circuit but arranged as a vertical array. The field is still a dipole but rotated through 90 degrees.

## "Delta" arrangement

Sticking with a single three-phase circuit, the other extreme is to arrange the phases not as a linear array but at the points of an equilateral triangle. At large distances, this gives perfect circular polarisation, and is still highly elliptical even at closer distances.

## Two-circuit power line

Now consider a typical high-voltage power line carrying two circuits. With untransposed phasing, the field is still a dipole, but because the conductors of each circuit are usually not exactly in a straight line and the two circuits are not exactly parallel, the field is a bit more elliptical than a single vertical array.

## Two circuits with transposed phasing

Most UK power lines have transposed phasing. This produces a quadrupole rather than a dipole. This is the same case as the plot of field lines at the top of this page. The major axes of the ellipses are aligned with the field lines in that plot, but now we can see that the field doesn't just lie in that direction, there is significant elliptical polarisation.

## Two circuits with unbalanced currents

The last case showed the effect of transposed phasing but with the currents in the two circuits equal. The pattern is a perfect quadrupole and the ellipses are symmetrical about the power line. In practice, the currents are rarely balanced. This case shows a typical set of currents (one circuit has 50% higher current than the other, and there is a small earth-wire current as well). More on the effect of unbalanced currents on the field.

The ellipses now vary all over the place. This exact pattern of ellipses is not intended to be representative of any particular power line. If the currents changed slightly, the ellipses would all shift. What we learn from this is that for real power lines with transposed phases, it is almost impossible to make predictions of the direction of the field without knowing the exact currents. All we can say is that the field lies in a vertical plane transverse to the power line, and the field usually has significant elliptical polarisation.

### Electric fields

In principle the same issues apply to the electric field. But in practice, near ground level, the electric field from a power line is generally nearly vertical and nearly linearly polarised, a consequence of the fact that the ground itself is conducting, which means that the field lines have to meet it at right angles. (At ground level, the field has to be absolutely vertical, but above ground, this becomes less true - see below for the details.)

### The numbers for electric fields

We said above that electric fields are often pretty nearly vertical and linearly polarised. The following table gives the horizontal component of electric field as a percentage of the vertical component (i.e. a pure linearly polarised vertical field would be 0%) for some standard scenarios - all are for an L12 line with 12 m clearance.

Height above ground | ||||

Centre line | Under conductors | Centre line | Under conductors | |

0 m | 0 | 0 | 0 | 0 |

1 m | 33% | 4% | 0 | 5% |

2 m | 69% | 7% | 0 | 9% |

So where the field is dominated by one set of conductors - underneath the conductors, or, with untransposed phasing where the bottom conductor on both sides has the same phase, on the centre line - it's a good approximation. But where conductors of different phases are in play - on the centre line with transposed phasing - it becomes less true the further away from the ground you are. You can see this on the diagram of field lines above, which is for transposed phasing - nearly vertical under the conductors, but bending quite a bit on the centre line.

### More on these calculations

All these calculations are performed at 1 m above ground with 12 m ground clearance of the lowest conductor of the power line. The fields are calculated at 10 m intervals. Although the ellipses are plotted on the same horizontal axis as the distance, obviously the ellipse itself shows the field not distance! The field falls off with distance from the power line. All the ellipses are scaled so that the rms of the ellipse is constant. So the ellipses shown here do not tell you about the size of the field, just its polarisation and direction.

The two-circuit calculations use an actual 400 kV UK power line (the L12 design). The horizontal and vertical arrays use idealised designs with 5 m conductor spacing. In practice, high-voltage lines would have a bigger spacing, low-voltage lines a smaller spacing. Changing the spacing of the conductors simply scales the whole field-line pattern.