We normally calculate the magnetic field from a power line by assuming that it is infinitely long and straight. Doing it that way keeps the calculation easy.
Often this is a pretty good approximation - but not always. Sometimes you have only a finite length. So how long does that finite length have to be before it becomes effectively infinite - before the calculation made assuming infinite conductors gives basically the right answer anyway?
The answer depends on how far away from the power line you are.
Consider a power line or underground cable made up of a number of individual conductors (it doesn't matter how many or what the geometry of them is - we've shown three here to give the general idea):
The black lines show the infinite conductors, and the red lines the actual finite-length conductors we have. We're interested in calculating the field at the green dot, a distance d to the side, and the finite conductors extend a length l each side of that point. The key parameter is the ratio l/d. This graph shows how much the finite calculation is less than the infinite calculation for various values of l/d:
If the actual conductors stretch in each direction only for the same distance that we are out to the side - l/d=1 - the difference is 30%. It drops below 10% when we have roughly twice as much cable in each direction as the distance to the side, below 5% at 3 times, and below 1% at 7 times.
If the point we're interested in is not half way along the finite cable, no problem: we just apply the graph to each direction separately and take the average.
The conductors change direction rather than stop?
If, at the end of the finite section we are looking at, the conductors don't stop altogether but change direction, that section after they've changed direction will still be contributing something to the field. So the field will be closer to the infinite-straight-line calculation. But exactly how close, you have to calculate on a case-by-case basis - it depends on the exact angle etc.
All the calculations on this page are for magnetic fields. Something similar happens with electric fields but it's harder to generalise because you have to take account of what happens at the ends.
- General principles of how to calculate fields including a tutorial on calculating fields from power circuits
- Specific issues about calculating fields from power lines
- The other reason straight-line calculations don't always work - when the conductors are curved.