The Field from a Long Straight Wire

Note that, in "Field Lines" mode, double-click on a point to draw the magnetic field line passing through that point. Don't double-click on the wire (shown as a red dot) itself - use a point or points some distance from the wire.

Let's use Ampere's Law to find the magnetic field from a long straight wire.

What shape should we choose for our amperian loop?

  1. a circle
  2. a square
  3. a triangle
  4. it doesn't matter as long as the wire is somewhere inside the loop
  5. it doesn't matter as long as the wire is at the center of the loop

What does the field look like? The field follows circular loops centered on the wire.

In theory Ampere's Law can be applied for any loop, but the one that makes the calculation easy in this case is a circular loop. To find the field a distance r from the wire, use a loop of radius r centered on the wire. The enclosed current is I directed out of the page, producing a counter-clockwise field. Carry out the integral in a counter-clockwise direction so the dot product will be positive.

Because the field is the same magnitude at all points on the loop, and the field is tangent to the loop everywhere:

Bdl = B dl = B dl = μo I

dl is the length of the loop, which is 2πr.
This gives: B =
μo I
2π r