Infinite wire -- Magnetic field from a current in a long L-shaped wire

[Hubbles]

Homework Statement

A long wire with a current changes direction by 90 degrees. Calculate the magnetic field at the point at a perpendicular distance of S from the wire before it changed direction and a distance of T from the segment of the wire after it changed direction.

Homework Equations

I suspect Biot-Savart or perhaps Ampere's law.

The Attempt at a Solution

I thought about separating the two perpendicular wire segments to manage them as separate semi infinite wires. But by doing that I encounter some problems. Using Amperes law and basically halving the field of a true infinite wire I don't take into account the whole wire segment. Doing it that way only works if the semi infinite segment extends from a perpendicular line connected to the point we measure, right?

 

[haruspex]

Doing it that way only works if the semi infinite segment extends from a perpendicular line connected to the point we measure, right?

Yes.

 

[Hubbles]

Could you treat it as two half infinite wires with Biot-Savart and add two finite segments on top of that? Or just two semi infinites from the correct distance. But then again I'm not sure how well Biot-Savart handles semi infinites.

 

[haruspex]

Could you treat it as two half infinite wires with Biot-Savart and add two finite segments on top of that? Or just two semi infinites from the correct distance. But then again I'm not sure how well Biot-Savart handles semi infinites.

You write as though Biot-Savart only applies to (half) infinite wires. It is a quite general integral.
There is no benefit in dividing each straight segment into two separate integrals. Just do one integral for each straight segment. It is not difficult.