Magnetic Field near a curving infinite wire in 3d space

[speedofdark8]

Homework Statement

Problem as given: A three-dimensional wire of infinite length carries a current I₀ starting at (-∞,0,0) along a straight line to (0,0,0), bending and traveling along a straight line to (0,1,0), then bending and traveling to (0,1,1) and finally bending and traveling out to (∞,1,1). Determine the magnetic field at (0,0,1).

Homework Equations

Possibly using |B| = μ₀I/2∏r ? Not sure whether/how to combine the fields of the different segments using this general formula for the B-field of a current carrying wire.

The Attempt at a Solution

I haven't seen a problem like this in our class, so I'm mostly fishing for a start. I am aware of finding the magnetic B field of a current carrying wire using the equation above, but we never talked about a wire oriented in space with coordinates as such. To start, I would assume the wire is bent at a 90 degree angle at each given point where applicable, find the magnetic field of each segment, and from there I am not too sure where to go.

 

[tiny-tim]

welcome to pf!

hi speedofdark8! welcome to pf!

A three-dimensional wire of infinite length carries a current I₀ starting at (-∞,0,0) along a straight line to (0,0,0), bending and traveling along a straight line to (0,1,0), then bending and traveling to (0,1,1) and finally bending and traveling out to (∞,1,1). Determine the magnetic field at (0,0,1).
…
Possibly using |B| = μ₀I/2∏r ? Not sure whether/how to combine the fields of the different segments using this general formula for the B-field of a current carrying wire.

yes, find the individual fields, and add them

integrate the Biot-Savart law for the short sections

(you can probably see how to get it from B = μ_oI/2πr for the long sections)

 

[speedofdark8]

I am not familiar with the Biot Savart Law. For the other sections though, would I be correct with the equation I posted earlier?

 

[tiny-tim]

for the biot-savart law, see http://en.wikipedia.org/wiki/Biot–Savart_law#Equation

your equation was for a wire infinite in both directions …

how will you alter it for the wires in the question?​

 

[speedofdark8]

Thank you for the replys. I have since gotten together with some classmates and we found a solution.