# Magnetic Field of a bent infinite wire

1. Mar 5, 2013

### evanclear

1. The problem statement, all variables and given/known data

A long hairpin is formed by bending an infinitely long wire, as shown. If a current of 1.20 A is set up in the wire, what is the magnitude of the magnetic field at the point a? Assume R = 3.20 cm.

http://lon-capa.mines.edu/res/csm/csmphyslib/type62_biotsavart_ampere/HairpinCurve.gif [Broken]
2. Relevant equations

dB=μ0*I*dlx$\overline{r}$
r^3
3. The attempt at a solution

I tried using the equation for two separate infinite lines and a full circle divided in half, and was unsuccessful. The same result occurred when i attempted to use the equation of a full line and a half circle. I came to the conclusion that i don't really know what Im doing when it comes to magnetism. any help would be greatly appreciated.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 6, 2017
2. Mar 5, 2013

3. Mar 5, 2013

### evanclear

Set it as an attachment. Thanks for the heads up

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4. Mar 5, 2013

### evanclear

Fixed my own problem.

To anyone who might care, to solve this problem you can treat it as the sum of Biot-Savart Equations for an infinite line and a half circle, using R as your distance in both equations. I had attempted this once but didn't catch a sign error. Thanks anyway though.

5. Mar 5, 2013

### rude man

Set up x-y system with origin at point a. Then use Biot-Savart separately
1) for the semicircle; easy integration since r is constant = R
2) top straight stretch, and
3) bottom straight stretch.

For 2) and 3) you will be integrating dl from 0 to infinity where dl is an element of wire.

6. Mar 5, 2013

Good point!