Magnetic Field of a bent infinite wire

[evanclear]

Homework Statement

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

Homework Equations

dB=μ₀*I*dlx$\overline{r}$
r^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 I am doing when it comes to magnetism. any help would be greatly appreciated.

 

[rude man]

Can't access the link.

 

[evanclear]

Set it as an attachment. Thanks for the heads up

 

[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.

 

[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.

 

[rude man]

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.

Good point!