Magnetic Field of a bent infinite wire

AI Thread Summary
The discussion focuses on calculating the magnetic field at point A due to a bent infinite wire carrying a current of 1.20 A. The Biot-Savart law is applied, treating the wire as a combination of an infinite line and a semicircle. The user initially struggled with the calculations but later identified a sign error in their approach. They emphasized the importance of integrating the contributions from both the semicircle and the straight sections of the wire. Ultimately, the correct method involves using the Biot-Savart equations for each segment of the wire.
evanclear
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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.
 
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Set it as an attachment. Thanks for the heads up
 

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  • HairpinCurve.gif
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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.
 
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.
 
evanclear said:
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!
 
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