# Question about magnetic field of a current

1. Aug 7, 2008

### homomorphism

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

a long hairpin is formed by bending a piece of wire. if the wire carries a current $$i = 1.15 A$$.

the figure looks like this:

$$\subset$$

point a is at the center of the semicircle part (so that there is a radius r from a to the outside of teh semicircle. i flows counterclockwise. the point b is in the middle of the two parallel lines.

a) what are teh magnitude and direction of $$\vec{B}$$ at point a?
b) at point b, very far from a?

2. Relevant equations

$$\vec{B}_{wire}=\frac{\mu_{0}i}{2d\pi}$$

where d = r in this case.

$$\vec{B}_{semicircle}=\frac{\mu_{0}i}{4d}$$

$$\oint{\vec{B}\cdot d\vec{s}=\mu_{0}i}$$

3. The attempt at a solution

I know that I have to add up the contributions of the semicircle, and the two wires to get the total magnetic field at a. However, when i looked at teh solution to part a, they say that each wire contributes $$\frac{1}{2}\vec{B}_{wire}=\frac{\mu_{0}i}{4d\pi}$$. I understand teh contribution of the semicircle. how come the total contribution the wires is not $$2\vec{B}_{wire}=\frac{\mu_{0}i}{d\pi}$$ ?? This seems to be the magnetic field contribution from both wires for part b) though. does this have to do with how they enclose the wires in an amperian loop?

Last edited: Aug 7, 2008
2. Aug 7, 2008

### Redbelly98

Staff Emeritus
The "straight wire" formula is for a wire that extends for a long distance in both directions from the given point. Compare this description to the situation at point A.

3. Aug 7, 2008

### homomorphism

ah i understand now. thank you