# Find the magnitude and direction of a magnetic field(Biort-Savart Law)

1. Oct 20, 2009

### Raziel2701

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

A current path shaped as shown in the figure(I included the picture at the end of post) produces a magnetic field at P, the center of the arc. If the arc subtends an angle of θ = 60.0° and the radius of the arc is 0.400 m, what are the magnitude and direction of the field produced at P if the current is 4.00 A?

2. Relevant equations

$$B=\frac{\mu_{0}I \theta}{4\pi\,a}$$

It's straight from the book. And I know it's relevance due to the shape I'm dealing with.

3. The attempt at a solution

Doing that calculation I get an answer of 1.0472E-6 Tesla. The book wants the answer in nT, which I assume to be nano Tesla. I figure I need to move the decimal point three spaces. Giving me a result of .0010472 nano Tesla. The book, well, webassign is telling me this is wrong. I'll try to get the picture in here if I can get it to work.

What I substituted into the equation shown above is the following:

$$\mu_0=4\pi * 10^{-7}$$
I= 4A
$$\theta=\frac{\pi}{3}$$
a=0.4m

I noticed a discrepancy between the angle shown in the drawing and the one given in the problem, but I think it's a matter of webassign directly taking the drawing from the book and placing it here. The problem in the book does have an angle of 30 degrees, but webassign randomizes the given numbers. Meaning that I don't think the drawing's angle reflects my given numbers.

I don't see what I am doing wrong. The image of the problem is number two by the way.

What am I missing?

2. Oct 20, 2009

### ehild

"Doing that calculation I get an answer of 1.0472E-6 Tesla.
The book wants the answer in nT, which I assume to be nano Tesla.
I figure I need to move the decimal point three spaces. Giving me a
result of .0010472 nano Tesla. "

If your high is 1.7 m and somebody wants it in cm-s, you would say that you are 0.017 cm high, as you needed to move the decimal point by two?

Your first result 1.0472E-6 T is correct. And 1 T=109 nT. Do you get a smaller or higher number if you give the result in smaller units?

ehild

3. Oct 20, 2009

### Raziel2701

How could I be so dense? It hit me like a train.