Biot-Savart Law Difficult Problem

[1st1]

Homework Statement

A short, straight wire segment of length l carries current I and is oriented so that it makes an angle of 30° with the horizontal. Point P is a distance r below the wire segment.

Which expression below is the best approximation for the magnetic field caused by the wire segment at point P?

http://online.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys212/oldexams/exam2/fa09/fig15.gif

(a) (μoIlcos30°) / (4π^2)
(b) (μoIlsin30°) / (4π^2)
(c) (μoIl) / (4π^2)

Homework Equations

dB = (μo Idl x r(unit vector)) / (4πr^2)

The Attempt at a Solution

It seems I have to integrate to get the answer, however the geometry behind this problem is really confusing me. I believe I have to integrate r from when it touches the beginning of the wire segment to the end of the wire segment, however I can't figure out how to manipulate the Biot-Svart law to do that. This is what I have so far:

(μo I)/(4π) = S sin(theta)ds/r^2 (S = integral :p)

Now, what do I do with ds?
Can anyone help me out, help would be greatly appreciated :]!

Btw π = pi and μo = mu(0), don't know if you can tell.

 

[rl.bhat]

You can keep r fixed. Resolve current element I*l into two components, I*l*cos(theta) and I*l*sin(theta). The point P lies on equatorial line to I*l*cos(theta). So it contributes to magnetic field.
The point P lies on axial line to I*l*sin(theta). So it does contributes to magnetic field.

 

[1st1]

Ok, but then where does the pi^2 term come from in the denominator?
Also, the answer is (a) which makes since for the cos, but the pi^2 is what I don't get...

 

[kuruman]

There is no integral involved. Just think it through. Which of the three choices gives what you expect when the angle between the wire and the doted line is zero instead of 30^o? What about if it is 90^o instead of 30^o?

 

[1st1]

Ok, I know the answer just by looking at the choices. What I am trying to figure out is where part of that answer comes from. I don't see where that pi^2 in the denominator comes from.

 

[kuruman]

I don't see where it comes from either. The posted set of possible answers is dimensionally incorrect. Compare with the law of Biot-Savart equation that you posted. The dimensions should be dimensions of μ₀ times dimensions of current divided by Length.