Biot-Savart Law Difficult Problem

In summary: So I need to find μ0.In summary, the magnetic field at point P is caused by the wire segment at point P.
  • #1
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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.
 
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  • #2
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.
 
  • #3
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...
 
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  • #4
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 30o? What about if it is 90o instead of 30o?
 
  • #5
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.
 
  • #6
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.
 

Related to Biot-Savart Law Difficult Problem

1. What is the Biot-Savart Law Difficult Problem?

The Biot-Savart Law Difficult Problem refers to a challenging physics problem that involves calculating the magnetic field produced by a moving charged particle. It is based on the Biot-Savart Law, which states that the magnetic field at a point due to a current-carrying wire is directly proportional to the current, the length of the wire, and the sine of the angle between the wire and the point.

2. Why is the Biot-Savart Law Difficult Problem difficult to solve?

The Biot-Savart Law Difficult Problem is difficult to solve because it involves complex mathematical calculations and often requires the use of advanced calculus and vector analysis. Additionally, the problem can become more complicated when dealing with multiple moving charged particles or non-uniform magnetic fields.

3. What are the key steps to solving the Biot-Savart Law Difficult Problem?

The key steps to solving the Biot-Savart Law Difficult Problem include identifying the relevant variables and parameters, applying the Biot-Savart Law equation, and using mathematical techniques such as integration to solve for the magnetic field at a specific point.

4. How is the Biot-Savart Law Difficult Problem used in real-world applications?

The Biot-Savart Law Difficult Problem has numerous real-world applications, including in the design and analysis of electromagnets, electric motors, and generators. It is also used in the study of fluid mechanics and plasma physics.

5. What are some common mistakes made when solving the Biot-Savart Law Difficult Problem?

Some common mistakes made when solving the Biot-Savart Law Difficult Problem include not properly identifying and accounting for all relevant variables, not applying the Biot-Savart Law equation correctly, and making errors in mathematical calculations. It is important to carefully check all steps and calculations to avoid these mistakes.

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