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Magnetic Field [Perpendicular wires]

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  1. Oct 16, 2015 #1
    1. The problem statement, all variables and given/known data
    upload_2015-10-16_20-37-55.png

    2. Relevant equations
    Biot-Savart Law: ## dB = μIdl/4πr^2
    F = ILxB

    3. The attempt at a solution

    I have not tried to solve it. BUT, please check my approach. I wanna make sure my method is correct and whether there is a flaw or no.

    I am trying to set up an integral here. I am to integrate it from from ## d+L ## to ## d ##. To do so, I will ignore the current in ## I_2 ## while integrating. Then, once I found ## B ## created by ## I_1 ## (which is "into the plane." [Meaning force acting on ## I_2 ## is in the same direction as ## I_2 ##

    What is wrong up until now?

    Well, here I am not sure how to find F acting on ## I_2 ##... Does ## F = IL(dot)B ## work?

    Thank you.
     

    Attached Files:

  2. jcsd
  3. Oct 16, 2015 #2
    I don't think you need to integrate along the infinite wire to find the magnetic field ##\vec{B}## it creates. You can just use the well-known result.

    But you will need to integrate along the short wire, using the limits of integration you mentioned. Integrate

    ##d \vec{F}=I \ d \vec{L} \times \vec {B}##

    to find the force.
     
  4. Oct 17, 2015 #3
    So, I can just use B = μI/2πr, where r is distance from wire 1 to wire 2, to find the Magnetic field that ## I_1 ## creating?

    Can you shortly explain the reason behind not integrating to find ## B ##? I am not quite clear on that...
     
  5. Oct 17, 2015 #4
    The distance from (the closest point along) Wire 1 to each differential element ##d \vec{L}## in Wire 2, yes.

    Integrating along the infinitely-long Wire 1 to determine the magnetic field ##\vec {B}## will result in the well-known expression ##\frac{\mu_oI}{2 \pi r}## for its magnitude. You will then have to use that result to perform the other integration (the one I described in my first post) to find ##\vec{F}##. I don't think it's your prof's intention that you do both integrals as the first one is found in every textbook.
     
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