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Size of current in parallel wires

  1. Oct 31, 2015 #1
    1. The problem statement, all variables and given/known data
    Two parallel wires are positioned at l = 2.76 cm apart. Initially a current I1 = 9.57 A flows up the screen through wire 1, and wire 2 has no current in it.

    A current is then sent through wire 2. The magnetic field between the two wires, is found to be 0T.

    What is the size of the current flowing through wire 2?

    2. Relevant equations
    78f8ff3a3398f1e13c3becdc6cf58a96.png

    3. The attempt at a solution
    I tried to use upload_2015-11-1_0-19-23.png by rearranging to make i the subject:
    i = 2pi*rB/μ
    = 2pi*0.0276x0/4pix10^-7
    then I realised the answer is zero but that is totally incorrect. Am I using the correct formula here? Or should I be using 78f8ff3a3398f1e13c3becdc6cf58a96.png ? (But then here I have 2 unknown variables.... F and I2) Help please! Thanks
     
  2. jcsd
  3. Oct 31, 2015 #2

    gneill

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    Staff: Mentor

    What is meant by "The magnetic field between the two wires"? Is that everywhere between the wires or at some particular location? Is the problem quoted exactly as given to you?

    Regardless, you're looking for the net magnetic field B at some location, not the force on another current-carrying wire. Do you have a formula for the magnetic field of a current-carrying wire?
     
  4. Oct 31, 2015 #3
    yes, that's how the question is worded :/
    Is it the formula upload_2015-11-1_0-19-23-png.91145.png ? I tried using in the attempt above
     
  5. Oct 31, 2015 #4

    gneill

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    Staff: Mentor

    Since the magnitude of the magnetic field due to a current in a long wire is inversely proportional to the distance from the wire, the location matters. So the question is badly posed. I think the best plan would be to assume that they mean the midpoint between the wires. If that is the assumption, then...

    ...If the total field is to be zero midway between the wires, what must be the current magnitude and direction in the second wire? Hint: Investigate the Right Hand Rule for magnetic fields around a current-carrying wire.
     
  6. Oct 31, 2015 #5
    Magnetic field into the screen so current is upwards? Not sure about the magnitude.....
     
  7. Oct 31, 2015 #6
    Would the magnitude be the same as wire 1? If they travel in same direction then they attract...?
     
  8. Oct 31, 2015 #7

    gneill

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    Staff: Mentor

    Attraction or repulsion doesn't play a direct role in addressing the question (although it is a consequence of the interaction of the fields). What is important is the magnitude and relative directions of the parallel currents.

    Your conclusion (guess??) about the magnitude of the current is correct, and you should be able to see that it follows from the symmetry of the situation. What is your argument for the current direction though? Did you investigate the right hand rule? If you want the net field to be zero how should the directions of the fields from each wire relate to each other?
     
  9. Nov 1, 2015 #8
    The first wire goes up the screen so magnetic field goes into the page. For net field to be zero, it should cancel out? so the 2nd wire also goes up the screen (magnetic field into screen? So the current in the second wire is 9.57A?
     
  10. Nov 1, 2015 #9

    gneill

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    Staff: Mentor

    Yes, that looks good.
     
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