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Find direction of current in a magnetic field

  1. Oct 11, 2016 #1
    1. The problem statement, all variables and given/known data
    The diagram shows a uniform magnetic flux density B in the plane of the paper. Q and R mark the points where two long, straight and parallel wires carry the same current, I, in the same direction and perpendicular to the paper. The line through QR is at right angles to the direction of B.

    4bb2108f924a.jpg

    P is a point where the resultant magnetic flux density is zero, i. e. it is a neutral point. P is closer to R than to Q.

    (a) Explain whether the direction of the current I is into or out of the paper and sketch a diagram which shows the directions of the different magnetic flux densities present at P.

    (b) If I is increased slightly, will the neutral point at P move towards Q or towards R?

    (c) There is a second neutral point on the line through QR. State whether it is to the left of Q, between Q and R or to the right of R.

    2. The attempt at a solution
    (a) I have no idea how to find the direction of current. Boths wires are parallel and have one direction. How to find it?

    9697cce90dfd.jpg

    This is how I see it.

    (b) Nothing will change, right? Why would it?

    Or maybe if the current is increased, the point will move towards R, towards the stronger wire? The P point is closer to R so I assume the field is stronger there. And we increase I, R the current at R will attract the P point even more. Maybe like this?

    (c) Since both of the wires are the same, I would say that another point will be between Q and R, at the same distance from Q as P is from R. But not sure whether this is right.
     
    Last edited: Oct 11, 2016
  2. jcsd
  3. Oct 11, 2016 #2

    Doc Al

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    Only one direction of current will make it possible for the total B field at point P to be zero. Try each direction and see. (Hint: If you just consider the field from the wires alone, what direction is their resultant field?)
     
  4. Oct 11, 2016 #3
    I tried each direction, but it's just circles of field in one direction or the other.

    proxy.php?image=http%3A%2F%2Fs06.radikal.ru%2Fi179%2F1610%2Fe1%2F9697cce90dfd.jpg
     
  5. Oct 11, 2016 #4

    Doc Al

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    Ask yourself: Which wire, Q or R, creates the greater field at point P? Thus: Which direction is the net field from the wires at point P? And then: Does that oppose or add to the given uniform field?
     
  6. Oct 11, 2016 #5
    I would say wire R should have a greater field at point P.

    What does it mean? How can we calculate the net field?
     
  7. Oct 11, 2016 #6

    Doc Al

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    Exactly.

    Since you know that wire R creates a greater field than wire Q, what does that tell you about the direction of the net field due to the two wires?

    (Hint: At point P, do the fields from wires Q and R point in the same or opposite direction?)
     
  8. Oct 11, 2016 #7
    I thought about from the start, but it is said that the wires have current in the same direction.
     
  9. Oct 11, 2016 #8

    Doc Al

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    The current is in the same direction, but at point P are their fields in the same direction?
     
  10. Oct 11, 2016 #9
    They should be in different directions.
     
  11. Oct 11, 2016 #10

    Doc Al

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    Exactly.

    Now go back to my question:
    Answer it for both cases: Current going into the page and current going out of the page.
     
  12. Oct 11, 2016 #11
    Out of paper: anti-clockwise (like R).

    Into paper: clockwise (like R).

    Like here:

    Fproxy.php%3Fimage%3Dhttp%253A%252F%252Fs06.radikal.ru%252Fi179%252F1610%252Fe1%252F9697cce90dfd.jpg
     
  13. Oct 11, 2016 #12

    Doc Al

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    Just answer my questions for point P. (It will be either "up" or "down" the page at that point.)
     
  14. Oct 11, 2016 #13
    If we are talking about the dimension of the image, then out of paper will be down and into paper will be up.
     
  15. Oct 11, 2016 #14

    Doc Al

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    Good. And which is needed to get zero total field at P?
     
  16. Oct 11, 2016 #15
    Out of paper, because the field is already upwards?
     
  17. Oct 11, 2016 #16

    Doc Al

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    Exactly. To cancel the upward uniform field, we need a downward field from the two wires.
     
  18. Oct 11, 2016 #17
    Alright, the (a) part looks logical now.

    What about (b)?
     
  19. Oct 11, 2016 #18

    Doc Al

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    If the current increases, does the field from the wires increase or decrease at P? (How does the field from a wire depend on distance?)
     
  20. Oct 11, 2016 #19
    B = μ0 I / 2 π r? If we increase the current the field will also increase. If we increase the radius the field will decrease.

    P should move closer to R?
     
  21. Oct 11, 2016 #20

    Doc Al

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    Right. But that's for one wire. In between the two wires, the net field will be proportional to I (1/r1 - 1/r2).


    Since I is increasing, P must move in whatever direction that makes (1/r1 - 1/r2) smaller.
     
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