Solving an Unexpected Problem: Newton's Third Law

  • #1
my professor kind of sprung this problem out of nowhere for the class, and I'm having just a little trouble getting started? The problem goes like this:
A current wire pointing in the +j direction has an Idl. A second current wire in the +i direction has a different Idl.
The question he proposed was, is Newtons third law violated? [Broken]
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  • #2
for the bottom wire the 2's should be one's, my mistake.
Can anyone give me a hint?
  • #3
Can you restate the problem?
  • #4
Here's a new picture of the problem, the first one was not drawn correctly. [Broken]
The question is, given the two current elements as shown above, with current in the direction of the arrow, is Newtons third law violated. This is what I got. B on 2 due to 1 is in the (+k) direction given by the right hand rule. F on 2 due to B on 1 = I2dl2 X B1 = I2dl2B1 (+j x +k) = (+i) (the numbers are subscripts and the x's represent cross products. B on 1 dues to 2, is 0 because the current is in the same direction as p, the point where we are trying to measure the B. (dl X r) = 0. Therefore there is no force on 1 due to 2. This means that Newton's third law is violated. But the professor told us that it only appears that it's violated and now we have to prove why its not violated.

Can anyone tell me why? I can't seem to figure it out.
thanks a lot, nertil
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  • #5
nobody knows
  • #6
This question is ill-posed as written because you can't consider the magnetic field from an infinitesimal current element in isolation. This point is made in every E&M book I'm aware of (see the discussion on the Law of Biot Savart).

If you're being asked to consider two infinitely long wires along i and j directions, of which just a little is pictured, then it's easy to show that the net force on each wire produced by the other is zero, and the third law holds as expected.

As for point P, I don't know what it's supposed to represent in your diagram.

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