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All right, hello.
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In this question, we're given this setup.
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We have two current -carrying wires carrying currents in opposite directions.
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And we know the current on the right wire.
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We don't know the current on the left wire.
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But we do know that it's pointing down.
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And we're told that the magnetic field at point c here, bc, is going to be equal to 0.
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And with that information, we want to figure out what i1 is going to be.
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So in order to do this, we need to figure out what the direction of these magnetic fields is going to be pointing.
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I take my right hand and point my thumb down the page for the left wire here and curl my fingers.
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On the right side, i'm going to have a magnetic field that comes out of the page, because that's the way my fingers are going to be pointing.
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And so it's going to be on the right side all around.
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And at point c, b1 is coming out of the page.
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So that's b1 in red.
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Likewise, if i point my thumb up the page and curl my fingers on the right, i'm going to have them pointing away from me.
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So b2 is going to be pointing away from me on the right side here.
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And it's going to be pointing towards me on the left side.
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So it's going to be pointing out there as well.
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So i know that my magnetic field at point c as a vector is going to be b1 plus b2.
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And i know that those are pointing in opposite directions.
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But i know this is going to equal 0.
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So i know that b1 magnitude is going to equal b2 magnitude...