Lecture%2022C - Physics 1B Lecture 22C Superposition As...

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Physics 1B Lecture 22C
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Superposition As with any vectors, magnetic field vectors can be added together by superposition You have to take both magnitude and direction into account. The vectors could get ugly, but just recall RHR2 and vector rules of addition and everything should turn out well in the end.
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Superposition Example Three parallel wires have current flowing in them. Wire 1 and wire 3 both have currents of 1A that flows into the board. What current (magnitude and direction) does wire 2 need to have in order for the combined magnetic force on wire 3 to be zero? Answer First, you must define a coordinate system. Let’s choose the center of wire 3 as r = 0. I 1 X I 3 X I 2 ? 0.2m 0.1m
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Answer In order for the magnetic force on wire 3 to be zero, the combined magnetic field from wires 1 and 2 need to be zero. Thus, at the location of wire 3: So, at the location of wire 3, the magnetic field due to wire 2 must be equal in magnitude and opposite in direction to the magnetic field of wire 1. B tot = B 1 + B 2 = 0 B 1 = − B 2 μ o I 1 2 π r 1 = − o I 2 2 r 2 I 1 r 1 = − I 2 r 2 I 1 X I 3 X I 2 ? 0.2m 0.1m
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This leads to: So, the current is 0.5A. Check the direction by RHR2. For wire 1, the direction of the magnetic field will be down. Thus, the direction of the magnetic field from wire 2 must point up at the location of wire 3. A current coming out of the board will create magnetic field in that direction. I
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This note was uploaded on 01/30/2012 for the course PHYSICS 1B 1B taught by Professor Grosmain during the Winter '10 term at UCSD.

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Lecture%2022C - Physics 1B Lecture 22C Superposition As...

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