# M4 - Phy sics 7B WS M4 (rev. 2.0) Page 1 M-4. Ampres Law C...

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Physics 7B WS M4 (rev. 2.0) Page 1 M-4. Ampère’s Law r B " d r s C # = μ 0 I enc Questions for discussion 1 . A uniform magnetic field B points upward, as shown. (The source of this field could be a pair of current sheets. But in any case, these current sheets are far enough away not to be shown in this diagram.) The figure also shows an imaginary closed path, in the shape of a planar equilateral triangle of side D. a) What is the value of the line integral of the magnetic field around this imaginary closed path? (You should be able to answer very quickly using Ampère’s Law.) b) Calculate the line integral of the magnetic field along segment 1 of the imaginary triangle. Do this directly using the definition line integral of B along segment 1 B " d s segment1 # . c) Do the same for segments 2 and 3 of the imaginary triangle.

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Physics 7B WS M4 (rev. 2.0) Page 2 d) Add your results, and see if your overall value of B " d s triangular path # matches the result from part (a). 2 . The situation is the same as for Discussion Question 1, but this time the triangle is scalene . a) What is the value of the line integral of the magnetic field around this imaginary closed path? (Again, you should be able to answer very quickly using Ampère’s Law.) b) Identify those legs of the triangle, if any, along which B " d s leg # is positive . Next, identify those legs, if any, along which B " d s leg # is negative . Finally, identify those legs, if any, along which B " d s leg # is zero . c) Considering your results from part (b), explain how it comes about that the line integral around the imaginary path has the value you found in part (a).
Physics 7B WS M4 (rev. 2.0) Page 3 3 . Two parallel wires fixed in place near one another carry equal and opposite currents i. The left current is into the page, the right current is out of the page. a)

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## M4 - Phy sics 7B WS M4 (rev. 2.0) Page 1 M-4. Ampres Law C...

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