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Phy 202
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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set 54 prob 3
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This is from set 54 Problem 3
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Problem
A coil consists of 140 coplanar loops, each of approximate radius .2 meters. Find the magnetic field at their common center point if a current of 1.3 Amps flows clockwise in the coil.
Solution
The center point is at the same distance from every point of the loop.
Assume that the loop lies in the x-y plane.
A clockwise current will result in every segment contributing a downward field component, so all contributions reinforce one another.
A line from the center to a point of the circle will be perpendicular to the direction of the flow, so the displacement vector is perpendicular to the segment, and sin(`theta) = 1.
The total length of the loops is the circumference 2`pi r = 2`pi ( .2 m) = 879.2 m, multiplied by the number of loops 140, for a total of 123000 m.
The field is B=k ' (IL)/r ^ 2 = .0000001 Tesla / Amp meter)( 159900 Amp m)/( .2 m) ^ 2 = .3997 Tesla.
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I understand how to solve this problem, but I am confused by your arithmetic. In your solution, you have 2'pi (0.2m)= 879.2m when I would assume the answer would be 1.6m.
Is this a typo error?
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Errors do sometimes occur with the randomized variable values.
2 pi * 0.2 m is about 1.3 meters (the arithmetic comes out 1.256 meters, but that is an unreasonable number of significant figures).
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Errors do sometimes occur with the randomized variable values. The procedure of the solution is, as far as I know, correct on every problem, but on occasion you will have to rectify obvious arithmetic errors. Bottom line: don't take the arithmetic too seriously.
2 pi * 0.2 m is about 1.3 meters (the arithmetic comes out 1.256 meters, but that is an unreasonable number of significant figures).
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