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Unformatted text preview: 25. Each wire produces a ﬁeld with magnitude given by B = µ0 i/2πr, where r is the distance from the
corner of the square to the center. According to the Pythagorean theorem, the diagonal of the square
√
√
√
has length 2a, so r = a/ 2 and B = µ0 i/ 2πa. The ﬁelds due to the wires at the upper left and lower
right corners both point toward the upper right corner of the square. The ﬁelds due to the wires at the
upper right and lower left corners both point toward the upper left corner. The horizontal components
cancel and the vertical components sum to
µ0 i
2 µ0 i
cos 45◦ =
4√
πa
2πa
−7
2(4π × 10 T · m/A)(20 A)
= 8.0 × 10−5 T .
=
π (0.20 m)
√
In the calculation cos 45◦ was replaced with 1/ 2. The total ﬁeld points upward.
B total = ...
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 Fall '08
 SPRUNGER
 Physics

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