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852_Physics ProblemsTechnical Physics

# 852_Physics ProblemsTechnical Physics - 192*P30.13 Sources...

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192 Sources of the Magnetic Field *P30.13 (a) We use equation 30.4. For the distance a from the wire to the field point we have tan30 2 °= a L , aL = 02887 . . One wire contributes to the field at P B I a I L I L I L =− = ° ° == µ π θθ 0 12 0 0 0 4 40 2 8 8 7 30 150 1732 2 8 8 7 150 cos cos . cos cos . . . . bg af a f Each side contributes the same amount of field in the same direction, which is perpendicularly into the paper in the picture. So the total field is 3 450 00 .. I L I L F H G I K J = . a P θ 2 1 I L 2 FIG. P30.13(a) (b) As we showed in part (a), one whole side of the triangle creates field at the center 0 4 I a . . Now one-half of one nearby side of the triangle will be half as far away from point P b and have a geometrically similar situation. Then it creates at P b field 42 21 7 3 2 4 I a I a = . The two half- sides shown crosshatched in the picture create at P b field 2 7 3 2
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