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856_Physics ProblemsTechnical Physics

# 856_Physics ProblemsTechnical Physics - 196 P30.23 Sources...

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196 Sources of the Magnetic Field P30.23 From Ampere’s law, the magnetic field at point a is given by B I r a a a = µ π 0 2 , where I a is the net current through the area of the circle of radius r a . In this case, I a = 1 00 . A out of the page (the current in the inner conductor), so B a = × × = 4 10 1 00 2 1 00 10 200 7 3 π π µ T m A A m T toward top of page e j a f e j . . . Similarly at point b : B I r b b b = µ π 0 2 , where I b is the net current through the area of the circle having radius r b . Taking out of the page as positive, I b = = − 1 00 3 00 2 00 . . . A A A , or I b = 2 00 . A into the page. Therefore, B b = × × = 4 10 2 00 2 3 00 10 133 7 3 π π µ T m A A m T toward bottom of page e j a f e j . . . P30.24 (a) In B I r = µ π 0 2 , the field will be one-tenth as large at a ten-times larger distance: 400 cm (b) B k k = + µ π µ π 0 1 0 2 2 2 I r I r ± ± e j so B = × F H G I K J = 4 10 2 1 0 398 5 1 0 401 5 7 50 7 π π T m 2.00 A A m m nT a f . .
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