858_Physics ProblemsTechnical Physics

858_Physics ProblemsTechnical Physics - 198 P30.30 Sources...

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198 Sources of the Magnetic Field P30.30 (a) See Figure (a) to the right. (b) At a point on the z axis, the contribution from each wire has magnitude B I az = + µ π 0 22 2 and is perpendicular to the line from this point to the wire as shown in Figure (b). Combining fields, the vertical components cancel while the horizontal components add, yielding B I I z Iz y = + F H G I K J = ++ F H G I K J = + 2 2 0 0 0 θ sin ej The condition for a maximum is: dB dz Iz z I y = + + + = 0 2 0 2 0 a f , or 0 0 I + = Thus, along the z axis, the field is a maximum at da = . (Currents are into the paper) Figure (a) Figure (b) FIG. P30.30 Section 30.4 The Magnetic Field of a Solenoid P30.31 B N I = 0 A so I B n == × ×⋅ = 0 4 7 100 10 0400 10 1 000 31 8 .. . T m 4 T m A mA *P30.32 Let the axis of the solenoid lie along the y –axis from y = 0 to y = A . We will determine the field at ya = . This point will be inside the solenoid if 0 << a A and outside if a < 0 or a > A . We think of solenoid as formed of rings, each of thickness dy . Now I is the symbol for the current in each turn of wire and the number of turns per length is N A F H G I K J . So the number of turns in the ring is
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