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1、1一铁心上绕有线圈100 匝，已知铁心中磁通量与时间的关系为tsin.51008，求在s.t21001时，线圈中的感应电动势。2如图所示，用一根硬导线弯成半径为r 的一个半圆。使这根半圆形导线在磁感强度为B 的匀强磁场中以频率f 旋转，整个电路的电阻为R，求感应电流的表达式和最大值。解：由于磁场是均匀的，故任意时刻穿过回路的磁通量为cos)(0BSt其中0等于常 量，S为半圆面积，ftt200)2cos(21)(020ftBrt根据法拉第电磁感应定律，有)2sin(dd022ftfBrt因此回路中的感应电流为)2sin()(022ftRfBrRtI则感应电流的最大值为RfBrI22m3如图所示
2、，金属杆AB 以匀速 v=2.0 m.s-1平行于一长直导线移动，此导线通有电流I=40 A。问：此杆中的感应电动势为多大？杆的哪一端电势较高？解 1：杆中的感应电动势为V1084.311ln2d2d)(501.11.00ABABIvxvxIlBv式中负号表示电动势方向由B 指向 A，故点 A 电势较高。解 2：对于右图，设杆AB 在一个静止的U 形导轨上运动，并设顺时针方向为回路ABCD 的正向，根据分析，在距直导线x 处，取宽为 dx、长为 y 的面元 ds，则穿过面元的磁通量为xyxId2dd0SB穿过回路的磁通量为11ln2d2d01.11.00IyxyxIS回路的电动势为V1084.
3、311ln2dd11ln2dd500IvtyIt由于静止的U 形导轨上电动势为零，所以V1084.35AB式中负号说明回路电动势方向为逆时针，对 AB 导体来说电动势方向应由B 指向 A，故点 A 电势较高。g h f e 4如图所示，在“无限长”直载流导线的近旁，放置一个矩形导体线框，该线框在垂直于导线方向上以匀速率v向右移动，求在图示位置处，线框中感应电动势的大小和方向。解 1：根据分析，线框中的电动势为)(2d)(2d2d)(d)(121001000ghefhgef22lddlIvllldIvldIvlllBvlBv由hgef可知，线框中的电动势方向为efgh。解 2：设顺时针方向为线框
4、回路的正向。根据分析，在任意位置处，穿过线框的磁通量为120020ln2d)(21lIlxxIll相应电动势为)(2dd)(1210llIvlt令d，得线框在图示位置处的电动势为)(21210lddlIvl由0可知，线框中电动势方向为顺时针方向。5 圆柱形空间存在着轴向均匀变化磁场，0ddtB，在与轴垂直的平面内有一长为a的金属棒距轴为h，如图（a）所示求该棒的感应电动势。解：方法补偿法在图（b）上，将棒端与轴心相连，金属棒构成封闭三角形，选顺时针方向为绕行正方向，穿过该三角形面积的磁通量ahBBS21文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码
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8、7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P
9、3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A
10、10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5
11、B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8tBahtdd21ddE因半径上感生电场与半径垂直，感应电动势为零，故三角形闭合回路感应电动势即是金属棒感应电动势。负号表示沿逆时针方向。方法感生电场分布法在图（c）上，自圆心作棒的垂线与棒交点为坐标原点O，沿棒向右为x轴正方向，位于xxxd线元的感生电场大小
12、dtdBrEk21，方向与该点径矢垂直，它在x方向投影hdtdBrhdtdBcosEEkkx2121而xEdkACcAEtBhaxExxdd21d2kx1沿x轴正方向。文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:C
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14、R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 H
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16、8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3 ZZ9A10I8Y5B8文档编码:CS5C7T1R1K4 HI10N7L8U8P3
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