9-2 在电流强度为 I_(0) 的长直导线产生的磁场中,有一等腰直角三角形线圈, 线圈平面与长直导线在同一平面内 ,线圈通过的电流强度为 I,如图 9 -2 (a)所示, 求各边受到的磁场力及整个线圈受到的合力.

题目解答
答案
解 三角形线圈处于长直导线产生的非均匀磁场中,根据安培力公式可分别 求出每边受到的磁场力,进而求出线圈所受的合力. 建立如图9-2(a)所示的坐标系.长直导线电流6M4aUROtjU4LhMWGjxaWTQ==产生的磁场为 :Nfly8Yx8f5qTldcAp4R9f8VxmINsca0h3BcIkoL8SC1TIP5l2ewEvkokzuEYboTN, 方向垂直纸面向里,因为线圈上任意电流元45qOj350SfgAqp6V3zmBbdz/a0DNMrgocss8q6BPrTw=的方向都与该处GTnOCR9hNPsOuxGSyBGTAE4D+bwdNZdKWKqAkIkho7A=垂直, 所以各 边所受磁场力计算如下. 对于iW5Ht7EzAojfQ+hbsC5yyQ==边,将其分割为无限个电流元45qOj350SfgAqp6V3zmBbdz/a0DNMrgocss8q6BPrTw=,由于每个电流元所在处磁感应强 度大小相等,方向一致 .由安培力公式可知t63PfoTgcqfVoM75RsJYY09X7l4+T91rzqnMJSiz6GA=的大小为 BiFZtGphSBXjS/cU/3/TuifJz8OQjMb8F7dv8yVzJOkue8lKbJvawu2Moj3xuVds2DB0jI8+Ps6lwTE8U+VQ6HvHzK5IYvpK9EKHhzDQvESpTlXpPl8CcyjjnugmXiTW 方向沿ZKO2xs0EgSemzoH7MSmYTA==轴负方向 对于YhwKgXfACmgRWs7sDf5LRw==边,每个电流元受到的安培力方向相同,但每个电流元所在处的磁感 应强度大小不同, 所以 qeiYnKXLEhyhuGRg8yLtr2rc2xayo2R7FynzoDaQLPu3LmiI6Q08dHblAm4VppbFbQ1g6PrDiYWEkeiDt0rVpUWwmRV11AtuIPAJ8DKDQwAurSrAyqMwBXQrlUGtTRiUH+K6a1UqJAJTJ2C/h1tDjpgoS0u3Ylmd2KyTaM6dBL28jLzn5p5e6wpxfl0HaXRqaqxPTqJxfmRQrzwhJpnDxNEJq6JjJRe7XgZLTToaoOOjF9auL5wTsrllvjUuVISNZz9sgRde0ODt4O0qIWqaYqCzKjCHM+R+QEFMzrvkA3ze8R9tc1RAW3L9lXdbIyPM 方向沿yBR4oiFoTexGaFalQ7m8kg==轴正向. 对于2xL4o4znorayplGiR2Qdow==边 ,每个电流元受安培力方向相同 ,如图9-2(b)所示,因而 qeiYnKXLEhyhuGRg8yLtr4M90juK6rr1VMEPvBRkwmQK7/7AVxERipR5qFBy1yQN9/1nvCzIompVdIT/p8rBi4uUPj5KO9EIjZSLuirh0OsbiaxYtZXvXYqEQ8+K5CSdibXrPoOKbhix6R1T+hLjyXbxfV4JMOsIbMtaNg8Rm2VeylSNRANBQVF1RnUFHsRd 统一积分变量,由几何关系可知 g88xugfdjtyTg8QUohNUawlDZ4PbFq4UL/Vl93EGtSdKomQX+iWeojJoQ4bfH/pka8mA1kn0Mh4n3c1DLq5Htw== 代人7LlJFwLa/n4Tl7+Qb54oEA==公式可得 qeiYnKXLEhyhuGRg8yLtrzo8GvSP4xculy5DO3Sob6IVWUjD4wl7h5qnJhdAlUpbSH6v1u7xQrusijHeQfEkrWEDlbWTeb1fjhmskBz3P6rKiklM1EvrAp3Pe9PHJwgySWlJFCOechLtIjJ2jcgMsxZKV+JCamyQ3rHOnhtDMfR1ljaXkHx2lCOyopyLp8xs8ORBA9Z6Djlu89orqubpz1ysyCKfUEkNz16GtRRg+R9G+bZb8+7xWL1rwgLciUKMql0XAQlUWydX9xauHSWbq2KGpjyX9Hmhcy60AfOonkb7FvXu/Md9RF+QyixbSpAwhlyN9CxWkwkPM2dKfeYHfhfozQ0p/KMj3OODnaEAn3fh7LFQSdO8eevpzdeK6wUV 把7LlJFwLa/n4Tl7+Qb54oEA==投影到坐标轴上, OgF2J4O5k8Yd5uNUqOEHWsWIyI4r7w9iAHmGDQFwkjYwmRlS7uSLsZVMRPytmYUSsQnA+gvRuE5h7ALnV27lDC024O55vNcRLXEn9KMfNJtDifqpYQqYWp//buzTCzMk, 方向沿ZKO2xs0EgSemzoH7MSmYTA==轴正向. KL7aTgrYstWeby2wcR39PZKvzRaMoKVU32uFsGqbM6qTFO0KmVKssakDZ+10mBkyguLi3xvQGWVST9gVRB9lNLe0HK73wnjytOxnr4kRO67psISWGmYHlxFi9BcmyOnA, 方向沿yBR4oiFoTexGaFalQ7m8kg==轴负向. 线圈受到的合力为 qeiYnKXLEhyhuGRg8yLtr9+cJto1DklJwybL4XeaTH2LbogCqhTYtBLBxC+xdPYn48qZvqePMWFRrzGT8AYGAZEWn/cdB4YE+FY/lTTOpHDIPbpSHt8G30NNgr7uM6seiRzwI3QB/00SyAL5G1ULMT8n7EioVXOFmvRP+gIz9Lte4LINZ09GYxx6BKuMBKIqf+vsGz+oH2iLobV9TFXkyLYEw5lqEJ/ZP0uMpi/CmvFG2JHnf5nyJsG160rkf5ZhvDTjtxeP9DFQmNpWIs+Wxg==