Question

如圖所示,水平導軌間距為L,左端接有阻值為R的定值電阻,在距左端x₀處放置一根質(zhì)量為m、電阻為r的導體棒,導體棒與導軌間無摩擦且始終保持良好接觸,導軌的電阻可忽略,整個裝置處在豎直向上的勻強磁場中.問:在下列各種情況下,作用在導體棒上的水平拉力F的大小應如何?

(1)磁感應強度為B=B₀保持恒定,導體棒以速度v向右做勻速直線運動;

(2)磁感應強度為B=B₀+kt隨時間t均勻增強,導體棒保持靜止;

(3)磁感應強度為B=B₀保持恒定,導體棒由靜止始以加速度a向右做勻加速直線運動;

(4)磁感應強度為B=B₀+kt隨時間t均勻增強,導體棒以速度v向右做勻速直線運動.

Answer 1

解:(1)導體棒以速度v向右做勻速直線運動,

E=BLv                                                                       ①

I=                                                                     ②

F₁=B₀IL=.                                                             ③

(2)由法拉第電磁感應定律

E=Lx₀                                                              ④

=k                                                                      ⑤

所以E=kLx₀

F₂=BIL=(B₀+kt).                                                 ⑥

(3)因為v=at                                                                  ⑦

由牛頓第二定律F₃-BIL=ma                                                     ⑧

所以F₃=B₀IL+ma=at+ma.                                                 ⑨

(4)電路中產(chǎn)生了動生電動勢和感生電動勢,

所以E=BLv+kL(x₀+vt)=(B₀+kt)Lv+kL(x₀+vt)                                       ⑩

所以F₄=BIL=.                     11