Question

如圖所示,在空中有一水平方向的勻強(qiáng)磁場(chǎng)區(qū)域,區(qū)域的上下邊緣間距為h,磁感應(yīng)強(qiáng)度為B.有一寬度為b(b＜h)、長(zhǎng)度為L(zhǎng)、電阻為R、質(zhì)量為m的矩形導(dǎo)體線(xiàn)圈緊貼磁場(chǎng)區(qū)域的上邊緣從靜止起豎直下落,當(dāng)線(xiàn)圈的PQ邊到達(dá)磁場(chǎng)下邊緣時(shí),恰好開(kāi)始做勻速運(yùn)動(dòng).求：

(1)線(xiàn)圈的MN邊剛好進(jìn)入磁場(chǎng)時(shí),線(xiàn)圈的速度大小;

(2)線(xiàn)圈從開(kāi)始下落到剛好完全進(jìn)入磁場(chǎng)經(jīng)歷的時(shí)間.

Answer 1

解析：(1)設(shè)MN邊剛進(jìn)入磁場(chǎng)時(shí)速度為v₁,PQ邊剛到達(dá)下邊緣時(shí)速度為v₂,此過(guò)程線(xiàn)圈機(jī)械能守恒：mv₁²+mg(h-b)=mv₂²                                              ①

PQ到達(dá)下邊緣時(shí)做勻速運(yùn)動(dòng),有

mg=BIL                                                                     ②

I==                                                                 ③

由①②③可得v₁=.

(2)設(shè)線(xiàn)圈從開(kāi)始下落到剛好完全進(jìn)入磁場(chǎng)所用時(shí)間為t,由動(dòng)量定理mgt-I_F=mv₁-0       ④

I_F=B·t                                                                    ⑤

===                                                           ⑥

代入U(xiǎn)₁值,由④⑤⑥式可得

t=+.