【題目】如圖所示,兩根相距為L(zhǎng)=1m的足夠長(zhǎng)的平行光滑金屬導(dǎo)軌,位于水平的xOy平面內(nèi),一端接有阻值為R=6Ω的電阻。在x>0的一側(cè)存在垂直紙面向里的磁場(chǎng),磁感應(yīng)強(qiáng)度B只隨t的增大而增大,且它們間的關(guān)系為B=kt,其中k=4T/s。一質(zhì)量為m=0.5kg的金屬桿與金屬導(dǎo)軌垂直,可在導(dǎo)軌上滑動(dòng),當(dāng)t=0時(shí)金屬桿靜止于x=0處,有一大小可調(diào)節(jié)的外力F作用于金屬桿,使金屬桿以恒定加速度a=2m/s2沿x軸正向做勻加速直線運(yùn)動(dòng)。除電阻R以外其余電阻都可以忽略不計(jì)。求:當(dāng)t=4s時(shí)施加于金屬桿上的外力為多大。
【答案】513N
【解析】t=4s時(shí),金屬桿移動(dòng)的位移x=at2=×2×16m=16m
此時(shí)的速度v=at=2×4m/s=8m/s
切割產(chǎn)生的動(dòng)生電動(dòng)勢(shì)E1=BLv=ktLv=4×4×1×8V=128V
磁場(chǎng)變化產(chǎn)生的感生電動(dòng)勢(shì)E2=Lx=4×1×16V=64V
根據(jù)楞次定律和右手定則知,兩個(gè)電動(dòng)勢(shì)的方向相同
則總電動(dòng)勢(shì)E=E1+E2=192V
則感應(yīng)電流的大小I==32A
根據(jù)牛頓第二定律得,F(xiàn)-BIL=ma
解得F=BIL+ma=4×4×32×1+0.5×2N=513N
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