【題目】如圖所示為一速度選擇器,也稱為濾速器的原理圖K為電子槍,由槍中沿KA方向射出的電子,速率大小不一。當(dāng)電子通過方向互相垂直的勻強電場和磁場后,只有一定速率的電子能沿直線前進(jìn),并通過小孔S。設(shè)產(chǎn)生勻強電場的平行板間的電壓為300 V,間距為5 cm,垂直于紙面的勻強磁場的磁感應(yīng)強度為006 T,問:

1磁場的指向應(yīng)該向里還是向外?

2速度為多大的電子才能通過小孔S?

【答案】1磁場方向垂直于紙面向里 2105 m/s

【解析】1由題圖可知,平行板產(chǎn)生的電場強度E方向向下,帶負(fù)電的電子受到的電場力FE=eE,方向向上。

若沒有磁場,電子束將向上偏轉(zhuǎn),為了使電子能夠穿過小孔S,所加的磁場對電子束的洛倫茲力必須是向下的。根據(jù)左手定則分析得出,B的方向垂直于紙面向里。

2電子受到的洛倫茲力為:FB=evB,它的大小與電子速率v有關(guān)。只有那些速率的大小剛好滿足洛倫茲力與電場力相平衡的電子,才可沿直線KA通過小孔S。據(jù)題意,能夠通過小孔的電子,其速率滿足下式:evB=eE

解得:v=

又因為E=

所以v=

將U=300 V,B=006 T,d=005 m代入上式,得v=105 m/s

即只有速率為105 m/s的電子才可以通過小孔S

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