如图所示,真空室中电子枪连续均匀发出的电子(初速不计)经过
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EU%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmath%3E)
V的加速电场后,由小孔S沿两个互相垂直的偏转电极
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EY%3C%2Fmtext%3E%3Cmtext%3EY%3C%2Fmtext%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmath%3E)
和
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EX%3C%2Fmtext%3E%3Cmtext%3EX%3C%2Fmtext%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmath%3E)
的中心线射入。偏转电极
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EY%3C%2Fmtext%3E%3Cmtext%3EY%3C%2Fmtext%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmath%3E)
的板长为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EL%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmath%3E)
m,极板相距
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ed%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmath%3E)
m,偏转电极
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EX%3C%2Fmtext%3E%3Cmtext%3EX%3C%2Fmtext%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmath%3E)
的板长也为
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EL%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmath%3E)
m,极板相距
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3Ed%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E0%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmath%3E)
m,且高度足够高。偏转电极
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EY%3C%2Fmtext%3E%3Cmtext%3EY%3C%2Fmtext%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmath%3E)
的右侧与偏转电极
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EX%3C%2Fmtext%3E%3Cmtext%3EX%3C%2Fmtext%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmath%3E)
的左侧相距为L,荧光屏与中心线垂直,且与偏转电极
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EX%3C%2Fmtext%3E%3Cmtext%3EX%3C%2Fmtext%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmath%3E)
的右侧相距为L/2。两个偏转电极都不加电压时,电子束沿中心线打到荧光屏中心产生亮斑。现在电极
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EY%3C%2Fmtext%3E%3Cmtext%3EY%3C%2Fmtext%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmath%3E)
间加电压
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EU%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3EY%3C%2Fmtext%3E%3Cmtext%3EY%3C%2Fmtext%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
, 在电极
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmtext%3EX%3C%2Fmtext%3E%3Cmtext%3EX%3C%2Fmtext%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmath%3E)
间加电压
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EU%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3EX%3C%2Fmtext%3E%3Cmtext%3EX%3C%2Fmtext%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
,
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EU%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3EY%3C%2Fmtext%3E%3Cmtext%3EY%3C%2Fmtext%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
和
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmsub%3E%3Cmrow%3E%3Cmi%3EU%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmtext%3EX%3C%2Fmtext%3E%3Cmtext%3EX%3C%2Fmtext%3E%3Cmn%3E%27%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsub%3E%3C%2Fmath%3E)
的电压随时间t变化的图线分别如图所示。设极板间电场可看作是均匀的,且极板外无电场,在每个电子通过电场区域的极短时间内,电场均可视作恒定,能通过两偏转电极的电子均能打到荧光屏上。已知电子的电量
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Eq%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E.%3C%2Fmn%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E0%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmtext%3EC%3C%2Fmtext%3E%3C%2Fmath%3E)
, 不计电子重力和电子间的相互作用。
![](http://tikupic.21cnjy.com/2022/03/01/1a/c1/1ac180132a1aa71680db5af0d96baa4c_1058x164.png)