如图甲所示,y轴右侧空间有垂直xoy平面向里的匀强磁场,同时还有沿-y方向的匀强电场(图中电场未画出)。磁感应强度随时间变化规律如图乙所示(图中B0已知,其余量均为未知)。t0时刻一质量为m、电荷量为+q的带电粒子以速度v0从坐标原点O沿x轴射入电场和磁场区,t0时刻粒子到达坐标为(x0,y0)的点A(x0>y0),速度大小为v,方向沿+x方向,此时撤去电场。t=t0+t1+t2时刻,粒子经过x轴上x=x0点,速度沿+x方向。不计粒子重力,求:
(1)0-t0时间内OA两点间电势差UOA;
(2)粒子在t=0时刻的加速度大小a;
(3)B1的最小值及对应t2的表达式。
![](https://img.xkw.com/dksih/QBM/2017/4/6/1659979633065984/1663300954816512/STEM/7b643a84-dd0d-4142-956e-f24463e18c93.png?resizew=486)
(1)0-t0时间内OA两点间电势差UOA;
(2)粒子在t=0时刻的加速度大小a;
(3)B1的最小值及对应t2的表达式。
![](https://img.xkw.com/dksih/QBM/2017/4/6/1659979633065984/1663300954816512/STEM/7b643a84-dd0d-4142-956e-f24463e18c93.png?resizew=486)
更新时间:2017-04-11 09:37:21
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【知识点】 带电粒子在叠加场中的一般曲线运动
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【推荐1】在一真空室内存在着匀强电场和匀强磁场,电场与磁场的方向相同,已知电场强度
,磁感应强度
。如图所示,在该真空室内建立
三维直角坐标系,其中z轴竖直向上。质量
,带负电的质点以速度
沿
方向做匀速直线运动,速度方向与电场、磁场垂直,取
。
(1)电场和磁场的方向;
(2)若在质点通过O点时撤去磁场,求撤去磁场后带电质点单位时间内电势能的变化量;
(3)若在质点通过O点时撤去磁场,试写出带电质点经过空间某点的z轴坐标数值为A时的动能表达式。
![](https://img.xkw.com/dksih/QBM/2022/1/16/2895560793784320/2895883225505792/STEM/293fab286ee34eb29322ceb8c9900755.png?resizew=34)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc50354ae87f51107050ce98f4cab52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11f626267206cfa0f944648e198d5388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a834024400d0730af3e640ca4d5f54b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d023e678ee204eb9dda036132fda88c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0499dfe41c9032628bb3bc50937c1bad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde4419a36437d5487b6023c3c6eb7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799edf593e3ba2b2372a83d9782be3a2.png)
(1)电场和磁场的方向;
(2)若在质点通过O点时撤去磁场,求撤去磁场后带电质点单位时间内电势能的变化量;
(3)若在质点通过O点时撤去磁场,试写出带电质点经过空间某点的z轴坐标数值为A时的动能表达式。
![](https://img.xkw.com/dksih/QBM/2022/1/16/2895560793784320/2895883225505792/STEM/293fab286ee34eb29322ceb8c9900755.png?resizew=34)
![](https://img.xkw.com/dksih/QBM/2022/1/16/2895560793784320/2895883225505792/STEM/584b6796-8a35-4cb7-9bdb-09eb42a7d34e.png?resizew=171)
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【推荐2】如图甲所示,垂直于纸面方向足够长的平行金属板M、N水平放置,板宽与板间距离均为
,M、N分别与一电压可调的电源正负极相连。板间有垂直纸面向里的匀强磁场,磁感应强度为
,板右侧空间有垂直纸面向里的有界匀强磁场
(
未知,图中未画出),宽度为
。两板中心线左端点O有一粒子源,可以水平向右持续发射相同初速度的质量为m、电量为
(
)的带电粒子,粒子在板间运动时间很短,每一个粒子在板间运动时均认为电压恒定,不计粒子重力及粒子间的相互作用。
(1)当
时,粒子打在上板中央位置,要使所有粒子在板间做直线运动,求
;
(2)撤去板间磁场,要使所有粒子均能进入右侧磁场且不从右边界穿出磁场,求
的最大值及右侧磁场
的最小值;
(3)撤去板间磁场后,在M板上方加一竖直向上的匀强磁场
(如图乙),若
,
,
,求粒子打在M板上的痕迹长度
。
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41d793c851a2f72f787913ba23e459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7005224d482d104b0a4ff6d593eefd4.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6229637004581c51e91f53ef04a4707a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce07efe9f381f2740c3bd46e17a9a0ac.png)
(2)撤去板间磁场,要使所有粒子均能进入右侧磁场且不从右边界穿出磁场,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce07efe9f381f2740c3bd46e17a9a0ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
(3)撤去板间磁场后,在M板上方加一竖直向上的匀强磁场
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/862ef68dc991b5086311285e3905597d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f95f4aef25f8b8b67f13896ef07507.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4377c5b83ec68125f9265cdf7b510263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
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【推荐3】如图所示,水平光滑绝缘轨道
与竖直平面内半径
的光滑绝缘半圆弧形轨道
在
点平滑连接,轨道
上方有三个与水平面平行的区域I、Ⅱ和Ⅲ,区域I的高度为
,区域Ⅱ的高度为
;竖直线
左侧空间(包括边界线
)区域I内有水平向右的匀强电场
,区域Ⅱ和区域
内分别有竖直向上的匀强电场
和
(水平边界线
上无电场);区域
内还有垂直纸面向里的水平匀强磁场。质量
、带电量为
的小球从
点静止释放,经过
从
点进入半圆弧形轨道并恰能通过
点,之后在电场
的作用下进入区域
,小球在区域Ⅲ内做匀速圆周运动,最终小球能回到区域
。重力加速度
取![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c4ee1b7d06ac4c703e4c086b425c9c5.png)
(1)匀强电场
和
的场强大小
(2)如果
,小球恰好落到水平轨道
上的
点,匀强磁场的磁感应强度
的大小。
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b264a8e697336e02a666ed7741cd0f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/054e130392b3298ecf44b98f522a2c5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e7f30167e1135806fe9de641870b1e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d873158f54a6cc76bd44d3dac934781d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735056c174e8dd7906257a2a50a962a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735056c174e8dd7906257a2a50a962a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f5e789d24077db7aa17a5b99421d2e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4dbe5d5c8b9c28c6f5eb92278a9f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f5e789d24077db7aa17a5b99421d2e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af3d94f0d0ca265aa902862d5222162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec0127d4f33a026492cdddbacb4a0ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/119fc12ccbcdeb8120d6b6b889d0a4c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf3d8dfe41a8dc4e4248bdf593a6266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276509f01529d982ab21e479a4619268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c4ee1b7d06ac4c703e4c086b425c9c5.png)
(1)匀强电场
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4dbe5d5c8b9c28c6f5eb92278a9f17.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc59068f7a85cd77cf0df6d1db9985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/2021/1/11/2633721214394368/2672215459184640/STEM/cf86826d-b48a-4c20-9225-1178fda27974.png?resizew=235)
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