一半径为R的无限长带电细棒,其内部的电荷均匀分布,电荷的体密度为ρ.现取棒表面为零电势,求空间电势分布并画出分布曲线.
正确答案:
取高度为l、半径为r且与带电棒同轴的圆柱面为高斯面,由高斯定理
当r≤R时
![](https://img.274949.com/Images/2020-04/04/w0smnk7f.jpg)
得![](https://img.274949.com/Images/2020-04/04/1fnbxq5b.jpg)
当r≥R时![](https://img.274949.com/Images/2020-04/04/237oxep4.jpg)
得![](https://img.274949.com/Images/2020-04/04/buo1c1ad.jpg)
取棒表面为零电势,空间电势的分布有
当r≤R时![](https://img.274949.com/Images/2020-04/04/ps0pr4yn.jpg)
当r≥R时
![](https://img.274949.com/Images/2020-04/04/kvkbcdc9.jpg)
当r≤R时
![](https://img.274949.com/Images/2020-04/04/w0smnk7f.jpg)
得
![](https://img.274949.com/Images/2020-04/04/1fnbxq5b.jpg)
当r≥R时
![](https://img.274949.com/Images/2020-04/04/237oxep4.jpg)
得
![](https://img.274949.com/Images/2020-04/04/buo1c1ad.jpg)
取棒表面为零电势,空间电势的分布有
当r≤R时
![](https://img.274949.com/Images/2020-04/04/ps0pr4yn.jpg)
当r≥R时
![](https://img.274949.com/Images/2020-04/04/kvkbcdc9.jpg)
![](https://img.274949.com/Images/2020-04/04/u2enwf8j.jpg)
答案解析:有
![](/editor/images/201705/qrcode_for_gh_573e2a458573_258.jpg)
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一半径为R的无限长带电细棒,其内部的电荷均匀分布,电荷的体密度为ρ.现取棒表面为零电势,求空间电势分布并画出分布曲线.
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