有一半径为R的均匀带正电的半圆环,电荷线密度为λ,求圆心的电场强度?

2025-03-16 23:11:02
推荐回答(1个)
回答1:

解题过程:

已知线密度λ,所以,线元上的电荷dq=λdl,而dl=Rdθ,所以,dq=λRdθ,然后求这个点电荷对环心的电场在x轴的分量,因为上下对称,所以对y轴的电场分量抵消掉了。没记错的话,Ex=λRcosθdθ/4πεRˇ2,最后积分,θ为90度到负270度。艾玛,困死我了,睡了,有错明天再纠正。

释义:

电场强度:

是用来表示电场的强弱和方向的物理量。实验表明,在电场中某一点,试探点电荷(正电荷)在该点所受电场力与其所带电荷的比值是一个与试探点电荷无关的量。于是以试探点电荷(正电荷)在该点所受电场力的方向为电场方向,以前述比值为大小的矢量定义为该点的电场强度,常用E表示。按照定义,电场中某一点的电场强度的方向可用试探点电荷(正电荷)在该点所受电场力的电场方向来确定;电场强弱可由试探电荷所受的力与试探点电荷带电量的比值确定。试探点电荷应该满足两个条件;(1)它的线度必须小到可以被看作点电荷,以便确定场中每点的性质;(2)它的电量要足够小,使得由于它的置入不引起原有电场的重新分布或对有源电场的影响可忽略不计。电场强度的单位V/m伏特/米或N/C牛顿/库仑(这两个单位实际上相等)。常用的单位还有V/cm伏特/厘米。


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