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E-Field Strength of a Infinite Long Charged Rod

Question:

There is a charged rod whose length is infinite. Find the at a distance a from the road. Given that the charge density is

Solution

Pick a little particle on the rod whose length is and the y-coordinate of the little particle is y on y-axis.
Then the distance can be represented as

The E-field given by is . Since the rod’s length is infinity, all y-component of is cancelled.

Then the differential equation is obtained.

OOPS… the bounds are ignored

It should be:

Put out from the polynomial:

It is spontaneous to find that

Use substitution:

Hence

我们都知道, 根据牛顿的运动学公式:

转换得到:

两侧同时积分

提出常数m

此时, 对于恒力:

当时:

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