- #1

darkpsi

- 23

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## Homework Statement

Find the electric field a distance

*z*above the midpoint of a straight line segment of length

2

*L*, which carries a uniform line charge

*λ*.

## Homework Equations

1) my textbook says :

**E**(

**r**) = 1/4

**πε**

_{o}∫

_{V}

*λ*(

**r**')/

*r*

^{2}

*r**dl*'

2) and this also works? :

**E**(

**r**) = 1/4

**πε**

_{o}∫

_{V}

*λ*(r')/

*r*

^{3}

*r**dl*'

both where

**is the unit vector from the charge to the point we are caluclating the field at**

*r*## The Attempt at a Solution

I can integrate once I get the setup down just fine. I just wanted to know when and why this two are the same. For example, in my book it says for the setup for this problem :

**E**(

**r**) = 2 * 1/4

**πε**

_{o}∫

_{V}

*(λdx*/

*r*

^{2})cos

*θ*

**z**

For one thing, how did that cos appear and since it equals z/

*r*couldn't 2) have just been used from the start? And if 2) can be used could I apply it to surface and volume integrals?