Electric Field: Find Distance z Above Line Segment

[leonne]

Homework Statement

Find the electric field distance z above one end of the straight line segment of length L which carrys uniform charge

Homework Equations

de=1/4pie Eo (Q/r^2) r^

The Attempt at a Solution

This was an example in a book and have few questions about it what they did was

using that formula de=1/4pie Eo (dQ/r^2) cos@
then plugs in, de=1/4pie Eo (y dx/(z^2+x^2) ) (z/(z^2+x^2)^1/2 y is the uniform charge.
My question is why did they do this as in how did they figure out r^2= (z^2+x^2) that dq= ydx and that r^ = cos@

I am bad at setting up the physics problem, i have no problem after everything is set up to solve it.
Thanks

 

[issacnewton]

hi leon

since you are trying to find the electric field at one end of the rod, you don't need to use
$\cos{\theta}$ in the formula. since you are presenting the solution from the book,are you sure they are finding the electric field at one end and not at the center of the
rod ? if author is trying to find the electric field at the center of the rod, distance z above it,
then having $\cos{\theta}$ there makes sense , since in that case we only count
the component of the electric field away from the rod...

 

[leonne]

Hey well actually it was a problem and found the solution on crampster, but after looking at the solution in the solution manual they have different answer, but they both use the cos ( maybe on crampster they simplified the final answer or something looks like they solved it same way)
well here's the step by step on what they did (idk if u have an account or not)
http://www.cramster.com/solution/solution/178791

 

[issacnewton]

hi

i see what's happening... i did calculation for the magnitude of E and they are doing calculations for the horizontal and vertical component of the E.. while calculating the components you will need to use cos and sin...but if you are just interested in the magnitude then you can do like I say...

 

[leonne]

o ok thxs

 

[issacnewton]

good luck