M's Electric Field Calculation for a Uniformly Charged Wire

[hmmm]

A uniformly charged wire with a charge density of 4 microCoulombs/meter lies on the x-axis between x=1m and x=3m. What is the y-component of the corresponding electric field at y=3m on the y-axis?

I'm not really sure where to go with this. I want to treat the rod as an infinite number of point charges but I'm not sure how to calculate (y-component of) the electric field caused by each of these points.

 

[epsilon infinity]

suppose there is a point charge on the point y=3 , find the electric fireld there, actually the electric field there for suppose due to the charge on the X=1 m can be broken up into two components one along -x and another along +y axis..they can be computed separately by integrating ..in this case i think you only need to compute for the y aixs one...for the integration take elemental lengths dx for the wire...

glad to be of help,
Arpan Roy
royarpan@hotmail.com

 

[HallsofIvy]

Note that, for each "dx" on one side of the point, there is a corresponding "dx" the same distance on the other side. The horizontal components of force of those will cancel but the vertical components will add.

 

[MathStudent]

Since this problem is not symmetrical, the horizontal components of the $\vec{E}$ do not cancel. The easiest approach is probably to calculate the vertical ( $\vec{E_y}$ ) component seperately.

Draw a diagram of the situation with the given axis, and choose an arbitrary piece of charge $dq$ of the wire.

Come up with an equation for the corresponding electric field $\vec{dE}$ due to $dq$ at the point (0,3).

Figure a way to represent $dq$ in terms of $dx$ so you can integrate with respect to x.
(hint: it involves the linear charge density )

Break the equation into the vertical component of $\vec{E}$ and integrate with respect to x
(hint: $\vec{dE_y} = \vec{dE} sin \theta$ where theta is the angle between a line parallel to the x-axis and $\vec{E}$ )
(another hint: you will have to come up with an equation for $sin \theta$ in terms of x so you can integrate )

good luck
-MS