# Uniformly charged wire

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.

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...

Arpan Roy
royarpan@hotmail.com

HallsofIvy
Homework Helper
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.

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

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