# Electric Field problem

1. Feb 7, 2009

### Seraph404

1. The problem statement, all variables and given/known data

A very long uniform line of charge has charge per unit length 4.88E-6 C/m and lies along the x-axis. A second long uniform line of charge has charge per unit length -2.44E-6 C/m and is parallel to the x-axis at y1 = 0.408 m.

What is the magnitude of the net electric field at point y2 = 0.198 m on the y-axis?

2. Relevant equations

E = kq/r^2

3. The attempt at a solution

E1 = (9E9)(4.88E-6)/(.198)^2
E2 = (9E9)(-2.44E-6)/(.21)^2

net E = E1 + E2 (both point in the positive y direction), but I'm not getting the right answer. Apparently, my answer is close, but not correct. Can somebody help me to spot my mistake?

Also, I know the problem gave linear charge density, but it didn't say how long the wire was. Maybe that's where my error lies. If so, how do I correct it?

2. Feb 8, 2009

### Hootenanny

Staff Emeritus
One cannot simply take the expression for the electric field of a point charge and apply it to an infinite line charge. Conceptually, to find the electric field do to a line charge one must sum up the contributions from each individual point charge. Since the charge distribution is continuous one does this via an integral rather than a sum.

See this page: http://hyperphysics.phy-astr.gsu.edu/HBASE/electric/elelin.html for more information.

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