# Conservation of electric feild

1. Feb 4, 2010

### amodedude1

1. In the figure below, short sections of two very long parallel lines of charge are shown, fixed in place and separated by L = 8.0 cm. The uniform linear charge densities are +5.8 µC/m for line 1 and -2.0 µC/m for line 2. Where along the x axis shown is the net electric field from the two lines zero?

(link to image: ) http://img190.imageshack.us/img190/8695/hrw72335.gif [Broken]

L=8cm=.08m
charge density1=+5.8 µC/m
charge density2=-2 µC/m

2. I used E1=E2

3. The attempt at a solution:

I solve E1=E2

I cancel the 1/(4pi E)'s , cross multiply and get charge density1(x-L/2)=charge density2(x+L/2), then get charge density1/charge density2= (x-(L/2))/ (x+(L/2))

but my very poor algebra limits me here. How do I go about solving this. (remember my algebra is hideous)

Last edited by a moderator: May 4, 2017
2. Feb 4, 2010

### Spinnor

The electric field varies as 1/r for a wire? If so we can superimpose the two fields along the x axis,

E(along the x axis) = q_1/x + q_2/(x + seperation of lines) = 0

solve for x