Electric field vector due to very long thread

[Aleksandre]

Homework Statement

Two parallel very long threads are uniformly charged with linear charge density of 10^-8 C/cm . Distance between them is 15 cm. Find electric field vector at a distance of 15 cm from both threads.

Homework Equations

E*dA=Qenclosed/permittivity of free space

The Attempt at a Solution

So I assumed that the electric fields created by each thread would be equal as they have same characteristics. So to solve the problem I just had to find electric field created by a long thread. To solve it, I used Gaussian law (enclosed the thread with a cylinder of radius R=15cm and length L), the equation above which led me to:

E*2pi*R*L=Qenclosed/epsilon where Qenclosed = charged density lambda * L

E*2pi*R*L = lambda * L / epsilon
Uknown Ls cancel out, R is a intial distance 0.15 m so I can solve for E. The final electric field found, will be same for second thread as well. Is this solution correct?

 

[jtbell]

You're OK so far, for the magnitude of the field due to each thread separately.

How do you propose to find the total field due to the two threads together?

 

[Aleksandre]

You're OK so far, for the magnitude of the field due to each thread separately.

How do you propose to find the total field due to the two threads together?

Just add them up? so 2*E?

 

[jtbell]

Just add them up? so 2*E?

Are they in the same direction? Remember $\vec E$ is a vector quantity.

 

[Aleksandre]

They have opposite direction and same magnitude so would it be zero?

 

[jtbell]

They have opposite direction

Can you draw a diagram that shows how that can be true at a point that is 15cm from each thread, while the threads themselves are separated by 15cm?

 

[Aleksandre]

No. Now I'm really stuck can I get a hint?

 

[jtbell]

In this diagram, the two threads are perpendicular to the screen or page, so they appear as points. There are two points on the screen that are 15cm from both threads. Where are they?

 

[Aleksandre]

Ok I got it thanks. I was looking to threads from left view and could not see that.