Electric field vector due to very long thread

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SUMMARY

The discussion centers on calculating the electric field vector produced by two parallel, uniformly charged threads with a linear charge density of 10^-8 C/cm, separated by a distance of 15 cm. Using Gauss's law, the electric field (E) is derived from the equation E*2πR*L = λL/ε, where λ is the linear charge density and ε is the permittivity of free space. The final electric field is the same for both threads, but since they are oppositely directed at a point equidistant from both, the total electric field at that point is zero. A diagram is suggested to clarify the spatial relationship between the threads and the observation point.

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Aleksandre
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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?
 
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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?
 
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jtbell said:
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?
 
Aleksandre said:
Just add them up? so 2*E?
Are they in the same direction? Remember ##\vec E## is a vector quantity.
 
They have opposite direction and same magnitude so would it be zero?
 
Aleksandre said:
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?
 
No. Now I'm really stuck can I get a hint?
 
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?

threads.gif
 

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  • threads.gif
    threads.gif
    4.1 KB · Views: 614
Ok I got it thanks. I was looking to threads from left view and could not see that.
 

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