Electric field vector due to very long thread

In summary, the problem involves finding the electric field vector at a distance of 15 cm from two parallel threads with a linear charge density of 10-8 C/cm. Using Gaussian law and the equation E*dA=Qenclosed/permittivity of free space, the electric field created by each thread can be calculated. To find the total field due to the two threads together, the magnitude of the field due to each thread is added together, taking into account their opposite direction. By analyzing a diagram, it is determined that the two points on the screen that are 15cm from both threads are perpendicular to the screen or page.
  • #1
Aleksandre
11
0

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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  • #2
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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Likes Aleksandre
  • #3
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?
 
  • #4
Aleksandre said:
Just add them up? so 2*E?
Are they in the same direction? Remember ##\vec E## is a vector quantity.
 
  • #5
They have opposite direction and same magnitude so would it be zero?
 
  • #6
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?
 
  • #7
No. Now I'm really stuck can I get a hint?
 
  • #8
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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  • #9
Ok I got it thanks. I was looking to threads from left view and could not see that.
 

1. What is an electric field vector?

An electric field vector is a mathematical quantity that describes the strength and direction of the electric field at a specific point in space. It is represented by a vector arrow, with the length of the arrow representing the strength of the field and the direction of the arrow indicating the direction of the field.

2. How is the electric field vector calculated for a very long thread?

The electric field vector due to a very long thread can be calculated using Coulomb's Law, which states that the magnitude of the electric field at a point is directly proportional to the magnitude of the charge and inversely proportional to the distance from the charge. For a very long thread, the charge is assumed to be evenly distributed along its length, so the electric field vector can be calculated by integrating the contributions from all points along the thread.

3. How does the direction of the electric field vector change along a very long thread?

The direction of the electric field vector along a very long thread will depend on the direction of the charge distribution. If the charge is positive, the field will point away from the thread, and if the charge is negative, the field will point towards the thread. Additionally, the direction of the field will change as you move along the thread, becoming more aligned with the thread as you get closer to it.

4. How does the electric field vector due to a very long thread differ from that of a point charge?

The electric field vector due to a very long thread differs from that of a point charge in two main ways. Firstly, the magnitude of the field will vary along the length of the thread, whereas for a point charge it is constant at all points. Secondly, the direction of the field will also vary along the thread, while for a point charge it will always point away from the charge if it is positive or towards the charge if it is negative.

5. How can the electric field vector due to a very long thread be visualized?

The electric field vector due to a very long thread can be visualized using field lines. These are imaginary lines that show the direction of the field at different points in space. For a very long thread, the field lines will be perpendicular to the thread and will be closer together near the thread, representing a stronger electric field. Additionally, the field lines will be continuous and will not intersect or cross each other.

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