Electric field at point between two finite charged wires

In summary, using superposition and integration by angle component, the electric field at point A between two parallel charged wires in vacuum with equal widths and distance between them is calculated to be EA=√2 λ/(πε0a). The book's solution of EA=λ/(2ε0a) is incorrect. The y-components of E do not cancel and the y direction must be perpendicular to the wires. Further details of the solution method are needed to confirm its accuracy.
  • #1
gruba
206
1

Homework Statement


Two parallel charged wires are in vacuum. Width of wires is equal to the distance between them. Calculate electric field in the middle (point A).

Homework Equations


Superposition

The Attempt at a Solution


Using superposition, y components on vector E are cancelled. I get that the electric field at point A is
EA=√2 λ/(πε0a)
In my books solution, it is
EA=λ/(2ε0a)
Is my solution correct?
Note: I used integration by angle component.

Thanks for replies.
 

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  • #2
What direction are you calling y? If the y direction is vertical (perpendicular to the wires), then how do you get that the y-components of E cancel?

However, I do think your answer is correct for the magnitude of the net field at A and that the book solution is incorrect. We would need to see your steps in order to check that your method is correct.
 

Related to Electric field at point between two finite charged wires

1. What is the definition of an electric field?

The electric field is a physical quantity that describes the direction and magnitude of the force exerted on a charged particle by other charged particles in its vicinity.

2. How is the electric field at a point between two charged wires calculated?

The electric field at a point between two charged wires can be calculated using Coulomb's Law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

3. What factors affect the strength of the electric field between two charged wires?

The strength of the electric field between two charged wires is affected by the magnitude of the charges on the wires, the distance between them, and the medium in which the wires are placed.

4. Can the electric field at a point between two charged wires be negative?

Yes, depending on the direction of the charges on the wires, the electric field at a point between them can be negative. This indicates that the force on a charged particle at that point would be in the opposite direction of the electric field.

5. How does the electric field at a point between two charged wires change as the distance between the wires increases?

The electric field between two charged wires decreases as the distance between them increases. This is because the force between the charged particles decreases with distance according to the inverse square law.

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