Electric field at point between two finite charged wires

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SUMMARY

The electric field at point A, located between two parallel charged wires in a vacuum, is calculated using the principle of superposition. The derived formula for the electric field is EA=√2 λ/(πε0a), while the book solution states EA=λ/(2ε0a). The analysis confirms that the user's solution is correct, and the book's answer is inaccurate. The cancellation of y-components in the electric field vectors is contingent upon the defined orientation of the coordinate system.

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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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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.
 

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