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## Homework Statement

A charge per unit length +λ is uniformly distributed along the positive y-axis from y = 0 to y = +a. A charge per unit length −λ is uniformly distributed along the negative y-axis from y = 0 to y = −a. Write an expression for the electric field at a point on the x-axis a distance x from the origin. (Use the following as necessary: k, λ, x, and a.)

## Homework Equations

E = k|q|/r

^{2}

I derived this equation by treating the ends of the wire as point charges.

E

_{y}= 2kqa/(y

^{2}+x

^{2})

^{3/2}

## The Attempt at a Solution

I quickly determined that the field vectors x and k would be 0.

For the y vector:

dE

_{y}= 2ak(dq)/(y

^{2}+x

^{2})

^{3/2}

dq/dy = Q/2a

∫dE

_{y}= (4akQ/2a)∫dy/(y

^{2}+x

^{2})

^{3/2}

= 2kQy/[x

^{2}(y

^{2}+x

^{2})

^{1/2}]

2kλy/[x

^{2}(y

^{2}+x

^{2})

^{1/2}]

The limits of integration are from 0 to a.

I am pretty sure this is not correct, and have been working at it for a while, so I would appreciate some help.