# Electric field of line charge with non uniform charge densit

## Homework Statement

A thin line of charge is on the x-axis from x = -L/2 to L/2. The charge density is non uniform and given by λ = ax where x are the points on the charge distribution. Calculate the electric field for all points along the y axis.

E = kQ/r^2

## The Attempt at a Solution

dq=axdx

y component of E = kaxdx/(x^2+y^2) cosθ = kaxdxy/(x^2+y^2)^(3/2)
after integrating from x = -L/2 to L/2 it comes out to be 0 which makes sense because the positive side cancels out the negative side of the charge charge distribution.

x component of E = kaxdx/(x^2+y^2) sinθ = kax^2dx/(x^2+y^2)^(3/2)
I can't figure out how to do the integral though

ehild
Homework Helper
Try integration by parts.

rude man
Homework Helper
Gold Member

## Homework Statement

A thin line of charge is on the x-axis from x = -L/2 to L/2. The charge density is non uniform and given by λ = ax where x are the points on the charge distribution. Calculate the electric field for all points along the y axis.

E = kQ/r^2

## The Attempt at a Solution

dq=axdx

y component of E = kaxdx/(x^2+y^2) cosθ = kaxdxy/(x^2+y^2)^(3/2)
after integrating from x = -L/2 to L/2 it comes out to be 0 which makes sense because the positive side cancels out the negative side of the charge charge distribution.

x component of E = kaxdx/(x^2+y^2) sinθ = kax^2dx/(x^2+y^2)^(3/2)
I can't figure out how to do the integral though
Try Wolfram Alpha or a table of integrals!