Finding electric field with a changing linear charge density

[bosteador3]

Homework Statement

a thin rod of length L is set along an X axis. we want to find the electric field at a point P at the origin, a distance "d" from the rod. The linear change density changes with X and it's given by λ=λ0 ((x-d)^3)/d^3 find the electric field at the point P...

(P)|---d---| |--------------L-----------------|

L is the length of the rod, d is just a distance from the rod to the point P. P is at the origin (x=0)

Homework Equations

λ=λ0 ((x-d)^3)/d^3

dq=λ dx

The Attempt at a Solution

i put q/x on differential form to get dq=lambda dx do i get dE=kdq/r^2 ,(L+ d - x)^2 => E= (k*λ)/d^3 ∫(x-d)^3/(L+d-x)^2 dx... idk if I am wrong or what but i don't know how to solve that integral, i'd appreciate some help on this problem.

 

[Redbelly98]

Welcome to Physics Forums.

The Attempt at a Solution

i put q/x on differential form to get dq=lambda dx do i get dE=kdq/r^2 ,(L+ d - x)^2 => E= (k*λ)/d^3 ∫(x-d)^3/(L+d-x)^2 dx... idk if I am wrong or what but i don't know how to solve that integral, i'd appreciate some help on this problem.

The distance r from a charge element dq to the origin would simply be x, not L+d-x. Looks good otherwise.