Calculating Electric Field in the First Quadrant: What is the Next Step?

[camrylx]

Homework Statement

A thin, semi-infinite rod with a uniform linear charge density (lambda) (in units of
C/m) lies along the positive x-axis from x = 0 to x = 1; a similar rod lies
along the positive y-axis from y = 0 to y = 1. Calculate the
electric field at a point in the x-y plane in the first quadrant.

Homework Equations

This is a calc based course. Intergration is required for this problem. If you need a diagram I do have one.

The Attempt at a Solution

 

[fluidistic]

Homework Statement

A thin, semi-infinite rod with a uniform linear charge density (lambda) (in units of
C/m) lies along the positive x-axis from x = 0 to x = 1; a similar rod lies
along the positive y-axis from y = 0 to y = 1. Calculate the
electric field at a point in the x-y plane in the first quadrant.

Homework Equations

This is a calc based course. Intergration is required for this problem. If you need a diagram I do have one.

The Attempt at a Solution

Hi and welcome to the forum!
In this forum you have to show an attempt, so that we can help you where you're stuck.

 

[camrylx]

This is one question that I am not that sure how to get started with.

 

[fluidistic]

$$d\vec E = \frac{kdQ \vec r}{r^3}$$. What is worth dQ in the case of a straight segment of length dx of the rod?
Once you have $$d\vec E$$, you just have to integrate (choosing the appropriate limits of integration) to get $$\vec E$$.
I suggest you to start by drawing the situation. Put a point $$(x_0,y_0)$$ in the first quadrant. Tackle the problem first with the x-axis rod. Calculate the E field due a small element dx of it, then integrate to get the E field (in point $$(x_0,y_0)$$) due to the whole x-axis rod.
Do the same for the y-axis rod and sum them up. Don't forget that they are vectors.

I hope it helps. Feel free to post any difficulties you encounter.

 

[camrylx]

ok so I understand that for intergrating the 2 rods you set them up as
$$\int dE1x+dE2x$$ and the same for the y component but I am kinda stuck on what is next.

 

[camrylx]

ok so I understand that for intergrating the 2 rods you set them up as
$$\int dE1x+dE2x$$ and the same for the y component but I am kinda stuck on what is next.