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

AI Thread Summary
To calculate the electric field at a point in the first quadrant due to two semi-infinite rods with uniform linear charge density, integration is required. The approach involves calculating the electric field contribution from a small segment of each rod and then integrating over the length of the rods. It is suggested to first focus on the x-axis rod, determining the electric field from a small element and integrating to find the total field at the specified point. The same process should be repeated for the y-axis rod, and the vector components of the electric fields from both rods must be summed. Clarification on the integration limits and the expression for dQ is needed to proceed effectively.
camrylx
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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

 
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camrylx said:

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

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