How Do You Calculate Electric Field Components of a Uniformly Charged Rod?

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To calculate the electric field components of a uniformly charged rod, one must integrate the contributions from each infinitesimal segment of the rod. The electric field at point P on the y-axis, a distance d from the origin, can be expressed using the equations E_x = r sin(θ) [(kQ)/r^2] and E_y = r cos(θ) [(kQ)/r^2]. When d is much greater than L, the field components can be approximated based on the geometry of the setup. It is crucial to define the variables in terms of the integration limits and the geometry of the rod. Understanding these components and the integration process is essential for accurately calculating the electric field.
jls
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1. Problem Statement
A uniformly charged rod of length L and total charge Q lies along the x-axis as shown in in the figure below. (Use the following as necessary: Q, L, d, and ke.)

(a) Find the components of the electric field at the point P on the y-axis a distance d from the origin.

(b) What are the approximate values of the field components when d >> L?

2. Equations
I have a diagram and understand that E=kQ/r^2, however, I can not figure out how to define each component.

3. Attempt
I know that I must integrate to solve once I have defined the component, however I do not know how to define them.
Would Ex=rsin(θ)[(kQ)/r^2] and Ey=rcos(θ)[(kQ)/r^2] be at all in the right direction?
 
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Hello jls, and welcome to PF.
Can't find a picture... or is the figure below in your book only ? In that case:
Is the center of the rod at x=0 ? (would make things easier...)
 
jls said:
1. Problem Statement
A uniformly charged rod of length L and total charge Q lies along the x-axis as shown in in the figure below. (Use the following as necessary: Q, L, d, and ke.)

(a) Find the components of the electric field at the point P on the y-axis a distance d from the origin.

(b) What are the approximate values of the field components when d >> L?

2. Equations
I have a diagram and understand that E=kQ/r^2, however, I can not figure out how to define each component.

3. Attempt
I know that I must integrate to solve once I have defined the component, however I do not know how to define them.
Would Ex=rsin(θ)[(kQ)/r^2] and Ey=rcos(θ)[(kQ)/r^2] be at all in the right direction?
##E = \frac{kQ}{r^2}## only applies for a point charge. There's probably an example done in your textbook that you might find very helpful.
 
Yup. Now we set up the integral (which you already expected to be needed). We take a little chunk of rod from x to x+dx and write down the x and y components of ##\vec E## at point ##\vec P = (0, y_P)##. Is one way.

Your Ex=rsin(θ)[(kQ)/r^2] and Ey=rcos(θ)[(kQ)/r^2] looks like an integration over ##\theta##; is fine too.

Both cases you need to express the things that vary in terms of the integrand: r(##\theta##), Q(##\theta##) -- or rather the dQ from ##\theta## to ##\theta + d\theta##. Or express them in x and dx and let x run from 0 to L.
 
How do you turn that chunk (x to x+dx) into the components? I think I could figure it out if I knew what that meant..
 
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