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

[jls]

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?

 

[BvU]

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...)

 

[vela]

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.

 

[jls]

BvU, The rod begins at x=0 and goes for a distance (L). I am not sure if you can open this, but it has the image. https://www.webassign.net/serpse8/23-p-036.gif

 

[BvU]

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.

 

[jls]

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..