Calculate the x-component of the electric field

AI Thread Summary
To calculate the x-component of the electric field produced by a uniformly distributed positive charge Q along the x-axis, the distance R must be correctly defined as R = r + a - x for points where x > a. The electric field equation e = kQ/R^2 is applicable, but the integration requires expressing the differential charge dq in terms of dx, where dq = (Q/a)dx. The integral can be set up as (kQ/a) ∫(1/(r + a - x)^2) dx, ensuring to square the distance in the integrand. Proper substitution and integration techniques are necessary to simplify the expression and solve for the electric field. Understanding the distance and charge distribution is crucial for accurate calculations.
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Positive charge Q is distributed uniformly along the x-axis from x=0 to x=a. A positive point charge q is located on the positive x-axis at x=a+r, a distance r to the right of the end of Q.

Homework Statement


Calculate the x-component of the electric field produced by the charge distribution Q at points on the positive x-axis where x>a (i.e., r>0) in terms of some or all of the variables k, q, Q, a, and r, where k=\\frac{1}{4\\pi\\epsilon_0}.

The Attempt at a Solution


I'm having a problem visualizing the distance between the charge and the point. I understand that e=KQ/R^2. However, I have no idea how to get R.
I would do: (k*dQ)/(r+a-x)...
(kQ/a) [integral]1/(r+a-x)dxBut I don't think that looks right. Can anyone give me a few pointers?
 
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Looks great! Except you forgot to square the distance (r+a-x) in the integral.
Also, something must be done about dq to express it in terms of dx so it will be possible to integrate. The charge on a segment dx would be dq = (q/a)dx because the charge per unit length is q/a.
Finally, the integral is awkward with the r and a in there. You can get it with math techniques of course (let R= r+a-x), but it might be better to think of the distance as R and integrate it from R = a+r to r. Of course dR = dx.
 
Thank you for your help. I needed someone to confirm the distance for me since I was completely lost on that part.
 
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