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Coulomb force on a line charge 
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#1
Sep1408, 03:11 PM

P: 19

1. The problem statement, all variables and given/known data
We have a source charge that is a uniform sphere with a radius a (centered at origin) and uniform charge density, [tex]\rho[/tex]. There is a line charge with a length L that begins at Z_{0} and ends at Z_{0} + L (lies on the Z axis). This line charge has a uniform charge density of [tex]\lambda[/tex]. 2. Relevant equations Ill combine this with my attempt. 3. The attempt at a solution First, I am resolving the source charge as a point. The sphere is of a uniform charge density and centered on the origin. So the 'q' for this source charge is [tex]\frac{4}{3}\pi[/tex]*a^{2}*[tex]\rho[/tex]. Second, I am calling the line charge L*[tex]\lambda[/tex]. My solution so far : F_{q'onq(sphere/point on line charge)}= [tex]\frac{\lambda*\rho*a^{3}*L}{3*\epsilon}*\frac{\vec{R}}{R^{3}}[/tex] My problem (assuming the above is correct) is that I am uncertain how to express the vector, R, from the source charge to the line charge. In general, I am unsure of how to express a vector from a point to a continuous distribution of charges, or even from a continuous distribution to another. 


#2
Sep1408, 04:34 PM

Mentor
P: 12,074

I don't think you can treat the line charge as a point charge, as you can do with spheres.



#3
Sep1408, 05:37 PM

P: 19

Ok I've got it.My line charge was indeed wrong.
Basically, I chose my vector to be simple. The position with respect to the source was Z*Z(hat) and I ended up integrating from Z^{0} to Z_{0}+L with 1/Z^{2} as the integrand ( lambda is constant, was pulled out.) Some quick simplification results in the answer in the back of the book. I was thinking too hard about the vector I suppose. Thank you! 


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