# Coulomb force on a line charge

by Kudaros
Tags: charge, coulomb, force, line
 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, $$\rho$$. There is a line charge with a length L that begins at Z0 and ends at Z0 + L (lies on the Z axis). This line charge has a uniform charge density of $$\lambda$$. 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 $$\frac{4}{3}\pi$$*a2*$$\rho$$. Second, I am calling the line charge L*$$\lambda$$. My solution so far : Fq'onq(sphere/point on line charge)= $$\frac{\lambda*\rho*a^{3}*L}{3*\epsilon}*\frac{\vec{R}}{R^{3}}$$ 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.
 Mentor P: 11,966 I don't think you can treat the line charge as a point charge, as you can do with spheres.
 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 Z0 to Z0+L with 1/Z2 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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