(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Coulomb force on a line charge

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