How Does a Uniform Spherical Charge Influence a Linear Charge Along the Z-Axis?

[schattenjaeger]

A line charge of length L with lamba=const.(linear charge density) lies along the positive Z axis with its ends located at z=z0 and z0+L. Find the total force on the line charge due to a uniform spherical charge distribution with center at origin and radius a<z0

Sooo here's what I DID

I knew the total charge contained on the line charge was lamba*L, and the total charge contained in the sphere was 4/3 pi a^3 * rho where rho was its charge density, and it could be treated like a point particle with that total charge since the line charge didn't go inside it.

So my vector going from the origin to my field point was r=zk(k unit vector in z direction)and r'=0 since the source point was on the origin,so R^2=z^2

so the Force on a point on the line charge I took to be q*q'/r^2 in the z direction which was, after simplifying, (lamba*L*a^3*rho)/(3ez^2) where e is permitivitty of free space or whatever. so integrating over the whole line charge, ie F=S(allthat)*dz from z0 to z0+L, well, ALMOST gave me the right answer, I got an L^2 in the final answer when there should be just a single L

so I think earlier when I was finding the force at a point on the line charge, I had to JUST use lambda and not the whole line charge lamda*L?

 

[vaishakh]

I think you have got the problem, and cahrge on each elemnent of the stick is Lam.dr.