Hi. in my problem there is an infinite half cylinder uniformly charged with ρ.
What is the force is the cylinder is making on a test charge on a charge located on the position that is shown on the following picture:
The Attempt at a Solution
Well first, if I know the charge density is ρ, I can know the total charge, but the problem is that because it is an infinite cylinder, so that the volume will be infinite as well and I cannot use the equation:
dQ = ρdV
In my attempt I tried to divide the half cylinder to half circles and to sum them from z=-inf to z=inf
Something is going wrong with my calculations, and I have few questions:
1. The force on the charged because of symmetry is normal to the part of the cylinder that is cutted (x axis)?
2. I tried to use cylindrical coordinates:
so dV= rdrd(theta)dz
so r [0,R]
theta [0, pi]
but z is [inf, -inf], doesn't it mean that the force will be endless?
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