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## Homework Statement

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:

## Homework Equations

∫qdQ/(r

^{2})

## 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?

#### Attachments

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