# Charged cylinder (electric field, rotor, divergence)

1. Oct 10, 2009

### pakkanen

1. The problem statement, all variables and given/known data

Charged Cylinder has lenght L and radius a. Charge density increases within the equation rho = rho0(r/a)3 where rho0 is constant and r is distance measured from cylinder´s axis. Outside of the cylinder charge density is zero.

a, Calculate the electric field inside and outside of the cylinder as a function of measured distance from cylinder´s axis.
b, Calculate the divergence of the electric field , and the rotor also.
c, What is the total charge of the cylinder?

2. Relevant equations

rho = rho0(r/a)3

3. The attempt at a solution

I draw a picture that shows electric field of cylinder. Is the picture drawn right?

a, The total charge should be Q inside the surface area A right? So in distance R I use coulomb´s law and I got E = Q/(e0pi(2RL + 4(R-a)2 + 2a2) I divided cylinder in three parts (ball, top area of cylinder, and circular area of cylinder) is that right?

When inside the cylinder: should I just take Vinside/Vtot * E * rho? Does it make sense?

b, I don´t know what means to divergence and rotor. I konw the divergence means something like, how much flow is coming out or going in. And rotor means something differences between flows.

Should the divergence be 0 because I don´t see how charged cylinder creates more Q or electricity??? What about the rotor?? How do I prove these?

c, Total charge of cylinder is (Q/V)*V is that right? so it is V*rho and where r = a

Last edited: Oct 10, 2009