What is the energy from a hollow cylinder of surface charge density sigma, radius R and charge q?
Energy? DO you mean E, the electric field intensity?
If you mean Energy, it is an odd question, but the answer is that it is the work it took to put the charge q on the surface. In this case, a complex integration of dq.
The question is that there are two cylinders, the inner one with a volume density charge rho and the outer (hollow) one with some surface density charge.
The net charge is zero, and I need to find out what the surface density charge is equal to and the energy per unit lenght of the system. I already calculated what the field is inside the system, but I don't know how to solve for the contribution by the outer shell. I figured I'd need the energy anyway at the end to find the energy per unit lenght right?
The field from the outer is only on the outer side of the cylinder. If the charge is the same, but opposite, then (Gauss Law) the charge enclosed is zero, so field is zero. THe energy is from the field between the two cylinders...Integrate the E squared (energy density) function over the volume between the cylinders.
And the E value I would use is q/(2pi(E0)R) correct?
No. In the numerator, you should have lambda, charge per unit length. You can get it from the given geometry, R, q, and surface charge density.
To calculate the energy from a hollow cylinder of surface charge density sigma, radius R, and charge q, we need to use the concept of electric potential energy.
First, we need to find the charge per unit length of the cylinder, also known as the linear charge density or lambda. We can calculate lambda by dividing the total charge q by the circumference of the cylinder.
lambda = q / (2πR)
Once we have the linear charge density, we can calculate the electric field between the inner and outer cylinders using Gauss's Law. The electric field between the cylinders is given by:
E = lambda / (2πε0R)
where ε0 is the permittivity of free space.
Next, we need to calculate the energy per unit length of the system. The energy density u_e is given by:
u_e = (1/2)ε0E^2
where E is the electric field intensity.
To calculate the total energy per unit length, we need to integrate the energy density u_e over the volume between the inner and outer cylinders. The limits of integration would be from the inner radius to the outer radius.
The final result will give you the energy per unit length of the system.
Remember to correctly substitute the values for the variables sigma, R, and q into the equations, and be mindful of units used.