 #1
Gustav
 57
 5
 Homework Statement:
 A long straight nonconductive cylindrical rod with radius a has the permittivity ε. It is given by a uniform free space charge density ρ_f. (That this charge density is "free" means that it did not arise through polarization. However, the charges that build up ρ_f are not moving freely, but ρ_f has the same constant value throughout the rod.) Determine all bound charge densities by using the cylinder symmetry and verify from these that the total bound charge per unit length of the rod is zero.
 Relevant Equations:

Q = Q_b + Q_f
P = ε_0 X_e E
D = ε_0 E
I was trying to solve it using the formula for polaresation P = ε E  ε_{0} E. Then I tried to solve for E which is D/ε and D= ρ_{f}/ε. So at the end, I will have something as P = p_{f} (ε_{0}ε).
ρ_{b} = ∇ * P = 0 so σ_{b} = P * n = ...? I am unsure what the direction for the polaresation should be? I need guidance for my solution, I would appreciate any suggestens in changing anything in my solution.
ρ_{b} = ∇ * P = 0 so σ_{b} = P * n = ...? I am unsure what the direction for the polaresation should be? I need guidance for my solution, I would appreciate any suggestens in changing anything in my solution.