Electrostatics + Magneotostatics HW question

[lemonscent]

1. For a coaxial cable, calculate E, D, H, and B everywhere assuming a uniform current I in both conductors and uniform charge per unit length on both conductors. Then find: inductance and capacitance per unit length, leakage resistance across the dielectric per unit length, and conductor resistance per unit length.



2. Assume: Copper conductors
Polyethylene insulator
Inner conductor diameter: 2mm
Outer conductor diameter: 4mm
Outer conductor thickness: 0.2mm



3. All I know is we can consider the outer conducter to be infinately thin, DC currect is uniform, and we can consider air to be everywhere.

This is a large problem and could use any assistance in figuring each part out. Not really sure how to start any of the parts I am to answer.

 

[NateD]

Answer: In order to calculate the electric, magnetic, and other fields inside and outside a coaxial cable, we need to use Maxwell's equations. These equations describe the behavior of electric and magnetic fields in terms of their sources. In this case, the sources are the uniform current I in both conductors and the uniform charge per unit length on both conductors. We can then use the equations to calculate the electric and magnetic fields everywhere in the cable. The electric field E is given by: E = (I/2πr) * (1/ε0)Where r is the radius of the inner conductor and ε0 is the permittivity of free space (8.854 x 10-12 C2/Nm2). The magnetic field H is given by: H = (I/2πr) * (μ0/ε0) Where μ0 is the permeability of free space (4πx10-7 N/A2). The magnetic flux density B is given by: B = μ0 * HThe inductance per unit length of the cable is given by: L = μ0 * (ln(r2/r1))/(2π) Where r1 is the radius of the inner conductor and r2 is the radius of the outer conductor. The capacitance per unit length of the cable is given by: C = ε0 * (ln(r2/r1))/(2π) The leakage resistance across the dielectric per unit length is given by: R_leakage = ε_r/t Where ε_r is the relative permittivity of the dielectric material and t is the thickness of the dielectric material. For the given parameters of copper conductors and polyethylene insulator, ε_r = 2.3 and t = 0.2mm. The conductor resistance per unit length is given by: R_conductor = ρ/(π*(r2^2 - r1^2))