homework2 - EE4609 Spring 2009 Homework#2 1 Consider an...

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EE4609 Spring 2009 Homework #2 1) Consider an infinitely long coaxial cable. The center conductor has an outside radius of a (m). The outer conductor has an inside radius of b (m). The area in between the conductors is filled with a dielectric with relative dielectric constant ε r . z φ ρ ρ = b ρ = a Φ = V o ε r A battery is connected between the conductors which places a potential across them. The inner conductor is at the potential, Φ ( ρ =a) = V o while the outer one is at Φ ( ρ =b) = 0.
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Use Laplace’s equation to find the electric field (V/m) between the conductors. In this case, cylindrical coordinates ( ρ , φ , z) are appropriate. Since there is no charge in the region between the conductors, the electric potential satifies Because the line is infinitely long and there is symmetry about the z axis, there should be no variation of Φ with either z or φ . Thus the equation reduces to To solve this, integrate (with respect to ρ ) twice. The resulting expression is only a function of ρ and contains two integration constants. Use the potentials (boundary
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