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Analytic solution Solve the problem analytically using the potential distribution for an infinite domain with a hole centered at the origin. Here E0 is the electric field far away from the hole. The solution (Show this) is given by V(ρ,φ) = -E0(ρ + a^2/ρ) cosφ The current density is then given by j = -σ ∇V Apply the boundary condition at the potential boundaries ρ = L, φ = π and ρ = L, φ = 0 with the corresponding potentials V0 and -V0. Integrate to find the total current passing through AB in the plate. I = ∫_{AB} j · n̂ dS Calculate the resistance using R = 2V0 / I and compare with the numerical solution by choosing different values of the radius of the hole. Consider the difference between the results by plotting the quantity ε = (R_numerical - R_analytical) / (R_numerical + R_analytical) as a function of the hole radius. Use the values a = 0.01–10.0 [m].
Adi S.
these are my electromagnetic field final exam questions. could you solve them in details?
Sam S.
Question 3 (20 marks): The electric field intensity of a uniform plane wave in free space is given by E = 94.25cos(wt + 6z) ax V/m. Determine: i. The velocity of propagation. ii. The wave frequency. Express your answer in the form of angular frequency. iii. The wavelength. Express your answer in meters (m). A 180MHz wave travel in a medium characterized by ur = 1, er = 25, and sigma = 2.5mS/m. Determine: i. If this medium is a good dielectric? Hint: sigma / (w * e) <= 0.1, w = 2 * pi * 1.8 * 10^8 rad / s ii. The intrinsic impedance. Hint: sqrt(uo / eo) = 120 * pi. iii. The attenuation constant. iv. The phase constant. Hint: beta = w * sqrt(uo * eo) = (1.131 * 10^9) / (3 * 10^8) v. The propagation constant. vi. The phase speed. vii. The wavelength. Express your answer in cm.
Supreeta N.
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