电磁学代写 Electric constant代写 Magnetic constant代写

A05449

电磁学代写 1. (a) Explain briefly the method of images used to solve electrostatic problems. (b) A long cylindrical wire of radius r carries a positive charge λ per unit length,

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Answer two questions. If you answer more than two questions, credit will only be given for the best two answers.

1.

(a) Explain briefly the method of images used to solve electrostatic problems.

(b) A long cylindrical wire of radius r carries a positive charge λ per unit length, and is suspended parallel to the ground, which is at zero potential, with its axis of symmetry at a height of h. Assuming the ground to be a perfect conductor and using the method of image charges, determine the following.

i. An expression for the electric field at every point located directly below the wire, at a distance x < h − r above the ground. Indicate the direction of this field.

ii. An expression for the electrostatic potential difference between the wire and the ground.

iii. An expression for the capacitance per unit length. Determine its value for h = 10 m and r = 0.5 mm.

2. 电磁学代写

(a) Give the definition of electric susceptibility.

Describe the microscopic mechanisms that give rise to non-zero electric susceptibility of dielectrics.

Explain why, in the static limit, the electric susceptibility of water (χE = 80) is much higher than that of nitrogen (χE ≈ 10⁻³ ) at room temperature and pressure.

3. 电磁学代写

The Fresnel equations for the reflection and transmission coefficients for s and p polarised waves at a boundary of two dielectric materials have been derived in lectures assuming that the relative permeabilities of the two materials are µ₁ = µ₂ = 1.

(a) Derive the Fresnel equations in the general case, assuming that the relative permeabilities of the two materials are different: µ₁ ≠ µ₂.

(b) Demonstrate that the reflectivity for normally incident radiowaves is zero in the case ε₁ = µ₁ and ε₂ = µ₂.

(c) Derive an expression for tan α_B, where α_B is the Brewster’s angle, in terms of µ_1,2 and ε_1,2 in the case µ₁ ≠ µ₂.

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