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2. (15%) Charge is distributed with uniform density p₀, C/m³ in the spherical region a＜s ＜2a. Find the electric displacement field everywhere.

其他申論題

(b) Find the range of K for stability by Nyquist stability criterion. (10%.)

(a) Please derive the state space equation of the closed-loop control system. (10%)

(b)Please solve the gain Ka and K, for the closed-loop poles located at-2 ± j2.(15%)

1. (15%) A magnetic field is given in the xz-plane by, Wb/m2. Consider a regid square loop situated in the xz-plane with its vertices at (x, 0, 1), (x+1,0, 1), (x+1,0, 2), and (x, 0, 2). Find the emf induced around the loop in the sense defined by connecting the above points in succession.

(a) Find the magnetic field everywhere.

(b) Find the energy stored in the magnetic field of the current distribution per unit length in the z-direction.

4. (15%)Let us consider the charge distribution given bywhere ρo is a constant. Find the electric displacement field everywhere.

5.(15%) For a uniform plane wave propagating in the -z-direction in a material medium withσ=0, 6=4εo, μ=μo , the magnetic field intensity in the z=0 plane is given by (a) Find the impedance of the medium for the field.

(b) Find the phase velocity of the wave.

(c) Find the associated electric field

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