5. The plane boundary defined by z=0 separates air (z ≥ 0) from a block of iron (z ≤ 0), of which μ = 5000μ_₀. If = x̂4 - ŷ6 + ẑ12 is the magnetic field in air, what is the magnetic field in iron:
(A) = x̂0.0008 - ŷ0.0012 + ẑ12
(B) = x̂4 - ŷ6 + ẑ60000
(C) = x̂4 - ŷ6 + ẑ0.0024
(D) = x̂20000 - ŷ30000 + ẑ12

1. A circular disk of radius a is uniformly charged with ρs C/m². If the disk lies on the z=0 plane with its axis along the z-axis, What is the electric field that at point (0, 0, h)? (A)(B) (C) (D)

2. The linear electric quadrupole is a set of three charges as shown in the following figure. The separation s is again much smaller than the distance r to the point P. What is the potential V at the point of P: (A)(B)(C)(D)

3. There is a sector of a spherical shell with the cross section as shown in the figure (where 0≤α＜2π) What is the resistance between the top and bottom bases of the sector? (Assume that the electrical conductivity of the sector material is σ) (A) R = (B) R = (C) R =(D) R =

4. A parallel-plate capacitor has plates of area A separated by a distance s. Its dielectric has a conductivity σ=a+bx, where x is the distance to one plate and a uniform relative permittivity εᵣ. With an alternating voltage with the angular frequency ω across the electrodes, there is a current I flowing through the dielectric. What is the electric field in the capacitor? (A) (B)(C) (D)

6. Which material type in the following has negative magnetic susceptibility, thus the direction of the induced magnetic dipole moment is opposite to the corresponding applied magnetic field: (A) Paramagnetic material (B) Diamagnetic material (C) Ferromagnetic material (D) None of the above material have negative magnetic dipole moments

7. Which following equation is not one of the Maxwell's equations: (A) (B)(C) (D)

8. The plates of a parallel-plate capacitor has areas of 10 cm² each and are separated by 1 cm. The capacitor is filled with a dielectric material with ε = 4ε₀, where ε₀ = 8.85 × 10⁻¹² F/m, and the voltage across it is given by V(t) = 30cos(2π×10⁶t) (V). What is the displacement current? (A) Id = 2.4πε₀ × 10⁷sin(2π × 10⁷t) ( A ) (B) Id = 2.4πε₀ × 10⁹cos(2π × 10⁷t) ( A ) (C) Id = 2.4πε₀ × 10⁹sin(2π × 10⁷t) ( A ) (D) None of the above.

9. Considering a plane electromagnetic wave traveling in a material with a permittivity ε and a permeability μ, what is the phase velocity of the wave? (A) (B)  (C) με (D) none of the above.

10. The instantaneous expression of the electric field of a plane wave in vacuum is given by (z,t) = âx E₀cos(ωt - βz). The intrinsic impedance (also called the wave impedance) is η₀. What is the instantaneous expression of the Poynting vector? (A) (B)(C) (D) none of the above.

11. A linearly polarized plane wave () with a frequency of 100 MHz propagates in vacuum in the +z direction. It impinges normally on a perfectly conducting plane at z = 0 and gets reflected. The reflected wave is denoted by (). The incident and the reflected waves form a standing wave. Determine the location nearest to the conducting plane where the total magnetic field +is zero. (A) z = -3 (m) (B) z = -1.5 (m) (C) z = -0.75 (m) (D) none of the above.

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