Q1) Doping is introduction of impurities into the intrinsic semiconductor for the purpose of modulating electrical, optical and structural properties. Doping is important because it greatly conductivity of semiconductor and

1. a) State Biot-Savarts law. b) 3. The y - and z-axes, respectively, carry filamentary currents 10 A along ay and 20 A along -az. Find Hat (-3,4,5). 2. A conducting filament carries current I from point A(0, 0, a) to point B(0, 0, b). Show that at point P(x, y,0), a) State Ampere's circuit law. b) A hollow conducting cylinder has inner radius a and outer radius b and carries a current I along the positive z - direction. Find H everywhere. 4. An infinitely long filamentary wire carries a current of 2 A along the z-axis in the +z - direction. Calculate the following: a) B at (-3,4,7) b) The flux through the square loop described by 2 ≤ p ≤ 6,0 ≤z ≤ 4, = 90° 5. Determine the magnetic flux through a rectangular loop (a × b) due to an infinitely long conductor carrying current I as shown in Figure 7.1. The loop and the straight conductors are separated by distance d./nFigure 7.1.- For Problem 5 6. A brass ring with triangular cross section encircles a very long straight wire concentrically as in Figure 7.2. If the wire carries a current I, show that the total number of magnetic flux lines in the ring is 4 Molh 2лb [b-anª+b] Calculate if a = 30 cm, b = 10 cm, h = 5 cm, and I = 10 A. Brass ring Figure 2.- Cross section of a brass ring enclosing a long straight wire; for Problem 6/n7. Consider the following arbitrary fields. Find out which of them can possibly represent an electrostatic or magnetostatic field in free space. a) A = y cos ax ax + (y + e¯x)az 20 b) B=ap c) C = r² sin a 8. Reconsider Problem 7 for the following fields. EECE 3101 Homework 5 a) D = y²zax + 2(x + 1)yzay − (x + 1)z²az b) E= (z+1) Р cos pap + az sin o Р c) F=(2 cos 0 a, + sin 0 a.) Fall 2023/n9. For a current distribution in free space, A = (2x²y + yz)ax + (xy² − xz³)ay - (6xyz – 2x²y²)a₂ Wb/m a) Calculate B b) Find the magnetic flux through a loop described by x = 1, 0<y<2, 0<z< 2 c) Show that V. A = 0 and V. B = 0. 10. The magnetic vector potential of a current distribution in free space is given by A = 15e º sin pa, Wb/m Find Hat (3,7/4,-10). Calculate the flux through p = 5,0 ≤ ≤ π/2,0 ≤ z ≤ 10.

3.4 If r = xa, + ya, + za, the position vector of point (x, y, z) and r = r, which of the following is incorrect? (a) Vr = r/r (b) V.r = 1 (c) √²(r.r) = 6 (d) Vxr=0

3. The optical power after propagating through a fiber that is 450 m long is reduced to 30% of itsoriginal value. Calculate the fiber loss a in dB/km.the tfiber at

Based on wave attenuation and reflection measurements conducted at 1 MHz, it was determined that the intrinsic impedance of a certain medium is ηc = 28.1e45 and the skin depth is 5 m. Determine the conductivity of the material, the wavelength in the medium and the phase velocity.

Consider the following field The field exists only in the core of the cylinder, a section of which is shown below. Outside, the field is zero. The base of the cylinder is a circle of radius a. Determine the following: 2.1 Magnitude of F at r = and 2.2 Dot product of F and r. 2.3 ) Divergence of F in the cylinder core. 2.4 Flux, F. ds, coming out from the side. 2.5 Curl of F in the cylinder core.

2. The time-domain expression for the magnetic field of a uniform plane wave traveling in a nonmagnetic medium is given as H(x, t) = 20.2 cos(6π × 108 t – 10.2 x) Find (A/m) (a) the direction of wave propagation; (b) the relative permittivity e, and the intrinsic impedance n; (c) the time-domain expression of the associated electric field E; (d) the time-average power density Sav; and (e) the net time average power of the EM wave crossing a rectangular area of 30 × 20 cm oriented along yz plane, that is, the flat area has a normal vector î.

6. A brass ring with triangular cross section encircles a very long straight wire concentrically as in Figure 7.2. If the wire carries a current I, show that the total number of magnetic flux lines in the ring is 2mb [b-ana+b 4 = Calculate if a = 30 cm, b = 10 cm, h = 5 cm, and I = 10 A. Brass ring Figure 2.- Cross section of a brass ring enclosing a long straight wire; for Problem 6

Problem 2 The electric field of a plane wave propagating in a medium is given by E = [ŷ3 sin( × 107 -0.2x) + 24 cos( × 10² -0.2лx)] (V/m) 1. Find the propagation velocity of the field. 2. The medium has permeability o. Find its relative permittivity €. 3. Is the wave a plane wave? 4. Use both time-domain and phasor-domain Maxwell's equations to find the magnetic field H. 5. Determine the average power density carried by the wave.

2.27 Consider the imaginary rectangular box shown in Fig. P2.27. A wave traveling in the medium has electric and magnetic fields E = 100e -20y cos (27 x 10°t - 40y) (V/m), H = -20.64e-20y cos(2 x 10°t-40y-36.85°) (A/m). The box has dimensions a = 1 cm, b = 2 cm, and c=0.5 cm. Determine: (a) the net time-average power entering the box, (b) the time-average power exiting the box, and (c) the time-average power absorbed by the box. Figure P2.27: Imaginary rectangular box of Problem 2.27.

Consider the following field The field exists only in the core of the cylinder, a section of which is shown below. Outside, the field is zero. The base of the cylinder is a circle of radius a. Determine the following: 2.1 Magnitude of F at r = and 2.2 Dot product of F and r. 2.3 ) Divergence of F in the cylinder core. 2.4 Flux, F. ds, coming out from the side. 2.5 Curl of F in the cylinder core.