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.

Solved: 1. a) State Biot-Savarts law. b) 3. The y - and z-axes, respectively,

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1 a state biot savarts law b 3 the y and z axes respectively carry fil

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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