Ece 222 Problem Set: Ab Carries A Current Of 0.2a In The

ECE 222 PROBLEM SET

A. Magnetostatics 1. A current filament carrying 15A in the 𝒂𝑧 direction lies along the entire z axis. Find H in the cartesian coordinates at: (a) 𝑃𝐴 (√20, 0, 4); (b) 𝑃𝐵 (2, −4, 4). 2. Find H in cartesian components at P(2, 3, 4) if there is a current filament on the z axis carrying 8mA in the 𝒂𝑧 direction. B. Magnetic Forces, Materials and Inductance 1. The point charge 𝑄 = 18 𝑛𝐶 has a velocity of 5 × 106 𝑚/𝑠 in the direction 𝒂𝑣 = 0.04𝒂𝑥 − 0.05𝒂𝑦 + 0.2𝒂𝑧 . Calculate the magnitude of the force exerted on the charge by the field: (a) 𝐁 = −3𝒂𝑥 + 4𝒂𝑦 + 6𝒂𝑧 𝑚𝑇; (b) 𝐄 = −3𝒂𝑥 + 4𝒂𝑦 + 6𝒂𝑧 kV/m; (c) B and E acting together. 2. The semiconductor sample shown in Fig. 9.1 in page 277 of Hayt’s Engineering Electromagnetics book is n-type silicon, having a rectangular cross section of 0.9 mm by 1.1 cm, and a length of 1.3 cm. assume the electron and hole mobilities are 0.13 and 0.03 m2 /V ∙ s, respectively, at the operating temperature. Let 𝐵 = 0.07 T and the electric field intensity in the direction of the current flow be 800 V/m. find the magnitude of: (a) the voltage across the sample length; (b) the drift velocity. 3. A conducting filamentary triangle joins points A(3, 1, 1), B(5, 4, 2), and C(1, 2, 4). The segment AB carries a current of 0.2A in the 𝒂𝐴𝐵 direction. There is present a magnetic field 𝐁 = 0.2𝒂𝑥 − 0.1𝒂𝑦 + 0.3𝒂𝑧 T. Find the torque on the loop about an origin at A. C. The Uniform Plane Wave 1. The electric field amplitude of a uniform plane wave propagating in the 𝒂𝑧 direction is 250 V/m. if 𝐄 = 𝐸𝑥 𝒂𝑥 and 𝜔 = 1.00 Mrad/s, find: (a) the frequency; (b) the wavelength; (c) the period; (d) the amplitude of H. 2. A 9.375 GHz uniform plane wave is propagating in polyethylene. If the amplitude of the electric field intensity is 500 V/m and the material is assumed to be lossless, find: (a) the phase constant; (b) the wavelength in the polyethylene. D. Plane Wave at Boundaries and in Dispersive Media 1. A uniform plane wave in air is normally incident on a dielectric slab of thickness 𝜆2 /4, and intrinsic impedance 𝜂2 = 260 Ω. Determine the magnitude and phase of the reflection coefficient.

E. Essay

(.doc file and must contain 300-500 words or more)

What is the importance of studying electromagnetism to your field of study (EcE)?