Problem 1

  Microwave heating is generally uniform over the entire body of the product being heated if the thickness of the product does not exceed about 1 to 1.5 times its penetration depth. (4.1) consider a hamburger patty to be heated in a microwave oven operating at 2.45 GHz. The dielectric properties of raw hamburger at 2.45 GHz and 250C are εr′= 52.4 and tan δc = 0.33. What is the maximum thickness of this hamburger for it to be heated uniformly? (4.2) Microwave ovens operating at 915 MHz are evidently more appropriate for cooking product with large cross sections and high dielectric loss factors. The dielectric properties of raw hamburger at 915 MHz and 250C are εr′= 54.5 and tan δc = 0.411. Find the maximum thickness of the hamburger at 915 MHz and compare it with the result in part (4.1).(Hint: See attach file about microwave oven noteuploaded image)

Problem 2

   Let us assume a half-wave dipole antenna located at origin and oriented along z axis. The current through the antenna is given by i(t) = 10cos(2πx109 t) A. Find the expressions for magnetic and electric fields as well as for Poynting vector at some point located 2km away from antenna, characterized by the azimuth angle (the angle with z-axis ) θ=60°.(Hint: Look for HALF-WAVE dipole antenna on web (for example Wikipedia) and find the formula for Electric field. Then, you either derive Magnetic Field and Poynting vector from Electric field or look for Magnetic field and Poynting vector formulas for HALF-WAVE dipole antenna on web.)

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