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Page 4 PROBLEM 3. [25 points) A time-varying electromagnetic field is perpendicularly incident on a flat slab of a linear dielectric material that has a dielectric constant/relative permittivity Ey. Let the electric field vector be given by E = -E, sin wt 2 and let the slab lie in the xy-plane. (a) Find an expression for the magnitude of the displacement current Ja as a function of time in the slab of dielectric material in terms of €, Er, E, and w. (15 points) (b) As we discussed in class, the displacement current ("Maxwell's fix") is often assumed to be small or ignorable. However, in some situations the displacement current can be important. A reasonable electric field strength and frequency for a microwave oven would be E. =500 V/m oscillating at a frequency of v =2.5 GHz (2.5 x 10's). Let this electric field be perpendicularly incident on a horizontal slab of meat in the microwave oven; the dielectric constant for meat is er = 20. Using 10-11 kg As^m'as a rough value for the permittivity of free space E, and your result from part (a), find an estimate (one significant digit is fine; for example, n = 3, etc.) for the maximum magnitude of the displacement current in the meat using your result from part (a). [Note that 21 y = w.) (10 points)