Final Exam Problems - Radio Frequency Fundamentals | ENTC 3331, Exams of Wireless Networking

Download Final Exam Problems - Radio Frequency Fundamentals | ENTC 3331 and more Exams Wireless Networking in PDF only on Docsity! RF Fundamentals FINAL EXAM Due December 11 12:00 noon Each problem is worth 0 points. 1. A sphere of radius 2 cm contains a volume charge density  given by )/(cos4 32 mC  Find the total charge Q contained in the sphere. Hint:    sin cos  d d . 2. Three point charges, each with q = 3 nC, are located at the corners of a triangle in the x-y plane, with one corner at the origin, another at (2 cm, 0, 0), and the third at (0, 2 cm, 0). Find the force acting on the charge located at the origin. 3. In a given region of space, the vector magnetic potential is given by    mWbxy  sin2ˆcos5ˆ  zxA  . a. Determine β  . b. Use    WbdsA ˆ   to calculate the magnetic flux passing through a square loop with 0.25-m-long edges if the loop is in the x-y plane, its center is at the origin, and its edges are parallel to the x- and y-axes. 4. The electromagnetic generator shown in Fig. 6-12 is connected to an electric light bulb with a resistance of 100 . If the loop area is 0.1 m2 and it rotates at 3600 revolutions per minute in a uniform magnetic flux density, To 2.0 , determine the amplitude of the current generated in the light bulb. 5. Given  23 ˆsin10 mArJ   in spherical coordinates, find the current crossing the spherical shell, mr 02.0 . Hint: 2 2cos1 sin 2     . 6. In cylindrical coordinates,    Trβ ̂/0.2  . Determine the magnetic flux, , crossing the plane surface defined by mrm 5.25.0  and .0.20 mzm  Hint: r r dr ln . 7. A line of positive charge (L = charge/unit length) is aligned along the y-axis as shown, what is the electric field vector at the point P. 8. A standing wave consists of the coherent superposition of two electromagnetic waves. The combination of a wave moving in the +x direction with one moving in the -x direction gives rise to an electric field    .)sin()sin(, tkxtkxEtx m   yyE  a. Show that the electric field vanishes (for any time) whenever knx / . (These x locations are known as nodes. Hint: Use trig. identities for sum and differences of an angle. b. What is the magnetic field for this wave? c. Show that at time t = 0, the electromagnetic energy is completely contained in the electric field, while at t =  (quarter period) the energy is completely contained in the magnetic field. z  2.0 0.5 2.5 0 ŝd +L -L y x P a