Electromagnetic theory miscellaneous

Electromagnetic theory miscellaneous

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Electromagnetic Theory

Electromagnetic theory miscellaneous
  1. Which of the following equation represents the Gauss law in a homogeneous isotropic medium?








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    NA

    Correct Option: A

    NA

  1. For incidence from dielectric medium (∈1) into dielectric medium 2 (∈2), the Brewster angle θp and the corresponding angle of transmission θt for ∈2/ ∈1 = 3 will be respecitively—








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    Brewster angle
    tanθ1 = √∈2/∈1
    = √3
    Therefore, θ1 = 60º
    and sin θ1 = √∈2
    sin θ2 = ε1

    sin 60°
    		 = √3
    sin θ2

    solving, we getθ2 = 30º

    Correct Option: C

    Brewster angle
    tanθ1 = √∈2/∈1
    = √3
    Therefore, θ1 = 60º
    and sin θ1 = √∈2
    sin θ2 = ε1

    sin 60°
    		 = √3
    sin θ2

    solving, we getθ2 = 30º

  1. A transmission line of characteristic impedance Z0 = 50 ohms, phase velocity vP = 2 × 108 m/s, and length I = 1 m is terminated by a load ZL = (30 – j 40) ohms. The input impedance of the line for a frequency of 100 MHz will be—








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    VP = f λ
    Therefore λ = VP/ f
    = 2 × 108/ 100 × 106
    = 2 m
    Since length of the line is half wave length i.e.

    I =
    λ
    		 =
    2
    		 = 1
    22

    Therefore, Zin = ZL
    or Zin = (30 – j40) ohms.

    Correct Option: B

    VP = f λ
    Therefore λ = VP/ f
    = 2 × 108/ 100 × 106
    = 2 m
    Since length of the line is half wave length i.e.

    I =
    λ
    		 =
    2
    		 = 1
    22

    Therefore, Zin = ZL
    or Zin = (30 – j40) ohms.

  1. The directivity of an isotropic antenna is—








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    Directivity is the ability of an antenna to radiate power in a particular direction only. The directional pattern is a polar plot gives us the strength of radiated electromagnetic wave (in case of transmitting antenna) and strength of received electromagnetic wave (in case of receiving antenna) as a function of distance and angle. The directional pattern is affected by the shape and size of antenna, point of feed of RF signal etc.

    Correct Option: C

    Directivity is the ability of an antenna to radiate power in a particular direction only. The directional pattern is a polar plot gives us the strength of radiated electromagnetic wave (in case of transmitting antenna) and strength of received electromagnetic wave (in case of receiving antenna) as a function of distance and angle. The directional pattern is affected by the shape and size of antenna, point of feed of RF signal etc.

  1. If the electric field E = 0.1 te–t ax and ∈ = 4∈0, then the displacement current crossing an area of 0.1 m2 at t = 0 will be—








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    E = 0.1 t e– t ix
    D = ∈r∈0 E
    or D = ∈r∈0 0.1 t e– t ix
    or D = 0.4 ∈0 [– te– t + e– t] ix
    Dt = 0 = 0.4 ∈0 ix
    Displacement current = 0.1 × 0.4 ∈0 ix
    = 0.04 ∈0 ix

    Correct Option: B

    E = 0.1 t e– t ix
    D = ∈r∈0 E
    or D = ∈r∈0 0.1 t e– t ix
    or D = 0.4 ∈0 [– te– t + e– t] ix
    Dt = 0 = 0.4 ∈0 ix
    Displacement current = 0.1 × 0.4 ∈0 ix
    = 0.04 ∈0 ix