Antennas Questions and Answers – Radiation – Basic Maxwell Equations

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This set of Antennas Multiple Choice Questions & Answers focuses on “Radiation – Basic Maxwell Equations”.

1. The Maxwell equation ∇×E=\(\frac{-\partial B}{\partial t}\) is derived from which law?
a) Amperes law
b) Faradays Law
c) Lens law
d) Gauss law
View Answer

Answer: b
Explanation: Faradays law states that emf generated around a loop of wire in magnetic field is proportional to the rate of change of time-varying magnetic field through the loop.
Amperes law gives ∇×H=J
Lens law gives only the reason for the negative sign in the Faradays law of induction.
Gauss’s law states that the net flux of an electricfield in a closed surface is directly proportional to the enclosed electric charge.
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2. The minus sign in the Faradays law of induction is given by ______
a) Lens Law
b) Gauss law
c) Amperes Law
d) Gauss law
View Answer

Answer: a
Explanation:Lens law gives only the reason for the negative sign in the Faradays law of induction
emf=\(-\frac{\partial \phi}{\partial t}\)
The minus sign indicates the direction of induced current.

3. Which of the following Maxwell equation is obtained from Amperes law?
a) ∇×H=J
b) emf=\(-\frac{\partial \phi}{\partial t}\)
c) ∇×E=\(\frac{-\partial B}{\partial t}\)
d) ∇×D=ρv
View Answer

Answer: a
Explanation:

  • Faradays Law                : ∇×E=\(-\frac{\partial B}{\partial t}\)
  • Amperes Law                : ∇×H=J+\(\frac{\partial D}{\partial t}\)
  • Gauss Law for electric field     : D=ρv
  • Gauss law for magnetic field  : ∇.B=0
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4. Gauss for the Magnetic Field is given by ______
a) ∇.B=0
b) ∇×B=ρv
c) ∇×B=0
d) ∇.B=ρv
View Answer

Answer: a
Explanation: Gauss law for magnetic field states that the net flux out of any closed surface is zero.
∇.B=0
This Maxwell equation is one of the equation used to determine the boundary conditions.

5. Gauss for the Electric Field is given by ______
a) ∇.D=0
b) ∇×D=ρv
c) ∇×D=0
d) ∇.D=ρv
View Answer

Answer: d
Explanation:Gauss’s law for electric field states that the net flux of an electricfield in a closed surface is directly proportional to the enclosed electric charge. ∇.D=ρv
This Maxwell equation is one of the equation used to determine the boundary conditions.
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6. Which of the Following Maxwell equation is for nonexistence of isolated magnetic charge?
a) ∇×E=-\(-\frac{\partial B}{\partial t}\)
b) ∇×H=J
c) ∇.D=ρv
d) ∇.B=0
View Answer

Answer: d
Explanation: Gauss law for magnetic field states that the net flux out of any closed surface is zero.
∇.B=0
This is satisfied only when two different poles of magnet exist. So this Maxwell equation proves for the nonexistence of the isolated magnetic charge.

  • Faradays Law : ∇×E=\(-\frac{\partial B}{\partial t}\)
  • Amperes Law : ∇×H=J
  • Gauss Law for electric field : ∇.D=ρv

7. In which of the following Integral form of Maxwell equations, the surface is closed?
a) Amperes law
b) Gauss Law
c) Faradays Law
d) Both Amperes and Faraday law
View Answer

Answer: b
Explanation: The surface integral is closed for the Gauss laws of magnetic and electric fields. It is open for the amperes and Faradays law.
Maxwell Equations:

  • Gauss law electric field : \(\oint_sD.ds =\int_v\rho_v dv \)
  • Gauss law magnetic field : \(\oint_sB.ds =0\)
  • Faradays law : \(\int_cE.dl =-\int_s\frac{\partial B}{\partial t}.dS\)
  • Amperes law : \(\int_cH.dl =\int_s(\frac{\partial D}{\partial t} + J).dS\)
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8. Divergence of Magnetic field is ______
a) volume charge density ρv
b) zero
c) infinite
d) dependent on magnetic field vector
View Answer

Answer: b
Explanation: The Divergence of Magnetic is always zero.It is obtained from the Maxwell equation ∇.B=0 which is derived from the Gauss law of magnetic field.Gauss law for magnetic field states that the net flux out of any closed surface is zero. ∇.D=ρv.

9. Which of the following Maxwell equation is correct for a non-conducting and lossless medium?
a) ∇.D=ρv
b) ∇.D=0
c) ∇×D=ρv
d) ∇×E=0
View Answer

Answer: b
Explanation: Since it is given non-conducting medium, the charge density ρv=0 and current density J=0. The Maxwell equations are:

  • Faradays Law                : ∇×E=\(-\frac{\partial B}{\partial t}\)
  • Amperes Law                : ∇×H=\(\frac{\partial D}{\partial t}\)
  • Gauss Law for electric field     : ∇.D=0
  • Gauss law for magnetic field  : ∇.B=0
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10. Find skin depth of 5GHz for silver with a conductivity 6.1×107s/m and relative permittivity 1.
a) 0.00091m
b) 0.9113μm
c) 0.319μm
d) 0.1913μm
View Answer

Answer: b
Explanation: The skin depth is given by \(δ = \sqrt{\frac{1}{\pi fμσ}}\)
Given f=5GHz
Conductivity σ= 6.1×107 s/m
And μr = 1 =>μ=4π ×10-7
⇨ \(δ = \sqrt{\frac{1}{\pi fμσ}}=0.9113\mu m.\)

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter