# 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
c) Lens law
d) Gauss law

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.

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

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

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

4. Gauss for the Magnetic Field is given by ______
a) ∇.B=0
b) ∇×B=ρv
c) ∇×B=0
d) ∇.B=ρv

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

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

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
d) Both Amperes and Faraday law

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 : $$\int_cH.dl =\int_s(\frac{\partial D}{\partial t} + J).dS$$

8. Divergence of Magnetic field is ______
a) volume charge density ρv
b) zero
c) infinite
d) dependent on magnetic field vector

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

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

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

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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