Question

Match List I with List II and select the correct answer using the code given below the lists:

	List I		List II
A.	Characteristic impedance	1.	Δ.D = ρv
B.	Poynting vector	2.	\({\sqrt\frac{j\omega \mu}{\sigma+j\omega\epsilon}}\)
C.	Displacement current	3.	E × H
D.	Point form of Gauss law	4.	\(\frac{dD}{dt}\)

1. A – 2, B – 3, C – 4, D - 1
2. A – 1, B – 3, C – 4, D - 2
3. A – 2, B – 4, C – 3, D - 1
4. A – 1, B – 4, C – 3, D - 2

Answer 1

Correct Answer - Option 1 : A – 2, B – 3, C – 4, D - 1

Characteristic impedance:

The characteristic impedance of a wave traveling in a lossy medium is given by

\(Z = \sqrt {\frac{{j\omega μ }}{{\sigma + j\omega ϵ}}}\)

Put σ = 0 (free space and lossless medium)

\(Z = \sqrt {\frac{μ_0 }{ϵ_0}}\)

Where,

μ0 = Permeability of free space = 4π x 10-7 H / m

ϵ0 = Permittivity of free space = 8.85 x 10-12 F/m

Poynting vector:

1) It states that the cross product of electric field vector (E) and magnetic field vector (H) at any point is a measure of the rate of flow of electromagnetic energy per unit area at that point that is 

\( \vec S = \vec E \times \vec H\)

Where S = Poynting vector, E = Electric field and H = Magnetic field

2) The Poynting vector describes the magnitude and direction of the flow of energy in electromagnetic waves.

3) The unit of the Poynting vector is watt/m2.

Maxwell's Equations for time-varying fields is as shown:

S. No.	Differential form	Integral form	Name
1.	\(\nabla \times E = - \frac{{\partial B}}{{\partial t}}\)	\(\mathop \oint \nolimits_L^{} E.dl = - \frac{\partial }{{\partial t}}\mathop \smallint \nolimits_S^{} B.d S\)	Faraday’s law of electromagnetic induction
2.	\(\nabla \times H =J+ \frac{{\partial D}}{{\partial t}}\)	\(\mathop \oint \nolimits_L^{} H.dl = \mathop \smallint \nolimits_S^{} (J+\frac{{\partial D}}{{\partial t}}).dS\)	Ampere’s circuital law
3.	∇ . D = ρv	\(\mathop \oint \nolimits_S^{} D.dS = \mathop \smallint \nolimits_v^{} \rho_v.dV\)	Gauss’ law
4.	∇ . B = 0	\(\mathop \oint \nolimits_S^{} B.dS = 0\)	Gauss’ law of Magnetostatics (non-existence of magnetic monopole)

\(\frac{\partial D}{\partial t}\) = Jd (Displacement Current density)