1. (a) Statement:
“The surface integral of the curl of a function over any surface bounded by a closed path is equal to the line integral of a particular vector function round that path.”
The above statement is associated with
(i) Gauss’s law
(ii) Stokes’ law
(iii) Faraday’s law
(iv) Lenz’s law
(F) lossless line having 50 ohm characteristic impedance and length wavelength/4 is short circuited at one end connected to an ideal voltage source of 1 V at the other end. The current drawn from the voltage sources is
(i) O
(ii) 0.02
(iii) infinity
(iv) 50
g) Which of the following circuit elements will oppose the change in circuit current?
(i) Capacitance
(ii) Inductance
(iii) Resistance
(iv) All of the above
(b) Identify the advantage of using method of images.
(i) Easy approach
(ii) Boundaries are replaced by charges
(iii) Boundaries are replaced by images
(iv) Calculation using Poisson and Laplace equation
(c) The loss tangent is also referred to as
(i) attenuation
(ii) propagation
(iii) dissipation factor
(iv) polarization
(d) When the polarization of the receiving antenna is unknown, to ensure that it receives at least half the power, the transmitted wave should be
(i) linearly polarized
(ii) elliptically polarized
(iii) circularly polarized
(iv) normally polarized
(e) The law that the induced e.m.f. and current always oppose the producing them is due to cause
(i) Faraday
(ii) Lenz
(iii) Newton
(iv) Coulomb
(i) For an electromagnetic wave, the direction of Ex B gives the direction of
(i) electric field
(ii) magnetic field
(iii) wave propagation
(iv) the e.m.f. induced by the wave
(j) The attenuation constant is 0.25 units. The skin depth will be
(i) 0.5
(ii) 0-25
(iii) 2
(iv) 4
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2(a) A point charge Q₁ = 300 µC located at (1,-1,-3) m experiences force F = 8x-8y+42 N due to point charge Q2 at (3,-2,-1) m. Determine Q2.
(b) Three vectors extending from the origin are given as 7=7x+3y-2z, 72=-2x+7-32 and 73=2x-2y+3z. Find (i) the unit vector perpendicular to both and 72, (ii) a unit vector perpendicular to the vectors 71-72 and 2-3, (ii) the area of the triangle defined by and 72, (iv) the area of the triangle defined by the heads of and
3.(a) State divergence theorem. Show that VE is zero for the field of a uniform line charge.
(b) Let V = cos(20)/p V in free space. Find (i) the volume charge density at point A = (1/2, 60°, 1), and (ii) surface charge density on a conductor surface passing through the point B = (2, 30°, 1).
3(B) Let V = cos(20)/pV in free space. Find (i) the volume charge density at point A = (1/2, 60°, 1), and (ii) surface charge density on a conductor surface passing through the point B = (2, 30°, 1).
4. (a) State and give proof of uniqueness theorem for-
(i) a charge free region bounded by a surface with 0 volts;
(ii) a region with charge density and bounded by a surface with V volts.
(b) Find the capacitance per unit length between a cylindrical conductor of radius a = 2 cm and a ground plane parallel to the conductor axis and a distance h6m from it.
5.(a) What is displacement current? Write the set of Maxwell’s equations in free space.
(b) Given the potential field V = 100 xz/(x² + 4) V in free space,
(i) find D at the surface z = 0, (ii) show
that the z=0 surface is an equipotential surface (iii) assume that the z = 0 surface is a conductor and find the total charge on that portion of the conductor defined by 0<x<2 and -3<y<0.
- (a) Derive the Poynting theorem expression using the Maxwell’s equations.
(b) A radial field H = (2.39 × 106/r) coso A/m exists in free space. Find the magnetic flux & crossing the surface defined by -π/4≤φ≤π/4, 0 ≤ 2≤1 m.
7. (a) Derive the expressions for the reflection coefficient (Γ₁) and transmission coeffi- cient (t1) of perpendicularly polarized E-M wave incident at an angle 0; to the interface of two mediums with intrinsic impedances 111 and 12 respectively. Also, find the relation between (Γ₁) and (1).
(b) 6 If E(z, t) = 900 cos (5×10πt- nt-ẞz) V/m and H(z, t) = 3.8 cos (5×10πt-ẞz)ý A/m 6 represent a uniform plane wave propa- gating at a velocity of 1.5×108 m/s in a perfect dielectric. Find (i) β, (ii) 2, (iii) n and (iv) relative permittivity (ER) and permeability (HR).
9. A load, such as an antenna, of impedance (60+j100) is connected to a lossless transmission line with characteristic impedance Zo = 50 Ω. The line operates at 1 GHz and the speed of propagation on the line is c (speed of light). Find, using Smith Chart-
(a) the reflection coefficient at the load;
(b) the reflection coefficient at a distance of 20 m generator; from the load toward the
(c) input impedance at 20 m from the load;
(d) the standing wave ratio on the line;
(e) locations of the first voltage maximum and first voltage minimum from the load.
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