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Rajshaht University 1, (a) (b} 12] 2. (@ ) (c) 3. (a) ) ©) 4. (a) (b) 5. (a) >) 6. (a) © 7. (a) b) © 8. (a) 0) (c) B. Se.(Honors) Part - 11 Examination, 2006 Applied Physica and Blectronic Engineering Course: APE 306 a Electromagnetic Theory and Antenna » Total Marks; 75 Time: 4 Hours NB. Figures in the margin indicate full marks} Answer any FIVE auestions; State the four basic equations from which Maxwell's field equations can bg deduced, 3+3 Write down the Maxwell's fleld equations for linear isotrople media _ Given E = iE, sina — fir) in ftee space. Find the value for magnetic fleld intensity, 44 Hence show that and Hi are perpendicular (o each other, Deduce the Maxwell's electromagnetic wave equation expressed in terms of scalar 4+1 potential and hence deduce the Poisson's equation for scalar potential, Deduce the wave equation for £ for a linear, isotropic and stationary medium (Let a = 0, 3 p=0). Show that m= 4/c, for non-conducting and non-magnetic medium, (Symbols have their 4 usual meanings), A plane electromagnetic wave of angular frequency @ propagated in the free space in the 2x4 direction of unit vector 1, setting the wave vector & = ik, show that i) KE=0 ii) KxE-oy,H =0 ii) KA =0 iv) Fx +@e,E=0 Discuss the physical significance of Poyinting Vector, 4 Given that E = iE, coso(fepiz~1)+ jE, sin ox feui2 -1). Hence find the value for ® Poyinting vector. Show that the average value of the Poyinting vector in non-conductor is the product of 3 phase velocity and total (average) energy density. Deduce Fresnel's equations at the boundary of two dielectrics for an electremagnetic 8 wave polarized with its E vector normal to the plane of incidence. , Define Brewster angle. Find the Brewster and critical angles between air and glass 1 having a refractive index of 1.6. ‘What do you by cut-off wavelength of a waveguide? Show that for rectangular 2+8 waveguide 2 ¢) =| += a 6. ; A rectangular waveguide has dimensions of Ix2 cm’, Determine the guided wavelength 5 A, at a wavelength of 0.5 cm for dominant mode, a, = . where the symbols have their usual meanings. . “ ee th 6 Derive the equations for transmission line. ; , Determine impedance of a one-cighth wave length line af radio frequency. 6 Determine the condition for distortion less line. 3 . , 4 Define effective height and radiation resistance of an antenna. ; sedan ty Ce electric field intensity and rediation resistance for a short 7 entena. ; Show that the directivity of a half-wave dipole is 2.15 db, 4 expressi for e.m.f induced in a loop antenna by an external field. 6 vais voltage induced by a plane wave of field strength 0.02 Vim and wavelength 400 4 meters in a loop of 2 m? of 30 turns. The plane of the loop being in the direction of wave What are the differences between receiving and transmitting antenna? 5