B.TECH - Semester 5 applied electromagnetic theory Question Paper 2021 (mar)
Practice authentic previous year university questions for better exam preparation.
Sample Questions
- Give the physical significance and the mathematical expressions for the operators "Curl" and "Divergence".
- Two concentric spherical shells carry equal and opposite uniformly distributed charges over their surfaces as shown in Figure. Calculate the electric field on the surface of inner shell.
- When a magnetic flux cuts across 200 turns at the rate of $2 \mathrm{~Wb} / \mathrm{s}$, what will be the induced voltage?
- Distinguish between phase velocity and group velocity. P.T.O.
- State Snell's law and define Brewster angle.
- What do you mean by matched transmission line? What are the advantages of impedance matching on high frequency lines?
- Compare circular and elliptical polarization.
- Give the applications of Smith chart.
- Give the application of parallel plate waveguides.
- Define guide wavelength equation. ( $\mathbf{1 0} \boldsymbol{\times} \mathbf{2} \boldsymbol{=} \mathbf{2 0}$ Marks) PART - B Answer any one full questions from each Module; Carrying 20 marks.
- (a) Using Gauss's theorem, show that a symmetrical spherical charge distribution is equivalent to a concentrated point charge at the centre of the sphere as far as external fields are concerned
- (b) The one-dimensional Laplace's equation is given as $\frac{d^{2} V}{d x^{2}}=0$. The boundary conditions are $V=9$ at $x=1$ and $V=0$ at $x=10$. Find the potential and also show the variation of $V$ with respect to $x$.
- (c) State Poisson's equation. How is it derived? Using Laplace's equation for a parallel plate capacitor with the plate surfaces normal to X-axis, find the potential at any point between the plates. Given $V=V_{1}$ at $x=x_{1}$ and $V=V_{2}$ at $x=x_...
- (a) A spherical volume of radius $R$ has a volume charge density given by $\rho=K r$, where $r$ is the radial distance and $K$ is a constant. Develop expressions $\vec{E}$ for and $V$ and sketch their variation with respect to $r(0 \leq r \leq \infty...
- (b) What is the physical interpretation of Gauss's law for the magnetic field? How Gauss' law for the magnetic field in differential form can be derived from its integral form?
- (a) What is a uniform plane wave? Why is the study of uniform plane waves important? Discuss the parameters $\omega_{1} \beta$ and $v_{p}$ associated with sinusoidally time-varying uniform plane waves.
- (b) What are the boundary conditions for static electric fields in the general form at the interface between two different dielectric media? Explain with necessary equations and diagrams.
- (a) The conduction current density in a lossy dielectric is given as $J_{C}=0.02 \operatorname{Sin} 10^{9} t A / m^{2}$. Find the displacement current density if $\sigma=10^{3} \mathrm{mh} / \mathrm{m}, \in_{r}=6.5$ and $\epsilon_{o}=8.854 \times 10^...
- (b) Derive an expression for equation of continuity and explain its significance. 6
- (c) Prove the electric field normal components are discontinuous across the boundary of separation between two dielectrics.
- (a) How does dissipation-less transmission lines act as tuned circuit elements? Explain.
- (b) Derive general expressions for reflection coefficient and transmission coefficient for $\vec{E}$ and $\vec{H}$ fields when an electromagnetic wave is incident normally on the boundary separating two different perfectly dielectric media.
- (c) Explain the following:
- (i) Characteristic impedance. (ii) Distortionless line. (iii) Voltage Standing Wave Ratio (VSWR). (iv) Reflection coefficient.
- (a) What are the speed, direction of propagation and polarisation of an electromagnetic wave whose electric field components are given as $E_{x}=4 E_{0} \cos (3 x+4 y-500 t)$ $E_{y}=3 E_{0} \cos (3 x+4 y-500 t+\pi)$ $E_{z}=0$
- (b) A plane electromagnetic wave propagation in the $x$-direction has a wavelength of 5.0 mm . The electric field is in the $y$-direction and its maximum magnitude is 30 mV . Write suitable equations for the electric and magnetic fields as a function...
- (c) What length of transmission line should be used at 500 MHz and how should it be terminated for use as a
- (i) Parallel resonant circuit (ii) Series resonant circuit. 4
- (a) In a rectangular waveguide for which $a=1.5 \mathrm{~cm}, b=0.8 \mathrm{~cm}$, $\sigma=0, \mu=\mu_{0}$ and $\epsilon=4 \epsilon_{0}, H_{x}=2 \sin \left(\frac{\pi x}{a}\right) \cos \left(\frac{3 \pi y}{b}\right) \sin \left(\pi \times 10^{11} t=\be...
- (i) The node of operation (ii) The cutoff frequency (iii) The phase constant $\beta$ (iv) The intrinsic wave impedance $\eta$.
- (b) Define cut-off wavelength for a rectangular wave guide. A rectangular wave guide measures $3 \times 4.5 \mathrm{~cm}$ internally and has a 10 Hz signal propagated in Calculate the cutoff wavelength, the guide wavelength and characteristic wave im...
- (c) What is stub matching? Outline the solution for the single stub matching problem.
- (a) Consider a parallel-plate waveguide as shown. Find the power reflection coefficients for $T E_{1,0}$ and $T M_{1,0}$ waves at frequency $f=5000 \mathrm{MHz}$ incident on the junction from free space side. L - 5068
- (b) A rectangular wave guide has the following characteristics: $b=1.5 \mathrm{~cm}$, $a=3 \mathrm{~cm}, \mu_{r}=1, \epsilon_{r}=2.25$
- (i) Calculate the cutoff frequency for $\mathrm{TE}_{10}, \mathrm{TE}_{20}$ and $\mathrm{TM}_{11}$ modes. (ii) Calculate the guide wavelength and characteristic impedance. $Z_{0}$ at 4.0 GHz for $\mathrm{TE}_{10}$ modes.