EC303 Applied Electromagnetic Theory

QUESTION BANK

MODULE 1

1. State and prove Ampere's circuit law and coulomb’s law(KTU, May 2019,Apr2018, Sept
2020) (6)
2. Explain Scalar and vector magnetic potential (KTU, Dec 2019) (7)
3. State and explain Gauss Law (KTU, Dec 2019) (5)
4. Derive an expression for magnetic energy of a continuous distribution of current in a volume.
(KTU,May2019, Sept 2020) (7)

5. Find the potential function and electric field intensity for the region between concentric
right circular cylinders, where V = 0 at r = 1 mm and V = 100 V at r = 30 mm. (KTU, May
2019) (5)

6. A square loop of 4m side is placed in xy- plane with its centre at the origin and sides long
the coordinates axes. If the magnetic flux density in the region is givenby
𝐵 = (0.28𝑎𝑥 − 0.3𝑎𝑦 + 0.4𝑎𝑧)−0.1𝑡 𝑊𝑏/𝑚2, find the induced EMF in the loop at t=10s.
(KTU,May2019) (8)

7. An air filled parallel plate capacitor is with following specification, area = 2 m2 and spacing
between the plates = 0.l m. If a voltage = 20𝑐𝑜𝑠103𝑡 is applied across the capacitor plates,
find the magnetic field between the capacitor plates. (KTU,May2019) (5)

8. Point charges 5 nC and -2 nC are located at (2, 0, 4) and (-3, 0, 5), respectively.
(i) Determine the force on a 1nC point charge located at (1, -3, 7).
(ii) Find the electric field E at (1, - 3, 7). (KTU,Dec2018) (7)

9. Give Poisson’s and Laplace equation in electrostatics. Give application. (KTU, Dec 2018)(7)
10. Derive the expression of capacitance and inductance of two wire transmission line. (KTU,
Dec 2019, Dec 2018,Dec2017) (8)
11. Define electric field intensity. Derive the equation for electric field intensity at a
distance ‘r’ from a point charge of Q coulombs. (KTU,Apr2018) (7)
12. Define curl of a vector field. Derive the equation for curl of a vector field in Cartesian
co-ordinate system. (KTU,Apr2018) (10)

13. Derive the expressions for Energy stored in Electric Field. (KTU,Dec2017) (8)

14. Eight identical charges, Q each are placed on the corners of a cube of side ‘a’. Find the
resultant force on a charge. (KTU,Dec2017) (7)

MODULE 2

1. State and explain Maxwell’s equations in the integral and differential forms. (KTU, Dec
2019, May 2019, Dec 2018,Dec2017) (8)

2. Derive the solution of uniform plane wave in lossy dielectric medium.(KTU,May2019)(6)

3. State and prove boundary conditions for E and H in accordance with Maxwell’s
equations. (KTU, Dec 2018,Dec2017, Sept 2020) (7)

4. Starting from Maxwell equation, derive the wave equation for a conducting medium.
(KTU, Apr 2018,Dec2017) (7)

5. Derive the equation for Electric and Magnetic field intensities for an electromagnetic
wave propagating in the z-direction in a dielectric medium.
H=10e-αx cos(wt-0.5x)az A/m., impedance of medium is 173+j100Ω
Find the following:
i) Attenuation constant; ii)Phase velocity; iii)Phase constant; iv)Intrinsic impedance.
v)Direction of Propagation, vi) Loss tangent, vii) Skin depth
(KTU,Apr2018, Sept 2020)(9)

6. Define skin depth for a conductive medium? If σ denotes the conductivity, Derive the
equation for skin depth for a good conductor. (KTU,Apr2018, Sept2020) (5)

7. Derive the boundary conditions for electric field at the interface of two dielectrics. (KTU,
Dec2017) (6)

8. Explain Group velocity and Phase velocity. When a wave of 6 GHz propagates in parallel
conducting plates separated by 3 cm, find the Vpand Vg of the wave for dominant
wave.(KTU,Dec2017) (8)
 MODULE 3

1. Derive an expression for reflection coefficient of a plane wave incidence with parallel
polarization( or perpendicular polarization) at a dielectric interface. (KTU,Dec 2019,
May2019, Sept 2020) (5)

2. Derive an expression for net outward power flow associated with anelectromagnetic
wave, from a surface. (KTU,May2019) (10)

3. What is Snell's law? (KTU,May2019) (3)

4. What is Polarisation? Explain the different types of Polarisation? (KTU, Dec2018,

Dec2017, Sept 2020) (7)

5. Derive the expression for the ratio of reflected to incident electric field strength for an
insulator with oblique incidence. (KTU,Dec2018) (7.5)

6. Derive the expression for refraction and reflection coefficient of plane

electromagnetic waves that undergoing oblique incidence with vertical polarization
(considering boundary separation). (KTU,Apr2018) (7)

7. State Poynting theorem. Derive the equation of complex vector. (KTU,Dec2017) (8)

8. Derive Brewster angle. A parallel-polarized plane wave is incident from air onto a
dielectric medium with εr = 9 at the Brewster angle. What is the refractionangle?
(KTU,Dec2017, Sept 2020) (9)

MODULE 4

1. Define reflection coefficient and VSWR of a transmission line and derive the relation
between reflection coefficient and VSWR. (KTU, May 2019,Dec2018) (7)

2. Derive the current and voltage equation of a transmission line. (KTU,May2019) (7)

3. Draw the circuit of small section of transmission line of differential length and label the
circuit parameters. (KTU,May2019) (3)

4. AlosslesstransmissionlinehasprimaryconstantL=0.01μH/m,C=100pF/m.Find
the characteristic impedance or the line. (KTU,May2019) (5)

5. Deriveanexpressionforcharacteristicimpedanceofatransmissionlineandshowthat
it is resistive at radio frequencies. (KTU,Dec2018) (7)

6. Derive the ABCD parameters of a transmission line. (KTU,Dec2017) (8)

7. A lossless 50-Ω transmission line is terminated in a load with ZL = (50+ j25) Ω.
Calculate(i)ThereflectioncoefficientΓ.(ii)Thestanding-waveratio.(KTU,Dec2017, Sept
2020) (7)

8. Derive standard Transmission line equations. (KTU,Dec2017) (6)

9. Derive the equation of input impedance of a transmission line due to line terminated
by a load (KTU, Dec 2019) (7)
10. Derive the expression for characteristic impedance of a transmission line (KTU, Dec 2019) (8)

MODULE 5

1. What are distributed elements? (KTU,May2019) (4)

2. A load impedance 90 - j25 is to be matched to 50 Ω using single stub matching. Find the
length and location of stub using smith chart. (KTU,May2019) (10)

3. Derive the expression for r-circles and x-circles in Smith chart. (KTU,Dec 2018, Sept 2020)
(10)

4. Explain single stub matching using analytical method. (KTU, Dec 2019, Dec2018) (10)

5. Write short notes on single stub matching and double stub matching. (KTU,Apr2018) (8)

6. How a smith chart is useful in finding the stub length for impedance matching. (KTU,
Apr2018) (4)

7. Write note on half wave and quarter wave transmission lines. (KTU,Dec2017, Sept 2020)
(5)

8. A lossless 60Ω line is terminated by a 60 + j60Ω load. Find Γ, s, load admittance,

Reflection coefficient at 0.2λ from the load if Zin = 120 - j60 Ω. How far is the load from
generator (Solve with Smith chart)? (KTU,Dec 2017,Sept 2020) (6)

9. Design a stub to match 40 + j30 Ω load (antenna) to a lossless line of 100 Ω (use Smith
chart). (KTU,Dec2017) (9)

10. By analytical method, get the value of position where stub has to be placed from load
and stub length with single stub impedance matching in transmission lines. (KTU, Dec
2019,Dec2017, Sept 2020) (7)

11. Explain Half Wave and Quarter Wave Transmission lines. Given that ZL = 30 + j40 Ω,
Z0 = 50 Ω. Find the shortest length (‘l’) and point where stub has to be placed for a
matching. (Use Smith chart) (KTU,Dec2017) (10)
 MODULE 6

1. Derive the expressions for TE(or TM) mode in a rectangular wave guide. (KTU, Dec 2019, May 2019,
Apr 2018, Sept 2020) (10)

2. The longitudinal electric field for TM11 mode is givenby

𝐸𝑧= sin 5𝑥 sin 8𝑦 𝑒−𝑗𝛽𝑧 𝑉/𝑚. Find the cut off frequency of the mode. (KTU, May 2019) (7)
3 The cross section of a rectangular wave guide is 20 cm x 5 cm. Find 3 lowest order mode frequencies.
(KTU,May2019) (3)

4 Determine, assuming TE10 mode of propagation ,the cut-off frequency, cut-off wavelength, guide
wavelength, phase constant, phase velocity, group velocity and wave
impedanceinthecaseofahollowrectangularmetallicwaveguideofdimensions6cm
and 3 cm, respectively, when the applied signal frequency is 5 GHz. (KTU, Dec 2018, Sept 2020) (10)

5 A hollow rectangular waveguide has dimensions of a= 4 cm and b= 2 cm. Calculate the amount of
attenuation if the frequency is 3.5 GHz. Assume dominant mode. (KTU, Dec 2018) (10)

6 With a neat diagram explain the propagation of electromagnetic wave in a rectangular wave guide?
(KTU,Dec 2019, Apr 2018) (8)

7 What are called degenerate modes? Explain. (KTU,Dec2017) (5)

8 Draw the field distribution pattern for TE 20 mode inside a rectangular waveguide. (KTU, Dec2017) (4)

9 List all the modes which are supported in rectangular waveguides and why? (KTU, Dec 2017) (8)

10 Derive the relationship between guide wavelength, free space wavelength and cut off wavelength in
rectangular waveguide. (KTU,Dec 2017) (5)

11 Discuss the attenuation of waveguides. (KTU,Dec2017) (5)

12 Explain waveguides and its different modes of wave propagation. (KTU,Dec2017) (10)