 Electromagnetic Field and Wave Theory-Engineering-Mumbai University-Dec2019 - Grad Plus

# Electromagnetic Field and Wave Theory-Engineering-Mumbai University-Dec2019

## Semester: 4

[Total Time: 3 Hours]
[Total Marks: 80 M]
Note:1)Question No. 1 is Compulsory.

2) Attempt any three Questions out of remaining five Questions.
3) Assume suitable data if necessary and justify the same.

Q.1 Answer any four out of five questions.

a Explain Coulomb’s law in Electrostatics and hence define Unit Charge. [05M]

b Express the following vector in Cartesian co-ordinate system [05M]
A=2 cos θ âr +3 r âθ – 4 âz

c State and explain relationship between Electric Intensity and potential. [05M]

d What is Lorentz force equation for moving charge? Enlist two applications.[05M]

e Explain inconsistency in Ampere’s circuital law. [05M]

Q2 a Show that electric field due to infinite sheet of charge at a point is independent of distance at that point from the plane containing the charge. [10M]

b. Three equal point charges of 2 μc are in free space at (0,0,0), (2,0,0), (0,2,0) respectively . Find net force on fourth charge of 5μC at (2,2,0) [10M]

Q.3 a. Derive Poisson’s and Laplace equation. Two plates of a parallel 10 capacitors are separated by a distance ‘d ’and maintained at potential 0 and V1 respectively. Find potential at any point between plates. [10M]

b. Derive the set of Maxwell’s equation for Static field and Time varying Field. [10M]

Q.4 a. Explain Ampere circuital law and differentiate between 10 conduction current and displacement current. [10M]

b. Find the capacitance of a co-axial conductor of length L, where inner and outer radius are r1 and r2 respectively. [10M]

Q.5 a. A current sheet Kˉ = 10 âz A/m lies in X=4 m plane and a second sheet Kˉ = – 8 âz A/m is at X= – 5 m plane. Find Hˉ at points (i) (1,1,1) (ii) (0, -3, 10) [10M]

b. Derive magnetic field intensity due to finite and infinite wire carrying a current I. [10M]

Q.6 a Formulate the wave equation from Maxwell’s equations for perfectly conducting medium. [10M]

b. Consider an interphase in Y- Z plane .The region X < 0 is medium1 10 with μr 1= 4.5 and magnetic field, H= 4 â x+5 â y- 6 â z A/m. The region X > 0 is medium 2 with μr2 = 6 . Find H2 and B2 in medium 2 and also calculate the angle made by H2 with normal to interface. [10M]

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