Categories: 6th Semester

GUJARAT TECHNOLOGICAL UNIVERSITY

BE – SEMESTER ?VI (NEW) – EXAMINATION ? SUMMER 2018

Subject Code: 2163203 Date: 01/05/2018

Subject Name: Engineering Electromagnetics & wave Progogation

Time: 10:30 AM to 01:00 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.

Q.1 (a)Transform the given vector A=10 az into spherical coordinates at Point

P (r=4, ?=110?, ?=120?).

03

(b) Explain cross product and dot product in detail. 04

(c) Explain cylindrical coordinate systems. 07

Q.2 (a) Define volume surface and line charge density. 03

(b) Explain coulombs law and field intensity. 04

(c) Given the field D = 6?sin (f /2) a?+ 1.5?cos (f /2) af C/m

2

.

Evaluate both sides of the divergence theorem for the region bounded

by ?= 2, 0 < f < 180?, 0 < z < 5.

07

OR

(c) Find E at P (1, 5, 2) in free space if a point charge of 6 ?C is located at

Q(0, 0, 1), a uniform line charge of 180 nC/m lies along the z axis and a

uniform sheet charge 25 nC/m

2

lies in the plane z = -1

07

Q.3 (a) What do you mean by equipotential surface? 03

(b) State and prove maxwell?s first law in integral form. 04

(c) Derive the equation to find energy stored in the field of a system of

charges.

07

OR

Q.3 (a) Find the gradient of the following scalar field = e

-z

sin 2x cosh y. 03

(b) If V = 2 volts at x = 1mm and V = 0 volts at x = 0. Find Ex at x = 1 mm

in free space for the volume charge density -3?10

8

e0 x C/m

3

.

04

(c) Write short note on boundary condition for perfect dielectric. 07

Q.4 (a) Derive the expression of following capacitor: 1) coaxial 2) Spherical 03

(b) Derive Poission?s and Laplace?s equation. 04

(c) Write short note on magnetic boundary conditions 07

OR

Q.4 (a) Explain biot-savart law. 03

(b) Explain ampere?s circuital law 04

(c) Verify Stoke?s theorem for the field H = 6xyax ? 3y

2

ay and the

rectangular path around the region 2 = x =5, -1 = y =1 and z = 0. Let the

positive direction of ds be az.

07

Q.5 (a) Derive an equation of force on moving charge under effect of EM field. 03

(b) Explain wave motion in free space. 04

(c) Explain point and integral form of Maxwell?s equations. 07

OR

Q.5 (a) Define with respect to plane EM waves: 1) Phase 2) Phase constant 3)Phase velocity

03

(b) Explain skin effect. 04

(c) State and prove pointing vector theorem. 07

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