GTU BE 6th Semester 2163203 Engineering Electromagnetics and wave Progogation Summer 2018 Question Paper

Seat No.: ________ Enrolment No.___________
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