Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Summer 6th Sem Old 160906 Theory Of Electromagnetics Previous Question Paper
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI(OLD) ? EXAMINATION ? SUMMER 2019
Subject Code:160906 Date:16/05/2019
Subject Name: Theory Of Electromagnetics
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) What is dot product and cross product? Explain its significance and applications. 07
(b) A perpendicular vector field ?? ?
= ?? 2
?????? 2
? ?? ?? ? ? ?+ ???????? ? ?? ?
? ? ? is in cylindrical system.
Find the flux emanating due to this field from the closed surface of the cylinder 0
? z ? 1, r = 4, verify the divergence theorem.
07
Q.2 (a) Define surface charge density. Drive an expression for electric field intensity due
to a sheet of charge with uniform surface charge density ?? ?? ?? ?? 2
? on an infinite
plane.
07
(b) Show that the divergence of flux density due to point charge and uniform line
charge is zero.
07
OR
(b) If a sphere of radius ?a? has a charge density ?? ?? = ?? ?? 3
then find ?? ?
and ?. ?? ?
as a
function of radius r and sketch the result. Assume k constant.
07
Q.3 (a) Establish relation between ?? ?
and ?? ?
. Proof that gradient of a scalar is a vector. 07
(b) If ?? = ?? ? ?? + ???? + 2?? V, find ?? ?
at (1, 2, 3) and the energy stored in a cube of
side 2m centered at the origin.
07
OR
Q.3 (a) What is the principle of Continuity equation? Drive an expression for integral
and differential form of Continuity equation of current.
07
(b) Write a short note on ?Electrostatic boundary conditions between two perfect
dielectrics?.
07
Q.4 (a) The region between two concentric right circular cylinders contains a uniform
charge density ?. Solve the Poisson?s equation for the potential in the region.
07
(b) It is known that ?? = ???? is a solution of Laplace?s equation where X is function
of x and Y is function of y alone. Determine which function of the following
function are also solutions of Laplace?s equation.
(i) ?? = 100 ???? (ii) ?? = 100???? + 2?? (iii) ?? = ?? + 3??
(iv) ?? = 2???? + ?? 2
? ?? 2
(v) ?? = (?? ?? )
2
.
07
OR
Q.4 (a) State and Explain Biot Savart law. How Biot-Savart law can be applied to the
distributed sources.
07
(b) If a perpendicular field is given by
?? ?
= (?? + 2?? + ???? )?? ?? ? ? ?+ (???? ? 3?? ? ?? )?? ?? ? ? ?+ (4?? + ???? + 2?? )?? ?? ? ? ? then find the
constant a, b and c such that the field is irrotational.
07
Q.5 (a) Drive an expression for the inductance of
Solenoid (ii) Toroid (iii) Co-axial Cable.
07
(b) A charge of ?? = 5 ? 10
?18
?? is moving, through the uniform magnetic field?? ?
=
?0.4?? ?? ? ? ?+ 0.2?? ?? ? ? ?? 0.1?? ?? ? ? ? . T with a velocity
V= (2?? ?? ? ? ?? 3?? ?? ? ? ?+ 6?? ?? ? ? ? )10
5
?? /?? at ?? = 0.
1. What electric field is present at ?? = 0, if the net force on the electron is zero?
07
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Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI(OLD) ? EXAMINATION ? SUMMER 2019
Subject Code:160906 Date:16/05/2019
Subject Name: Theory Of Electromagnetics
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) What is dot product and cross product? Explain its significance and applications. 07
(b) A perpendicular vector field ?? ?
= ?? 2
?????? 2
? ?? ?? ? ? ?+ ???????? ? ?? ?
? ? ? is in cylindrical system.
Find the flux emanating due to this field from the closed surface of the cylinder 0
? z ? 1, r = 4, verify the divergence theorem.
07
Q.2 (a) Define surface charge density. Drive an expression for electric field intensity due
to a sheet of charge with uniform surface charge density ?? ?? ?? ?? 2
? on an infinite
plane.
07
(b) Show that the divergence of flux density due to point charge and uniform line
charge is zero.
07
OR
(b) If a sphere of radius ?a? has a charge density ?? ?? = ?? ?? 3
then find ?? ?
and ?. ?? ?
as a
function of radius r and sketch the result. Assume k constant.
07
Q.3 (a) Establish relation between ?? ?
and ?? ?
. Proof that gradient of a scalar is a vector. 07
(b) If ?? = ?? ? ?? + ???? + 2?? V, find ?? ?
at (1, 2, 3) and the energy stored in a cube of
side 2m centered at the origin.
07
OR
Q.3 (a) What is the principle of Continuity equation? Drive an expression for integral
and differential form of Continuity equation of current.
07
(b) Write a short note on ?Electrostatic boundary conditions between two perfect
dielectrics?.
07
Q.4 (a) The region between two concentric right circular cylinders contains a uniform
charge density ?. Solve the Poisson?s equation for the potential in the region.
07
(b) It is known that ?? = ???? is a solution of Laplace?s equation where X is function
of x and Y is function of y alone. Determine which function of the following
function are also solutions of Laplace?s equation.
(i) ?? = 100 ???? (ii) ?? = 100???? + 2?? (iii) ?? = ?? + 3??
(iv) ?? = 2???? + ?? 2
? ?? 2
(v) ?? = (?? ?? )
2
.
07
OR
Q.4 (a) State and Explain Biot Savart law. How Biot-Savart law can be applied to the
distributed sources.
07
(b) If a perpendicular field is given by
?? ?
= (?? + 2?? + ???? )?? ?? ? ? ?+ (???? ? 3?? ? ?? )?? ?? ? ? ?+ (4?? + ???? + 2?? )?? ?? ? ? ? then find the
constant a, b and c such that the field is irrotational.
07
Q.5 (a) Drive an expression for the inductance of
Solenoid (ii) Toroid (iii) Co-axial Cable.
07
(b) A charge of ?? = 5 ? 10
?18
?? is moving, through the uniform magnetic field?? ?
=
?0.4?? ?? ? ? ?+ 0.2?? ?? ? ? ?? 0.1?? ?? ? ? ? . T with a velocity
V= (2?? ?? ? ? ?? 3?? ?? ? ? ?+ 6?? ?? ? ? ? )10
5
?? /?? at ?? = 0.
1. What electric field is present at ?? = 0, if the net force on the electron is zero?
07
2
2. If the electric field intensity in entirely in ?? ?? ? ? ? direction and |?? ?????? | = 2???? at ?? =
0 find Ex.
OR
Q.5 (a) State Maxwell?s equations for static field. Write the expression for integrated and
derivative form of Maxwell?s equation derived from faraday?s law and Ampere?s
circuit law for static field.
07
(b) A point charge of 25 nC located in free space at P (2, -3, 5) and a perfectly
conducting plane at z = 2.
Find (i) V at (3, 2, 4) (ii) ?? ?
at (3, 2, 4) (iii) ?? ?? at (3, 2, 2) use method of image.
07
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This post was last modified on 20 February 2020