Download GTU BE/B.Tech 2019 Summer 4th Sem New 2140909 Field Theory Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Summer 4th Sem New 2140909 Field Theory Previous Question Paper

1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?IV(NEW) ? EXAMINATION ? SUMMER 2019
Subject Code:2140909 Date:20/05/2019
Subject Name: Field Theory
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Bold letters indicate vector quantity.


MARKS

Q.1 (a)
Explain cylindrical coordinate system in brief.
03
(b)
Explain unit vectors of Cartesian, cylindrical and spherical coordinate
systems.
04
(c) Transform the vector 4ax- 2ay- 4 azintospherical coordinates at a point
P(x = -2, y = -3, z =4).
07

Q.2 (a)
State and explain Coulomb?s law.
03
(b) Derive the expression for electric field due to infinite surface charge
distribution in free space.
04
(c)
An infinite uniform line charge having line charge density of ?L = 30 nC/m
placed at y = 3, z = 5. Find the total electric field intensity at (5,6,1).
07
OR
(c) Point charges of 120 nC are located at A(0,0,1) and B(0,0,-1) in free
space. Find (1) Find E at (0.5,0,0) (2) What single charge at origin
would provide the identical field strength.
07
Q.3 (a)
State and prove the Gauss?s law.
03
(b) Derive Maxwell?s first equation as applied to electrostatics, using
Gauss?s law.
04
(c) Calculate the divergence of Gat P(2,-3,4) if G = (a) x ax + y ay+ z az (b)
? a ? (c) r a r (d) 6r
2
sin?ar + 2 r
2
cos?a ?.
07
OR
Q.3 (a)
Explain physical significance of Divergence.
03
(b) Find divergence D at the origin if
D = e
-x
sin y ax- e
-x
cos y ay + 2z az
04
(c) A co-axial conducting cylinder has charge density of ?s on the outer
surface of the inner cylinder. Use Gauss? law to find ?D? in all the
regions. Assume that inner cylinder has radius of ?a? metres and outer
cylinder has radius of ?b? metres
07
Q.4 (a)
Derive Poisson?s and Laplace?s equation.
03
(b)
Explain electric dipole. Derive the expression for E at any distant point from
dipole.
04
(c)
Explain boundary conditions between two perfect dielectric materials.
07
OR
Q.4 (a) Explain concept of electric potential difference. 03
(b)
State and explain Ampere?s circuital law.
04
(c)
Write a short note on EMI & EMC.
07
Q.5 (a) State and explain BiotSavart?s law. 03
(b) Explain the physical significance of the term: Curl of a vector. 04
(c)
Explain Stoke?s theorem with its mathematics expression.
07



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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?IV(NEW) ? EXAMINATION ? SUMMER 2019
Subject Code:2140909 Date:20/05/2019
Subject Name: Field Theory
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Bold letters indicate vector quantity.


MARKS

Q.1 (a)
Explain cylindrical coordinate system in brief.
03
(b)
Explain unit vectors of Cartesian, cylindrical and spherical coordinate
systems.
04
(c) Transform the vector 4ax- 2ay- 4 azintospherical coordinates at a point
P(x = -2, y = -3, z =4).
07

Q.2 (a)
State and explain Coulomb?s law.
03
(b) Derive the expression for electric field due to infinite surface charge
distribution in free space.
04
(c)
An infinite uniform line charge having line charge density of ?L = 30 nC/m
placed at y = 3, z = 5. Find the total electric field intensity at (5,6,1).
07
OR
(c) Point charges of 120 nC are located at A(0,0,1) and B(0,0,-1) in free
space. Find (1) Find E at (0.5,0,0) (2) What single charge at origin
would provide the identical field strength.
07
Q.3 (a)
State and prove the Gauss?s law.
03
(b) Derive Maxwell?s first equation as applied to electrostatics, using
Gauss?s law.
04
(c) Calculate the divergence of Gat P(2,-3,4) if G = (a) x ax + y ay+ z az (b)
? a ? (c) r a r (d) 6r
2
sin?ar + 2 r
2
cos?a ?.
07
OR
Q.3 (a)
Explain physical significance of Divergence.
03
(b) Find divergence D at the origin if
D = e
-x
sin y ax- e
-x
cos y ay + 2z az
04
(c) A co-axial conducting cylinder has charge density of ?s on the outer
surface of the inner cylinder. Use Gauss? law to find ?D? in all the
regions. Assume that inner cylinder has radius of ?a? metres and outer
cylinder has radius of ?b? metres
07
Q.4 (a)
Derive Poisson?s and Laplace?s equation.
03
(b)
Explain electric dipole. Derive the expression for E at any distant point from
dipole.
04
(c)
Explain boundary conditions between two perfect dielectric materials.
07
OR
Q.4 (a) Explain concept of electric potential difference. 03
(b)
State and explain Ampere?s circuital law.
04
(c)
Write a short note on EMI & EMC.
07
Q.5 (a) State and explain BiotSavart?s law. 03
(b) Explain the physical significance of the term: Curl of a vector. 04
(c)
Explain Stoke?s theorem with its mathematics expression.
07



2


OR
Q.5 (a)
Classify magnetic materials.
03
(b)
Explain primary constant and secondary constant of transmission line.
04
(c)
Describe the physical description of transmission line propagation.
07

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