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

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GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER- IV (New) EXAMINATION - WINTER 2019

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Subject Code: 2140909 Date: 14/12/2019
Subject Name: Field Theory
Time: 10:30 AM TO 01:00 PM Total Marks: 70

Instructions:
1. Attempt all questions.

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2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

MARKS

Q.1 (a) Define scalar Field and Vector field with proper example. 03
(b) In Free Space V = x%y(z + 3) Find V and E at point (3,4,-6) 04

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(c) Explain Spherical co-ordinate system. Also give expression of differential 07
elements in the system.

Q.2 (a) Write mathematical Expression of Divergence in rectangle co-ordinate 03
system. Explain physical meaning of Divergence.
(b) State and Explain Stokes’ theorem. 04

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(c) Derive Maxwell’s first equation as applied to the electrostatics, using 07
Gauss’s law.

OR

(c) Derive expression of electric field intensity due to an infinite line charge 07
over z-axis having a uniform charge density of p; C/m.

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Q.3 (a) Explain concept of dot product and cross product. 03
(b) Explain concept of magnetic torque. 04
(c) If a particular Field is given by, 07
F= (x + 3y + az)a_x + (bx + 2y + 2)a_y + (4x +cy + 22)a_z,
Than Find the constant a,b,c such that the Field is irrotational.

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OR

Q.3 (a) Write Maxwell’s equations-for- steady field in integral and differential 03
form.
(b) Explain Electrical field as the Gradient of the electrical potential. 04
(c) Two uniform line charges of Density p_l =4nC/m lie in the x=0 plane at 07

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y = +4m. Find E at (4,0,10)

Q.4 (a) Explain Characteristics impedance and propagation constant of the 03
transmission line.
(b) Explain EMI control techniques. 04
(c) Discuss poisson’s and Laplace Equation 07

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OR

Q.4 (a) Write any three equations which Shows current density-J and field 03
density-D are Dual.
(b) Explain polarization with reference to dielectrics. 04
(c) Derive equation for lossless transmission line. 07

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Q.5 (a) State and explain source of EML 03
(b) Find the displacement current within a parallel plate capacitor where 04
ε =100ε₀, A= 0.01m², d=0.05 mm and
the capacitor voltage is 100 sin (2000πt) volts.
(c) State and Explain Ampere Circuital Law both in integral and differential 07

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form.

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OR

Q.5 (a) Explain Physical significance of displacement Current. 03
(b) Explain conduction current density and displacement current Density. 04

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(c) The magnetic field intensity is given in certain region of space as 07
H:[(x+2YZ)a_x+%Zz; A/m. Find 1. ∇xH 2. J 3.Use J to find
the total current passing through the surface Z=4, 1<x <2, 3<y<5.1In a-
direction

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