GTU Exams papers
GUJARAT TECHNOLOGICAL UNIVERSITY
B. E. Sem. – V – Examination – June- 2011
Subject code: 151002
Subject Name: Engineering Electromagnetics
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. The symbols have the usual meaning.
Q.1 (a) Define electric field intensity. Derive the expression for the intensity of
electric field due a line charge along the Z direction with uniform charge
density ρL c/m using Coulomb’s law and verify the same using Gauss’s law.
(b) Prove the following relations from the fundamental principle of
electromagnetic theory :
(ii) F = Q(E + v × B)
Q.2 (a) What is an electric dipole?Derive the expression for the potential and electric
field intensity due to a dipole at distances very large from the origin
compared to the spacing d between the charges +Q and – Q .
(b) Given the Potential field in cylindrical coordinates
V=1000 Φ+50 Volts.Calculate the value at P(0.4,30°,1) in air of (i)E (ii)D
(iii) ρv (iv) Energy density
Given that ñ
= C/m2 in cylindrical coordinates. Evaluate both sides
of the divergence theorem for the volume enclosed by ρ = 1m , ρ = 2m, z = 0
and z =10m
Q.3 (a) Assuming the potential function V varies as a function of ρ in cylindrical
coordinates systems ,obtain the solution of Laplace equation and deduce the
value of capacitance of a coaxial capacitor
(b) Curl free vector is an irrotational field, which is a conservative field
(c) E and F are vector fields given by E = 2xax + ay + yz az and
F = xy ax -y2ay+ xyz az .Determine
(a) | E | a t (l, 2, 3)
(b) The component of E along F at (1, 2, 3)
(c) A vector perpendicular to both E and F at (0, 1, – 3) whose magnitude is unity
Q.3 (a) An infinitely long coaxial cable is carrying current I by the inner conductor of
radius ‘a’ and –I by the outer conductor of radii ‘b’ and ‘c’. where c>b.
(i)Deduce the expressions for H at
i)ρ < a (ii) a <ρ < b (iii) b < ρ < c (iv) ρ > c.Sketch the plot of H as a function
of radius.(ii) Find the inductance of the coaxial cable
(b) Do as directed
(i) D = 8ρ sin φ aρ + 4ρ cos φ aφ C/m2. Find div D
(ii) Find the laplacian of the scalar V e x y z sin 2 cosh − = .
Q.4 (a) Using Gauss’s law explain the concept of divergence. Prove Divergence
theorem. Obtain Maxwell’s first equation
(b) (i) Express the vector field ( ) ( ) 2 2 1
x y D = x + y xa + ya − in cylindrical
components . Evaluate D at the point P ( 2, 60 , 5) 0 ñ = ö = z = . Express the
result in cylindrical and Cartesian components.
(ii) Find ∇× A for the vector field è A = 10sinèa in spherical coordinates at
Q.4 (a) Deduce the boundary conditions with necessary derivations (i)at the interface
between two dielectric materials with permittivities ε1 and ε2 and (ii) at the
interface between two magnetic materials with permeabilities μ1 and μ2
(b) A circuit has 2000 turns enclosing a magnetic circuit of 30 sq cm in section.A
current of 5A in the circuit produces a field of flux density 1 wb/cm2 and
when the current is doubled, the flux density increases by 50%.Determine the
value of the inductance of the circuit for the current varying between 5A and
10A.Also find the induced emf when the current increases from 5A to 10A in
Q.5 (a) Using Faraday’s law and the concept of displacement current density,
Ampere’s circuital law, divergence theorem, obtain all Maxwell’s equations
for time varying fields in point and integral forms .Derive the necessary equations.
(b) A wave propagating in a lossless dielectric has the components
E t z a V m x 500cos(10 ) / 7 = − â and y H 1.1cos(10 t z)a 7 = − â A/m.
If the wave is travelling with the velocity of υ =0.5C,find(i) μr (ii) εr (iii)β (iv) λ
Q.5 (a) State and prove Poynting theorem relating to the flow of energy at a point in
space in an electromagnetic field.
(b) A certain signal generator produces a uniform plane wave in free space
having a wavelength of 12 cm.When the propagates through a lossless
material of unknown wavelength,its wavelength reduces to 8 cm.The E
field amplitude is 50V/m and H field is 0.1 A/m. Find the generator
frequency, μr, εr of unknown material..
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