EE2202 ELECTROMAGNETIC THEORY ANNA UNIVERSITY PREVIOUS YEAR QUESTION PAPER April/May 2010 ...
Posted by R.Anirudhan
B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2010
Electrical and Electronics Engineering
EE2202 — ELECTROMAGNETIC THEORY
Time: Three hours Maximum: 100 Marks
Answer ALL Questions
PART A — (10 × 2 = 20 Marks)1. How are the unit vectors defined in cylindrical coordinate systems?
2. State divergence theorem.
3. Define electric potential and potential difference.
4. Write down Laplace’s and Poisson’s equations.
5. State Ampere’s law.
6. Define the terms: magnetic moment and magnetic permeability.
7. State Lenz’s law.
8. What is displacement current density?
9. Find the velocity of a plane wave in a lossless medium having a relative
permittivity of 5 and relative permeability of unity.
10. What is skin depth?
PART B — (5 × 16 = 80 Marks)11. (a) (i) Show that the vector field A
is conservative if A
possesses one of
the following two properties. (6)
(1) The line integral of the tangential component of A
path extending from a point P to a point Q is independent of
(2) The line integral of the tangential component of A
any closed path is zero.
(ii) If ϕ ρ ϕ ϕ ρ a a A sin cos + =
, evaluate ∫ • dl A
around the path shown
in Fig. 11(a)(ii). Confirm this using Stoke’s theorem. (10)
(b) (i) Determine the curl of these vector fields: (2 + 2 + 6)
(1) z x a xz a yz x P + = 2
(2) z a z a z a Q ϕ ρ ϕ ρ ϕ ρ cos sin 2 + + =
cos sin cos cos
T a r a a
θ φ θ θ φ θ = + +
(ii) Find the gradient of the following scalar fields: (2 + 2 + 2)
(1) y x e V z cosh 2 sin − =
(2) ϕ ρ 2 cos 2z U =
(3) ϕ θcos sin 10 2 r W = .
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12. (a) (i) Determine the electric field intensity at ( ) 3 . 2 , 0 , 2 . 0 − − P due to a
point charge of nC 5 + at ( ) 5 . 2 , 1 . 0 , 2 . 0 − Q in air. All dimensions are
in meters. (8)
(ii) A circular disc of radius ‘a’ m is charged uniformly with a charge
density of ‘ σ’ coulombs/ 2 m . Find the potential at a point ‘h’ m from
the disc surface along its axis. (8)
(b) (i) State and derive electric boundary conditions for a dielectric to
dielectric medium and a conductor to dielectric medium. (10)
(ii) Derive the expression for energy density in electrostatic fields. (6)
13. (a) (i) Derive the expression for coefficient of coupling in terms of mutual
and self inductances of the coils. (8)
(ii) An iron ring with a cross sectional area of 8 2 cm and a mean
circumference of 120 cm is wound with 480 turns of wire carrying a
current of 2 A. The relative permeability of the ring is 1250.
Calculate the flux established in the ring. (8)
(b) (i) State and explain Biot-Savart’s law. (6)
(ii) Derive an expression for the force between two long straight
parallel current carrying conductors. (10)
14. (a) Derive and explain Maxwell’s equations both in integral and point forms.
(b) (i) A circular loop conductor having a radius of 0.15 m is placed in
Y X − plane. This loop consists of a resistance of 20 . If the
magnetic flux density is B
= 0.5 sin z a t 3 10 Tesla, find the current
flowing through this loop. (8)
(ii) Explain the relationship between the field theory and circuit theory
using a simple RLC series circuit. (8)
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15. (a) (i) State and prove Poynting’s theorem and derive the expression for
average power. (12)
(ii) The current density at the surface of a thick metal plate is
100 2 m A . What is the skin depth if the current density at a depth
of 0.01 cm is 28 2 m A ? (4)
(b) (i) Derive wave equations in phasor form. (10)
(ii) A transmission line operating at 6 10 = ω radians/second, has α = 8
dB/m, 1 = β rad/m and ( ) + = 40 60 0 j Z and is 2 m long. If the line
is connected to a source of g V volts and terminated by a load of
( ) + 50 20 j , determine the input impedance. (6)