## EE2202 ELECTROMAGNETIC THEORY ANNA UNIVERSITY PREVIOUS YEAR QUESTION PAPER April/May 2010 ...

## 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

Third Semester

Electrical and Electronics Engineering

**EE2202 — ELECTROMAGNETIC THEORY**

(Regulation 2008)

Time: Three hours Maximum: 100 Marks

Answer ALL Questions

**PART A — (10 × 2 = 20 Marks)**

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 Ais conservative if A

possesses one of

the following two properties. (6)

(1) The line integral of the tangential component of A

along a

path extending from a point P to a point Q is independent of

the path.

(2) The line integral of the tangential component of A

around

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)

Fig. 11(a)(ii)

Or

(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 + + =

(3) 2

1

cos sin cos cos

r

T a r a a

r

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 = .

132 132 132

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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)

Or

(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)

Or

(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.

(16)

Or

(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)

132 132 132

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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)

Or

(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)