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Term End Examination - November 2013

Course : EEE109 - ngineering Electromagnetics Slot: F1Class NBR : 1532

Time : Three Hours Max.Marks:100

Answer any TEN Questions

(10 X 10 = 100 Marks)

1. a) The vector from the origin to point A is given as (6,2,4), and the unit vector directed from

the origin toward point B is (2,2, 1)/3. If points A and B are ten units apart, find the

coordinates of point B.

[4]

b) Express the uniform vector field F = 5ax in cylindrical and spherical components. [6]

2. a) A 2 C point charge is located at A (4, 3, 5) in free space. Find E, Eand Ez at P (8, 12, 2). [5]

b) Derive the expression for electric field intensity for an infinite line charge and infinite sheet

charge using Gausss law.

[5]

3. a) Within the spherical shell, 3 < r < 4 m, the electric flux density is given as

D = 5(r 3)3

arC/m2

.

i) What is the volume charge density at r= 4?

ii) What is the electric flux density at r= 4?

iii) How much electric flux leaves the sphere r= 4?

[4]

b) Derive the energy density equation for electrostatic fields. [6]

4. a) In spherical coordinates, E = 2r/(r2 + a

2)2ar V/m. Find the potential at any point, using the

reference i) V

= 0 at infinity ii) V = 100 V at r = a.

[6]

b) Derive the Maxwells equations related electrostatic fields. [4]

5. a) Let V = 20x2yz 10z

2 V in free space. (i) Determine the equations of the equi-potential

surfaces on which V= 0 and 60 V. (ii) Assume these are conducting surfaces and find the

surface charge density at that point on the V = 60 V surface where x = 2 and z = 1.

It is known that 0 V 60 V is the field-containing region.

[6]

b) Derive the formula for the capacitance of a spherical capacitor. [4]

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6. a) A current sheet K = 8axA/m flows in the region 2 < y< 2 in the plane z = 0. Calculate H at

P (0, 0, 3).

[6]

b) Derive the expression for magnetic field intensity due to infinite sheet of current. [4]

7. a) Derive the force equation for a current element when it is placed in a uniform magnetic field. [3]

b) The xy-plane serves as the interface between two different media. Medium 1 (z < 0) is filled

with a material whose r= 6, and medium 2 (z > 0) is filled with a material whose r= 4.

If the interface carries current (1/ 0) aymA/m, and B2= 5ax+ 8az mWb/m2. Find H1and B1.

[7]

8. The magnetic field intensity is given in a certain region of space as

H = [(x + 2y)/z2]ay+ (2/z)azA/m.

(a) Find H . (b) Find J. (c) Use J to find the total current passing through the surface z = 4,

1 x 2, 3 z 5, in the azdirection.

(d) Show that the same result is obtained using the other side of Stokes theorem.

[10]

9. a) Derive the Maxwells equations relevant to magneto-statics. [3]

b) Determine the self-inductance of a co-axial cable of inner radius a and outer radius b. [7]

10. a) In free space, E = 20 cos(t 50x) ayV/m. Calculate displacement current density Jd, H, . [5]

b) In free space, H = 0.2 cos(t x) azA/m. Find the total power passing through a square plate

of side 10 cm on plane x + y = 1.

[5]

11. a) State and derive the Poynting theorem. Also explain the various terms in the final equation. [6]

b) A 5 GHz uniform plane wave Eis= 10 e-jz

ax V/m in free space is incident normally on a large

plane, lossless dielectric slab (z > 0) having = 40, = 0 . Find the reflected wave Ersand

the transmitted wave Ets.

[4]

12. a) A Hertzian dipole of length /100 is located at the origin and fed with a current of 0.25 sin

108t A. Determine the magnetic field at r = /5, = 30.

[6]

b) Sketch the normalized E-field and H-field patterns for a half-wave dipole and a quarter wave

monopole.

[4]