Electromagnetic Field Theory July-2011

UNIT – I

1. (a) Define Curl of a vector field.

(b) A vector is given in Cartesian coordinates as A-xy ax – 2yav Express V xA in cylindrical and spherical coordinates.

(c) Give the physical interpretation of curl of a vector field.

OR

1 (a) A vector in cylindrical coordinates is given as A = 2cos(J)ap + pflQ verify Stoke’s theorem for the surface bounded by+x axis, +y

axis and arc of the circle of radius 1 unit with centre at the origin.

(b) Assume a scalar field T = x2 + 3yz + 4xy2. Determineb-> Show that J js Independent of path. Assume a = (0,0,0), a

b = (2,2,2) and use (i) the straight line path p(0,0,0) (2,0,0) —> (2, 2, 0) —»(2, 2, 2) and (ii) the straight line path from a to b.

UNIT – II

2. (a) State Gauss’s law of electrostatics for the electric field intensity g.

(a)  Obtain the differential form of Gauss’s law from its integral form.

(c)   Electric flux density D = 6xyz2ax + 3x2z2av +6x2yzazCjm2 .

Find the total charge lying within the region bounded by 1< x < 3m, 0 < y < \m and — \<z<\m-

(b) Derive the expressions for electrostatic potential and electric field intensity due to an electrostatic dipole.

OR

2    (a) Derive the boundary conditions for the normal and tangential components of electric field intensity ]? and electric flux density £> at the interface between two perfectly dielectric media.

(b) Solve Laplace’s equation for the potential field in the homogeneous dielectric region between two concentric conducting spheres with radii a and b, at \ = 0 at r — b and V — Vq at r-a. Assume b>a- Find the capacitance between them.

UNIT-III

3. (a) Using Biot-Savart’s law, determine the magnetic field intensity due to an infinitely long steady straight line current.

(b) Magnetic field intensity H = 10 p aip A/m . Determine the current density and the total current in the ^ direction passing through the surface 0<p<2, 0 < 0 < 27r, z = 0.

OR

(a) Show that, in free space, the energy stored in a magnetic 1 r 2 field of flux density B is given by £ =       / B dv.

(a)  Using Biot-savart’s law, show that V

(b) The magnetic vector potential of a current distribution infree space is given by A=——azWb/m. Calculate the magnetic flux through the region2<p<3m, (p = 7r/3, 0<z<5m.

UNIT – IV

4    (a) Express differential form of Maxwell’s equation for sinusoidal time varying fields in phasor notation and derive the vectorHelmnoltz equations for E and H in a charge free (pv = 0), linear, homogeneous, conducting medium (a** 0).

(b) Show that in a good conductor, a = Where a is the attenuation factor and j5 is the phase shift constant.

(c) Determine the skin depth of copper at a frequency of 100 MHz. Assume 6 = 58 MS/m and /i = /i0 = 4ttx10~7 Him.

OR

4. (a) A uniform plane electromagnetic wave with field varying sinusoidally with time, in medium

(1) is incident normally on the surface of medium

(2) Derive the expression for the reflection and refraction co-efficients.

(b)   Show that, if medium 1 is a perfect dielectric and medium

2 is a perfect conductor, standing waves of E and // will be formed in medium 1. Discuss the phase relationship and the locations of maxima and minima of the resultant fields in medium 1 for this case.

UNIT – V

5 (a) Determine the total power radiated by a small alternating fine current element I0dl cos cot.

(a)  Discuss the causes and sources of electromagnetic interference.

OR

5 (a) Determine the radiation resistance of a small line element of length 3 cm carrying an alternating current of frequency 100 MHz. ,

(b) Discuss different control techniques to suppress electromagnetic interference.