# Engineering Electromagnet 2006-07

Note:-Attempt all questions.

All questions carry equal marks

1 Attempt any four of the following :

(a) If A = a ax + 2ay + 10az and B = 4aax + Say -2aaz find out the value of a for which the two vectors are perpendicular.

(b) Write down the word statement of divergence theorem and Stokes theorem. Also find out the divergence and curl of the following vector : A = 2xy ax + xzz ay + z az.

(c) Express point P(-2, 6, 3) in cylindrical and spherical co-ordinates.

(d) Find the gradient of the following scalar fields :

(i)     £/ = <?-zsin2xcosx2j and (ii) p2zcos2(|).

(e) Consider differential volume dv determine the volume of the following :

(i)0<x<l, l < j < 2 > -3<z<202

(f) An infinite long line charge of uniform density Pl coulombs/cm is situated along the Z-axis. Obtain Electric field intensity due to this charge using Gauss’s law.

2.Attempt any four of the following :

(a)    Explain the term electrostatics. Two point charges with qi=2xl0~5 C and #2=-4xl0~5C are located in free space at (1, 3, -1) and (-3, 1, -2) respectively, in Cartesian co-ordinate system. Find the electric field intensity at (3, 1, -2).

(b) Four charges of 10 10 \x,C each are located in free space at (-3, 0, 0), (3, 0, 0), (0, -3, 0) and (0, 3, 0) in Cartesian co-ordinate system. Find the force on a 40 \\C located at (0, 0, +). All distances are in meters.

(c) Relate electric potential and electric field intensity. If

-» E = (3x2 + y)ax +xay V/m, find out the potential difference between two point (0, 0) and (3, 2).

(d) Given the potential V =— sinG cos<|), find the I2’‘)electric flux density at

(e) Derive the capacitance and break down voltage of parallel plate capacitor.

(f)  Use image theory to determine y and E at an

arbitrary point P(x, y, z) in the region z>0 due to a charge Q in free space at a distance d above a grounded conducting plane.

3. Attempt any two of the following :

(a) Derive Bio-Savart law for all the three possible types of current distribution. A circular loop located on x2 + y2 = 9, z = 6 carries a direct current of 10A

(b)Determine—along ax.  at (0, 0, 4). ->Derive Ampere’s circuital law. If H = 0.2 z ax for -» £ > 0 and H = 0 elsewhere verify Stokes theorem. Calculate <\$>H.de about a square path with sides d centered at (0, 0, Zj) in the y = 0 plane where

(c) Given that Hi =-2ar+ 6av +4a7 Aim in regionx y xy – x – 2 < 0 where [ii = 5 n0. Calculate

(1) MI md 2?i

(2) Ay, and g2 in region y-x-2>0 where

4.   Attempt any two of the following :

(a) Write down the word statement and mathematical form of all Maxwell’s equation in time varying form. A parallel plate capacitor with plate area of 5 cm2 and plate separation of 3 mm has a voltage 50 sin 103 + V applied to its plates. Calculate the displacement current assuming s = 2s0.

(b)   What is uniform plane wave ? A lossy dielectric has an intrinsic impedance of 200 Z 45° Q at a particular frequency. If at that frequency the plane wave propagating through the dielectric has the magnetic field component H = 10e-axcoslwt–x)ay Aim Determine E and a.

(c) What is Poynting vector ? In free space (z < 0) a plane wave with H = 10 cos [1011 t-fiz)ax mAlm is incident normally on a lossless medium (s = 2 Sq n = 10n0 j in region i > 0 • Determine thereflected wave u j? and transmitted waveHt, Et.

5. Attempt any two of the following :

(a) Describe the primary and secondary transmission line parameters. Derive transmission line equation.

(b) Find out the input impedance SWR, voltage reflection coefficient of any transmission line when it is terminated by

(1) Zl = 0

(2) Zl = Zr

(3) Zl = «)

(4) Zl = Z0

where Zo is the characteristic impedance and / is the length of transmission line

(c) Discuss about Smith chart.