# UPTU Previous Year Exam Papers

# BE 4th Semester

# Engineering Electromagnet 2006-07

**Note:-****Attempt all questions.**

**All questions carry equal marks**

**1 Attempt any four of the following : **

(a) If A = a a_{x} + 2a_{y} + 10a_{z} and B = 4aa_{x} + Sa_{y} -2aa_{z} 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 a_{x} + x^{z}z a_{y} + z a_{z}.

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

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

(i) £/ = <?-^{z}sin2xcosx^{2}j and (ii) p^{2}zcos2(|).

(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~^{5}C 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 = (3x^{2} + y)a_{x} +xa_{y} V/m, find out the potential difference between two point (0, 0) and (3, 2).

(d) Given the potential V =— sinG cos<|), find the I^{2}’‘)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 x^{2} + y^{2} = 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 a_{x} 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 =-2a_{r}+ 6a_{v} +4a_{7} Aim in regionx y xy – x – 2 < 0 where [ii = 5 n_{0}. Calculate

(1) MI ^{md} 2?i

(2) ^{A}y, and g_{2} 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 cm^{2} and plate separation of 3 mm has a voltage 50 sin 10^{3} + V applied to its plates. Calculate the displacement current assuming s = 2s_{0}.

(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-^{ax}coslwt–x)a_{y} Aim Determine E and a.

(c) What is Poynting vector ? In free space (z < 0) a plane wave with H = 10 cos [10^{11} t-fiz)a_{x} mAlm is incident normally on a lossless medium (s = 2 Sq n = 10n_{0} j in region i > 0 • Determine thereflected wave u j? and transmitted waveH_{t}, 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 = ^{Z}0

where Z_{o} is the characteristic impedance and / is the length of transmission line

(c) Discuss about Smith chart.