Osmania University (OU) 2007 B.E Electronics
Code No. 4118/N
FACULTY OF ENGINEERING B.E. 2/4 (ECE) I Semester Suppl. Examination May/June - 2008
Subject: Electro Magnetic Theory
Time : 3 hours ] [Max. Marks : 75
Note : Answer all questions of Part-A.
Answer five questions from Part-B.
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1. Write the equation for v x A in cylindrical co-ordinates. 2
2. Write the expressions for the dirac delta function 8(r*~ ry) in cylindrical and spherical co-ordinate systems. 2
3. For a two dimensional system in which r = write the expression for
vV 2
4. A circular disk of radius R has a surface charge density that increases linearly away from the center; the constant of proportionality being k\ Determine the total charge on the disk. 2
2 3
5. A sphere of 200 mm radius contains electrical charge of density-c/m .
rSinQ
What is the total charge contained within the sphere ? 2
6. A lOOjic point charge Q] is located in a rectangular co-ordinate system at (1, 1, 1). Another point charge Q2 of 50|ic is located at (-1, 0, -2). Find the vector force on the first charge. 2
7. Find the current distribution that produces a magnetic field of the form H= K Sin x ay where K is a constant and ay is the unit vector along y-axis. 2
8. A cylindrical conductor carries a current that produces H= 3r (A/m). Determine the current density within the conductor, is the unit vector along <[>. 2
9. Express the magnetic scalar potential in an integral form and identify its units. 2
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10. A lossy dielectric has jir = 1; er = 10, cj = 20 nS/m. An electric field E=200 Sin wt az (V/m) exists in the dielectric. At what frequencies will the conduction current density and the displacement current density have equal amplitudes ? 2
11. (a) Determine by integration the volume V of a region defined in a cylindrical
co-oridinate system as 1 < r < 2m; 0 < <|> < tc/3 radians and 0 < z < lm. Sketch the appropriate figure. 6
> y *
(b) Derive the identity div(g F) = g div F + (grad g). F where F is any vector field and g is any scalar field. 5
12. (a) A circular disk of radius 3m carries a uniformly distributed charge of 450
jinc. Calculate the force on a 75|ic charge located on the axis of the disk and 4m from its center. Draw the appropriate figure. 6
(b) A point charge q is located at a distance h above an infinitely conducting plane. Find the displacement density normal to the plane. Obtain an expression for the surface charge density on the plane. 5
13. (a) Obtain an expression for the far field expansion of an infinitesimal dipole
using an appropriate expression for the charge density. 6
(b) Obtain an expression for the capacitance of an isolated sphere of radius R\ 5
14. (a) Determine the capacitance per unit length between two infinitely long
concentric conducting cylinders with the outside radius of the inner cylinder being a and the inside radius of the outer conductor being b\ 5
(b) Derive a set of solutions to Laplaces equation in cylindrical co-ordinates starting with V = k <(> where k is a constant. 6
15. (a) Obtain an expression for the magnetic field intensity H within a cylinder at
a distance r from the center carrying a current I. The radius of the wire is R and the current density is constant across the cross-section of the conductor. 5
(b) A very long thin sheet of copper having a width b meters carries a current T in the direction of its length. If the sheet is assumed to lie in the x-z plane with the z-axis along its center line, determine the magnetic field components Hx, Hy along the strip. 6
16. (a) Using the statement of amperes work law foretemental area in cylindrical
co-ordinates derive the expansion for V x H in these co-ordinates. 5
(b) Prove for parallel polarization, that
Er nm(0! -02) _
_ | + q ). The symbols have their usual meanings. 6
17. (a) Show that the displacement current through a parallel plate capacitor
connected parallel to an alternating voltage source is equal to the conduction current I. 5
(b) Using Maxwells equation, show that H must always be zero for time varying fields within a perfect conductor, 6
C- 132/500
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Attachment: |
| Earning: Approval pending. |
