University of Mumbai 2007-5th Sem B.E Electrical and Electronics Engineering Electrical Magnetic Fields & Waves - exam paper
( 3 Hours) [Total Marks : 100
N.B. (1) Question No. 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Figures to the right indicate full marks.
(4) Assume suitable data whenever required.
(5) Vector notation should be used whenever necessary.
r -m . A ( (d
1. Attempt any four of the followings 20
(a) Explain the concept of conservative nature of electric field. J --
(b) Obtain the point form of continuity equation
(c) Explain method of images
(d) Explain the concept of scalar and vector magnetic potential
(e) Define the following term :
M. Zo. Yr
2. (a) The circular region, p < a, z = 0, carries a uniform surface charge density p#. Find E at 10
( 0, 0, h), h > 0.
(b) Evaluate both sides of the divergence theorem for the rogion r < 2 if kj
G = 5r sin20 cos2 $ ar .
3. (a) The volume in cylindrical coordinates between r = 2 m and r = 4 m contains a uniform 10
charge density pv (c/m3). Find D in the regions using Gauss's taw.
(b) A square of side 1 m has a point charge Q, = 1 pc at the upper right corner, a point charge jo Q2 = - 10 pc at the iower right corner and a line distribution of charge p,= 10 pc/m along the left edge Find V at point P at the center of the square.
4. (a) The region y < 0 contains a dielectric material for which <=R1 = 2-5, while the region -jq
y > 0 is characterized by * 4. Let E! = 30ax + 50ay + 70az v/m, and find ;
(a) (b) D* (c) D;, <d) P2 (e)0* .
(b) A filamentary current of 10 A is directed in from infinity to the origin on the positive x-axis 10
and then back out to infinity afong the y-axis. Use the Biot-Savart law to find H at P {0, 0, 1).
5. {a) Discuss the phenomenon of polarization in dielectric medium. Discuss how it gives rise to
to bond charge densities.
(b) Two circular coils arc located at the z * o plane and z = 5 m plane, centered about the z* -jq axis. The first coil having a radius of 1 m carries a current of 10 Amp. The second coif having a radius of 0-5 m carries a current of 20 Amp. Calculate the magnetic field intensity
H at (0. 0, 2-5 m).
6. (a) Give the general set of Maxwells Equations in point form. Derive the set of Maxwell's 10
Equations for static fields and harmonically time varying fields.
(b) The Electric field intensity of a 300 MHz uniform plane wave in free space is given as 10
E, =(20+J50) (ax 4 2ay)e|pz v/m,
(i) Find w, v and p.
(ii) Find E at t * 1 ns, z = 10 cm.
(iii) What is | ?
7. (a) Starting with Maxwells Equations obtain vector wave equation for lossy dielectric. Solve 12
It by considering that E has only y-component and the wave is travelling in x-direction.
Hence obtain an Expression for the complex intrinsic impedance.
(b) The transmitting antenna located at the origin of co-ordinate system produces the electric g
field intensity E(r,t) = ar V0 ' cos o>(t -J)(v/m) and the magnetic field ol this antenna
iv i V sinO ,, r/, measured in A/m is H(r,t) = a$ cos a> (t ~/q) where'C is the velocity of light.
nalmitata tha nnvntinn vnntnr the averane oower radiated from this antenna.
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| Earning: Approval pending. |
