University of Mumbai 2007-5th Sem B.E Electrical and Electronics Engineering Electrical Magnetic Fields & Waves Old - Question Paper
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Con. 5201-07. U CD-184
(OLD COURSE)
(3 Hours) [ Total Marks : 100 -
N.B.(1) Attempt any five questions.
(2) Assume suitable data if necessary and justify the same.
1. (a) It is required to nofd three equal point charges of + Q each in equilibrium at the corners 0
of an equilateral triangle. Calculate the point charge which will do this if placed at the centre of a triangle.
(b) A line charge of 2 nc/m lies along y-axis while surface charge densities of 0*1 x 10* 9 10 and - 0*1 x 10"9 c/m2 exist on the piane z = 3 and z = - 4m respectively
(I) Find E at a point (1,-7, 2)
(ii) Find co-ordinates of the point at which g is - Ve of the value in (I).
( 10 3 . g
2. (a) Given that Q = I "3" x J ax c ' evaluate both sides of the divergence theorem for 10
the volume of a cube 2 m on the edge, centered at the origin and edges parallel to the axis.
(b) Derive an expression for potential and electric field due to dipole and also define the 10 dipole moment.
3. (a) Find the value of electric potential at the point at which electric field is zero when point 10
charges of 3 \ic and 7 fic are located at (0, 0) and (0-5, 0) in the xy plane.
(b) The region y < 0 contains a dielectric material for which er, = 2-5, while the region y > 0 10
is characterized by er2 = 4. Let E, = - 30ax + 50ay + 70azv/m and find ;
(i) (ii) (iii) Dj (iv)P2 (v)03 .
4. (a) Derive the magnetic boundary conditions for the interlace between two magnetic materials. 10 (b) Find the vector magnetic field intensity in Cartesian coordinates at P2 (1*5, 2, 3) caused 10
by a current filament of 24A in the az direction on the z-axis and extending from :
(i) z = O to 1 = 6 (ii) z = 6 to z = 00 (iii) z = - <0 to z * .
5. (a) Derive the expression for voltage and current lr> terms of sending end voltage and 10
current for a transmission line of length /.
Hence prove that Z0 = VZoc Zsc
(b) State Maxwell's Equations for static fields. Explain how are they modified for time varying 10 electric and magnetic field.
6. (a) If Ey = E0 em ~c,) show that it a wave equation, if m is a real number. 4
(b) An area of 0*65 m2 in the Z = 0 plane encloses a filamentary conductor. 6 Find the induced voltage if
B = 0 05cos 103 *( a/g3Z j(T)-
(c) A lossy dielectric has nr = 1, er = 50 and a = 20 mho/s at 15-9 MH2, EM wave propagating 10 through this medium, find a, p, i> and x\.
7. Write short notes on any four : 20
(a) Uniqueness theorem
(b) Method of images
(c) Vector and scalar magnetic potential
(d) Electric dipole
(e) Polarization in magnetic material.
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