SPPU Electrical Engineering (Semester 7)
Electromagnetic Fields
December 2016
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary


Solve any one question fromQ.1(a,b) and Q.2(a,b)
1(a) Obatin the expression for E and D due to infinite line charge ρ1 C/m using Gauss's law.
6 M
1(b) A current distribution gives rise to vector magnetic potential \(\bar{A}= x^2y\hat{a}_x+y^2\hat{a}y-4xyz\hat{a}_z Wb| m. \)/ Calculate B at (1, 2-5).
4 M

2(a) Find the energy stored in free space for the given 2 < r < 3mm, 0<θ90°, 0<φ<90°, given the potential field \[V=\frac{200}{r}V.\]
6 M
2(b) Derive Poisson's equation \(\nabla^2 V=-\frac{\rho _v}{\varepsilon } \)/ from Gauss's law. Explain its physical significance.
4 M

Solve any one question fromQ.3(a,b) and Q.4(a,b)
3(a) Obtain the H (magnetic field intensity) due to a finite long straight conductor carrying current I at any point P using Biot Savart's law.
6 M
3(b) Two point charge Q1=3nC and Q2=-2nC are placed at (0,0,0) and (0,0-1) respectively.Assuming zero potential at infinity, find the potential at (0,1,0).
4 M

4(a) Derive an expression for the point form Ampere's circuital law, \[\nabla\times \bar{H}=\bar{J}\]
6 M
4(b) If \( \bar{J}=\frac{100}{\rho ^2}\hat{a}_p\ A/m^2,\)/ find the total current I passing through surface defined by ρ=2,0
4 M

Solve any one question fromQ.5(a,b) and Q.6(a,b)
5(a) Region 1 described by 3x+4y≥10, is free space, where as region 2 described by 3x+4y≤10, is a magnetic material for which μ=μ0. Assuming that the boundary between the material and free space is current free, find \[\bar{B}_2\ \text{if}\ \bar{B}_1=0.1\hat{a}_x+0.4\hat{a}_y+0.2\hat{a}_z Wb|m^2\]
8 M
5(b) Explain the concept of magnetization and permeability.
8 M

6(a) Derive an expression for energy in magnetostatic field.
8 M
6(b) The point charge Q=18nC has velocity of 5×106m/s in the direction \(\hat{a}_v=0.60\hat{a}_x+0.75\hat{a}_y+0.30\hat{a}_z. \)/ Calculate the magnitude of force exerted on charge by the field.
i) \(\bar{B}=-3\hat{a}_x+4\hat{a}_y+6\hat{a}_zmT; \)/
ii) \( \bar{E}=-3\hat{a}_x+4\hat{a}_y+6\hat{a}_z KV|m;\)/
iii) B and E acting together
8 M

Solve any one question fromQ.7(a,b) and Q.8(a,b)
7(a) State Lenz's law. Using Faraday's law, derive and expression for transformer emf.
8 M
7(b) Find the amplitude of the displacement current density in a metalic conductor at \( 60Hz\ \text{if}\ \varepsilon =\varepsilon _0,\mu =\mu _0,\sigma =5.8\times 10^{-7} \)/. S/m and \[\bar{J}= \sin \left ( 377t-117.1z \right )\hat{a}_x MA|m^2\]
8 M

8(a) Write Maxwell's equation in point form for static electromagnetic fields and time varying fields.
8 M
8(b) Explain motional electromotive force.
8 M

Solve any one question fromQ.9(a,b) and Q.10(a,b)
9(a) What is poynting vector? What is its significance? Derive the expression of Poynting vector?
10 M
9(b) Define uniform plane wave. Explain the significance of propagation constant and attenuation constant with respect to uniform plane wave.
8 M

10(a) State and explain Maxwell's equation in phasor form for time harmonic electromagnetic fields in a linear, isotropic and homogenous medium.
10 M
10(b) Write the wave equations in phasor for for conductor. Explain skin effect.
8 M



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