**RGPV Question Papers **

**Electromagnetic Theory May June 2006**

Note: Attempt any five questions.

1 (a) A sheet uniform charges p_{s} = 2nC/m^{2} is present ay plane x=3 in free space and a line charge p_{L}

=20nC/m is locked at x=1, z=4 . find magnitude of electric field intensity at p (4,5,6) .

(b) Define potential gradient and relate in to electric field intensity . Discuss the properties of

equipotential surface and conservative field .

2 (a) Derive Poisson’s and Laplace’s equation and prove that they have an unique solution .

(b) Drive and explain the equation of continuity for current .

© Find the magnitude of electric field intensity in a simple of silver having σ =6.17×10^{7}mho/m and

µ_{e}= 0.0056 m^{2}/ v-s if (i) drift velocity is 1 mm/s (ii) Current density is 10^{7}A/m .

3 (a) Discuss the nature of electric field at the interface of two dielectric materials and drive the

relevant boundary conditions.

(b) A potential is given as V=100 e^{-5x} sin by 3 y cos 4z volts . Let point p(0.1, π/12, π/24) be located at

a conductor free space boundary . At point P find the magnitude of (i) V (ii) Ē (iii) E_{n }(iv) E_{t} (v) P_{s} .

4 (a) State Ampere’s circuital law . What is the positive direction of current ? Use this law to find

Magnetic field intensity due to an infinite current sheet .

(b) A loop of wire is construed of three straight connecting (0,0,0)to (0.04,1,0.7) to (0,0,0) . A current

of 8mA is in the ā_{x} direction in the first segment . Given a uniform magnetic field B =ā_{x} -0.1ā_{z}

Wb/m^{2} . Find the torque on the loop about the origin .

5 (a) Define vector magnetic potential and derive an expression for it . relate with magnetic flux .

(b) Given a ferrite material operating in liner mode with B =0.05 t,µ_{R} =50 . Calculate magnetic

susceptibility, magnetization and magnetic field intensity.

(C) There exists a boundary between two magnetic materials at z= 0, having permittivity’s µ_{1} =4 µ_{0}

h/m for region 1, where z>0 and µ_{2} =7 µ _{0} H/m for region 2, where z<0 . For a field B_{1…………}=_{…}2a_{x}–

3a_{y} +2a_{z} mT in region 1, find tangential component of magnetic field intensity H_{t………..} in region 2

Surface density at boundary z=0 is 60a_{x}…….. a/m

6 (a) What is displacement current ? How is Maxwell’s equation modify to account for it in time varying

field?

(b) Find the amplitude of displacement current density in the air space at a point within a large

power distribution transform where

**B = 0.8 cos [1.257×10 ^{-6}(3×10^{8}t-x)]a_{y}T.**

(c) Write Maxwell’s equation integral from for time varying field and explain the interpretation .

7 (a) Tabulate the characteristics of a plane uniform electromagnetic wave in free space . A150mhz

uniform plane wave in a free space is travelling in the a_{x} …….. direction. The electric filed intensity

has a maximum aptitude of 200a_{y} + 400a_{z }v/m at p (10,30-40) at t =0.find (i) phase constant (ii)

wavelength (iii) characteristic impedance and (v) E ( x,y, z).

Given µ_{0 }=4π.10^{-7} and Є_{0}=1/36 π .10^{-9}

(b) Derive an expression for energy associated with plane electromagnetic wave and define pointing

vector. Use it to find time average power density due to uniform plane wave in perfect dielectric.

8. (a) Derive expressions for transmitted and reflected field .when a plane electromagnetic wave is

incident on on the surface of a perfect dielectric .define reflection coefficient, coefficient and

standing wave ratio and explain them.

(b) A 60 ohm distortion less transmission has a capacitance of 0.15 nF/m and attenuation on the line

is 0.01 dB/m. calculate:

(i) The line parameters, resistance, inductance and conductance per meter of the line.

(ii) The velocity of wave propagation.

(iii) Voltage at distance of 1 km with respect to sending end voltage .