VTU Previous Year Question Papers EC 3rd Semester
Field Theory June 2010
Note: Answer any FIVE full questions, selecting at least TWO questions from each part.
1 a. Explain the term ‘Electric field intensity’ and derive the expression for field due to an infinite line of charge.
b. Given D = 5rar c/m , prove divergence theorem for a shell region enclosed by spherical surfaces at r = a and r = b (b>a) and centered at the origin.
2 a. Prove that the energy density in an electrostatic field is given by-e E J/m b. Given V = 2x2y-5z at point P(-4, 3, 6). Find the potential, electric field intensity and volume charge density.
c. Derive the boundary conditions for E and D between two dielectrics.
3 a. State and prove uniqueness theorem.
b. Derive the expression for capacitance of a coaxial cable using Laplace’s equation.
4 a. State and explain Biot-Savart law for a small differential current element.
b. Derive the expression for magnetic flux density on the axis of a circular loop of radius ‘a’ carrying current I using Biot Savart law.
c. Vector magnetic potential in free space is given by A = 100e] 5az Wb/m. Find the magnetic field intensity and current density and hence prove Ampere’s circuital law for p = 1.
5 a. Deduce the expression for inductance of a toroidal coil having N turns and carrying a current of I amps.
b- A point charge Q ~ 18 nC has a velocity of 5xl06m/s in the direction a = 0.6ax + 0.75ay + 0.3az. Calculate the magnitude of the force exerted on the charge by the
c. field B = -3ax + 4ay + 6az mT.
A sq. loop carrying 2 mA current is placed in the field of an infinite filament carrying current of 15 Amp as shown, fig. Q5 (c). Find the force exerted on the sq.loop.
6 a. What do you mean by displacement current and equation of continuity? Derive Maxwell’s I equation fro Ampere’s circuital law.
b. Write Maxwell’s equations in point form and integral form.
c. A 9.375 GHz uniform plane wave is propagating in polyethylene (<=r=2.26). If the y amplitude of the E is 500 V/m and the material is assumed to be lossless, find
i) Phase constant ii) Wavelength iii) Velocity of propagation
iv) Intrinsic impedance v) Magnetic field intensity
7 a. What is meant by ‘uniform plane wave’? Derive the expression for UPW in free space.
b. Deduce the expressions for a and p for a wave traveling in lossy medium.
c. A 100 V/m wave of frequency 300 MHz is traveling through a lossy medium having er= 9, fir = 1 and 0-10 S/m. Find the power dissipated over a distance of 1 jam with surface area of 2 m2.
8 Write short notes on:
a. Poynting’s theorem.
b. Reflection of plane waves at normal incidence.