VTU Previous Year Question Papers EC 3rd Semester
Field Theory July 2008
Note : Answer FIVE full questions, selecting atleast two question from each part.
1 a. State and explain Coulomb’s law in vector form.
b. Two point charges of magnitudes 2 me and -7 me are located at places Pi(4, 7, -5), and P2(-3, 2, -9) respectively in free space, evaluate the vector force on charge at P2. (06 Marks)
c. From Gauss Law show that V.D = pv .
2 a. Find the potentials at yA = 5m and yB = 15m due to a point charge Q = 500 pc placed at the origin. Find the potential at yA = 5m assuming zero as potential at infinity. Also obtain the potential difference between points A and B.
b. Derive an expression for the potential of co-axial cable in the dielectric space between inner and outer conductors.
c. Discuss the boundary conditions between two perfect dielectrics.
3 a. State and prove uniqueness theorem.
b. From the Gauss’s law obtain Poisson’s and Laplace’s equation.
c. Determine whether or not the following potential fields satisfy Laplace’s equation –
i) V = x2-y2+z2, ii) V = rcos(j) + z.
4 a.Using Biot – Savart law find an expression for the magnetic field of a straight filamentary conductor carrying current ‘I’ in the Z – direction.
b. Given the magnetic field H = 2r (Z + ^sin^a*, verify Stokes theorem for the portion of a cylindrical surface defined byr = 2, —<<)><^,1<Z<1.5 and for its perimeter.
c. With necessary expressions, explain scalar magnetic potential.
5 a. Find the expression for the force on a differential current carrying elements.
b. Find the normal component of the magnetic field which traverses from medium 1 to medium 2 having |4.ri = 2.5 and^r2 = 4. Given that H = -30ax + 50ay + 70az v/m.
c. Derive an expression for the self inductance of a co – axial cable.
6 a. For a closed stationary path in space linked with a changing magnetic field prove that v x e , where E is the electric field and B is the magnetic flux density.
b. Determine the frequency at which conduction current density and displacement current density are equal in a medium with a = 2xl0~4s/m ander = 81.
c. List the Maxwell’s equations in differential and integral form as applied to time varying fields.
7 a. Starting from Maxwell’s equation, derive the wave equation for a uniform plane wave traveling in free space.
b. A 300 MHz uniform plane wave propagates through fresh water for which a = 0, (j,r = 1 er = 78. Calculate i) attenuation constant ii) phase constant iii) wave length iv) intrinsic impedance.
c. Explain the skin depth. Determine the skin depth for copper with conductivity of 58 x 106 s/m at a frequency of 10 MHz.
8 a. Show that at any instant t, the magnetic and electric field in a reflected wave are out of phase by 90°.
b. With necessary expression, explain standing wave ratio (SWR).