# VTU Previous Year Question Papers EC 4th Semester

# Field Theory December 2010

**Note: Answer any FIVE full questions.**

1 a. State and explain Coulomb’s law. Clearly indicate the unit of quantities used in the force equation.

b. State and prove the Gauss theorem.

c. Find E at P(l, 2, 3) due to Q_{3} – 5jnCat (-1, -2, -3) and Q_{2} = 1 Oj^C at (3, 5, -1).

2 a. Obtain an equation for the electric scalar potential.

b. Show that the electric field intensity is a negative of the gradient of the electric scalar potential.

c. Check whether the following potential equations are satisfying Laplace’s equation or not

i) V = 20x^{2}yz +10xy^{2}z^{2}

ii) V = 15x^{2} +10y^{2} ~25z^{2}

d. Define : i) Electric field intensity ii) Displacement flux density.

3 a. Derive Poisson’s and Laplace’s equations.

b. Derive equations of energy stored and energy density in an electrostatic field.

c. Discuss the boundary conditions between two different dielectrics.

4 a. Obtain the differential form of Ampere’s work law, in a steady magnetic field.

b. By using Biot-Savart’s law, obtain the equations of magnetic field intensity and magnetic flux density at any point on the axis of a coil.

c. Find the magnetic field intensity and the magnetic flux density at P, as shown in the figure Q4 (c).

5 a. Prove that V x E = —.

b. For a time varying field, having a capacitor, show that, the conduction current is equal to the displacement current.

c. Find the depth of penetration, when a 20 MHz signal is propagating the free space and penetrating into a conductor of conductivity cr = 5 x 10^{7} O/m.

d- Write Maxwell’s equation in,

i) Steady magnetic field.

ii) Time varying field.

6 a. State and prove the pointing vector theorem.

b. Derive the wave equation of E & H.

c. The electric field intensity at 10 km in free space from a radio station was found to be 2.2 mv/m. Calculate : i) The power density ii) The total power radiated from the station. Assume the radiation to be spherically symmetric.

7 a. Show that the uniform plane wave is transverse in nature.

b. Discuss the wave propagation in a good dielectric (absorption medium).

c. A 10 MHz signal with Ex ~ 100 mV/m is propagating in a nature of medium with e_{r}~ 1.5 and \x_{T} = 3.5. Find, i) Velocity ii) Phase constant iii) Wavelength iv) Intrinsic impedance and v)Hz.

8 a. Derive an equation for the force acting as a current element.

b. Derive an equation for the torque as a closed circuit.

c. Explain : i) Scalar magnetic potential ii) Vector magnetic potential.

d. Derive an equation for the inductance of a solenoid.