# Field Theory July 2008

Note : Answer FIVE full questions, selecting atleast two question from each part.

PART-A

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.

PART-B

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).