ELECTROMAGNETIC FIELD THEORY

ELECTROMAGNETIC FIELD THEORY
SEM-IV, 2012-13
B.TECH
UTTARAKHAND TECHNICAL UNIVERSITY
(UTU)

Time: 3 hours

Total Marks: 100

Attempt any four questions:

1. Points P and Q are located at (0, 2, 4) and (-3, 1, 5). Calculate:
   (i) The position vector P
   (ii) The distance vector from P to Q
2. State and explain
   (i) Divergence Theorem
   (ii) Stokes' Theorem
3. State and explain Gauss's Law in differential form and explain what do you mean by 
   
   
4. Express vector
   B = 10ar/r + rcosɵa_ɵ + a_ɸ in Cartesian. Find B (-3, 4 ,0)
5. For a scalar field V, shown that =0; that is, the curl of the gradient of any scalar field vanishes.
   
   
6. Given in cylindrical co-ordinates. Verify divergence theorem for the volume enclosed by r=2, z = 0 to 10.

Attempt any four questions:

1. Explain convection current and conduction current. Derive Ohm's law in point form.
2. Derive boundary condition for static electric fields in the general form across a common boundary separated by two different perfect dielectric media.
3. What is the Laplace's Equation in two dimensions?
4. Derive Poisson's Equations from fundamentals.
5. What do you mean by Duality? Are J and D fields are dual?
6. Three point charges 3, 4 and 5 coulomb are situated in free space at three corners of an equilateral triangle with sides 5 cm. Find the energy density due to electric field in the triangle.

Attempt any two questions:

1. Define Biot Savart's Law and Ampere Law. A long straight conductors cross section with
   
    radius a has a magnetic field strength within the conductor (r < a) and
   
   for (r >a). Find j in both the regions.
2. Explain boundary conditions in magnetostatic field.
3. Explain the concept of
   (i) Scalar magnetic potential
   (ii) Magnetic vector potential

Attempt any two questions:

1. State and explain the poynting theorem.
2. How the wave propagation takes place in dispersive medium? Light is incident from air to glass at Brewster's angle. Determine the incident and transmitted angles.
3. Write the differential form of Maxwell's equations. Are all four Maxwell's equation independent? - Explain.

Attempt any two questions:

1. Derive transmission line differential equation. Derive the condition for lossless transmission.
2. A 50 lossless transmission line is terminated by a load impedance Z_L = (50 – J75)Ω. If the incident power is 100 mW, find the power dissipated by the load.
3. Define any four from the following:
   (i) Propagation Constant
   (ii) Matched transmission line
   (iii) Voltage reflection coefficient
   (iv) Standing wave ratio
   (v) Single Stub Matching.

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