# CUSAT Previous Year Question Papers BE EE

# Electromagnetic Theory July 2009

# V Semester

**EC/EE/EI 501 Electromagnetic Theory**

**(1999 eme)**

1.(a) A vector field is given by the expression A = — a_{o} in cylindrical coordinates.

(b) Determine A in Cartesian form, at a point with jc — 1, y = 2 and z = 3 unit.

2. (a) State and explain Gauss’s Law in Electrostatics.

(b) Prove that the electric field intensity is equal to the negative gradient of the potential.

**OR**

3. (a)A vector field is given by the expression A ~ — a_{r} in spherical coordinates.

(b) Find A in Cartesian system, at a point with X = 3, y-= 2, z ~ 1 unit. Derive the expression for capacitance between coaxial cylinders.

Define the terms (i) Electric field intensity and (ii) Electric flux density.

4. (a)State and prove Stokes theorem.

(b)State Ampere’s Circuital law. Deduce the expression in differential vector form, of Ampere’s law.

**OR**

5. (a) A vector A is given by the expression A = (;e + y + az) i + (bx + y + z) j + (x + cy + z) k. Determine the constants a,b and c, if A is irrotational.

(b)Find the constant ‘a’ so that the vector A = i (x + 2y + 3z) + j (3x + y + 2z) + k{2x + 3y + az) is solenoidal.

6. (a) State and explain Biot – Savart’s law.

(b) State and explain Faraday’s Law of Electromagnetic induction.

Derive the expressions for magnetic flux density ^5^ and inductance { L) of a solenoid.

**OR**

7. (a) Derive the expression for the energy stored in a magnetic field. Write short notes on :

(i) Self and mutual inductances

(ii) Magnetic dipole

(i) Hysteresis loss.

8.(a)Derive wave equations for a conducting medium, b terms of E and in terms of H.

(b) Give Maxwell’s equations in differential form and integral form.

**OR**

9. (a) State and prove Peynting theorem.

(b) Explain briefly the properties of plane waves. Discuss the oblique incidence of waves on the surface of a perfect dielectric. Explain briefly the conditions of field continuity at boundary surfaces.

**OR**

10. (a) Discuss the oblique incidence of waves at the surface of a perfect conductor.

(b) Write short notes on the following :

(i) Characteristic impedance of transmission line

(ii) Standing wave ratio of transmission line.