Electromagnetic Theory

Two Mark Question – Unit I to Unit V

  1. A vector field is given by the expression F=(1/r)ar in a spherical coordinates. Determine F in Cartesian form at a point x=1, y=1 & z=1 unit.
  2. Sate Divergence Theorem.
  3. State Coulomb’s law and its limitation.
  4. Write down the continuity equation and relaxation time in electrostatics.
  5. State Biot-Savart’s law.
  6. Determine the force per unit length between two long parallel wires

separated by 5cm in air and carrying currents of 40A in the same direction.

  1. Compare electric and magnetic circuits.
  2. State Lenz’s law.
  3. Find the velocity of a plane wave in a lossless medium having a relative

permittivity of 5 and relative permeability of unity.

  1. What do you understand by the term skin depth?

16 Mark Questions – Unit I to Unit V

  1. (I)Verify Stoke’s Theorem for a vector field F=r2cosø ar + Zsinøaz around the path L defined by 0 ≤ r ≤ 3; 0 ≤ ø ≤ 450 & Z=0.

(II)Write the differential length, surface & volume vector in all the three co-ordinate system.

(III)Determine the divergence, curl and Laplacian of the following vector fields: (i) P = x2yz ax + xz az

(ii) Q = ?sinØ a?+ ?2z aØ + zcosØ az

(iii) T = (1/r2)cos? ar + r sin? cosØ a?+ cos? aØ

  1. (I)A circular disc of radius ‘a’ m carries a uniform surface charge density of ρs C/m2. Find the electric field intensity and electric potential at a height ‘h’ m from the disc surface along its axis.

(II)Derive the Electric field intensity at P(-2, 0, -2.3) m due to a point charge +15nc at Q(-2,0.1,-2.5) m in air.

(III)Show that the electric field intensity in between the plates of a parallel plate capacitor is ρs/εo V/m.

  1. (I)Derive the general expression for the magnetic flux density B at any point along the axis of a long Solenoid. Sketch the variation of B from point to point along the axis.

(II)Derive the conditions at the boundary between dielectrics in the electric fields which have permittivity’s ε1ε2.

(III)Determine the force per meter length between wires A & B

separated by 5 cm in air & carrying currents of 40 Amps in the same

direction.

  1. (I)(a) A rectangular T-turn coil with mean length ‘l’ and width ‘ w’ is wound on a cylindrical drum. If the drum rotates in a uniform field with a flux density B everywhere in the positive X-direction at a constant speed of N rpm, the axis being in alignment with z-axis, develop an expression for induced emf in the coil.

b) If the flux density varies harmonically with time as given by

B = Bosin?t, establish an expression for the induced emf in the above

case.

(II)Derive the Maxwell’s equation from the first principle in both Point & Integral form.

(III)Let the internal dimensions of a co-axial capacitor be a = 1.2 cm, b= 4 cm and length = 40 cm. The homogeneous material inside the capacitor has the parameters ε = 10-11 F/m, µ = 10-5 H/m and σ = 10-5 S/m. If the electric field intensity is E = (106/ρ) cos105t aρ; V/m, find a) J; b) the conduction current Ic through the capacitor; c) the total displacement current Id through the capacitor; and d) the ratio of the amplitude of Id to IC.

  1. (i)Explain how the rate of energy transportation by means of EM waves from one point to another point can be obtained from Maxwell’s equations.

(II)In a non-magnetic medium,

E = 4 sin (2π *107t – 0.8x)ax V/m

Find

a)εr, η.

b) The time-average power carried by the wave.

c) The total power crossing 100 cm2 of plane 2x +y =5.

(III)Derive the wave equation in phasor form.

(IV)Define Brewster angle and derive its expression.