VTU Field Theory - May 2016 Exam Question Paper

VTU Electronics and Communication Engineering (Semester 3)
Field Theory
May 2016

Total marks: --
Total time: --

INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1(a) Three point charges Q₁ = -1 μc, Q₂ = -2 μc and Q₃ = -3 μc are placed at the corners of an equilateral triangle of side 1 m. Find the magnitude of the electric field intensity at the point bisecting the joining Q₁ and Q₂.

7 M

1(b) Derive an expression for the electric field intensity due to infinite line charge.

8 M

1(c) Let

$\vec{D}=\left ( 2y^2 z-8xy \right )\hat{a}_x + \left ( 4xyz-4x^2 \right )\hat{a}_y + \left ( 2xy^2-4z \right )\hat{a}_z.$ Determine the total charge within a volume of 10^-14m³ located at P(1, -2, 3).

5 M

2(a) infinite number of charges each of Qnc are placed along x axis at x = 1, 2, 4, 8, ....... ∞. Find the electric potential and electric field intensity at a point x = 0 duw to the all charges.

6 M

2(b) Find the work done in assembling four equal point charges of 1 μc each on x and y axis at ±3m and ±4m repectively.

6 M

2(c) Derive the expression for a capacitance of a parallel plate capacitor.

8 M

3(a) Explain Poisson's and Laplace's equations.

6 M

3(b) Find

$\vec{E}$ at P(3, 1, 2) for the field of two co-axial conducting cylinders V = 50V at ρ = 2m and V = 20 V at ρ = 3m.

8 M

3(c) Using Poisson's equation obtain the expression for the potential in a p-n junction.

6 M

4(a) An infinite filament on the z-axis carries 20π mA in the

$\hat{a}_z$ direction. Three uniform cylindrical sheets are also present 400 mA/m at r = 1cm, - 250 mA/m at r = 2 cm, 400 mA/m at r = 3m. Calculate H_ϕ at r = 0.5, 1.5 and 2.5 cm in cylindrical co-ordinates.

10 M

4(b) If the vector magnetic potential at a point in a space is given as

$\vec{A}=100\rho ^{1.5}\hat{a}_z \text {wb/m,}$ find the following :

$(i)\vec{H}\ \ (ii)\text {J and show that}\oint \vec{H}.d\vec{c}=I \ \ \text{for the circular path with}\rho=1.$

10 M

5(a) A conductor 4 m long lies along the y-axis with a current of 1.0 A in the

$\hat{a}_y$ direction. Find the force on the conductor if the field in the region is

$\hat{B}=0.005 \hat{a}_z$ Tesla.

4 M

5(b) Discuss the boundary between two magnetic of different permeabilities.

8 M

5(c) A solenoid with air core has 2000 turns and a length of 5000 mm. Core radius is 40 mm. Find its inductance.

8 M

6(a) Find the frequency at which conduction current density and displacement density are equal in a medium with σ = 2×10^-4 ℧/m and ∈_r = 81.

4 M

6(b) Given

$\vec{H}=H_m e^{j(\omega t+\beta z)}\hat{a}_x \text{A/m in free space.Find}\ \vec{E}.$

6 M

6(c) Explain the concept of retarted potential. Derive the expressions for the same.

10 M

7(a) The magnetic field intensity of uniform plane wave in air is 20 A/m in

$\hat{a}_y$ direction.The wave is propagating in the

$\hat{a}_z$ direction at an angular frequency of 2×10⁹ rad/sec. Find:
(i) Phase shift constant
(ii) Wavelength
(iii) Frequency
(iv) Amplitude of electric field intensity.

8 M

7(c) The depth of pentration in a certain conducting medium is 0.1 m and the frequency of the electromagnetic wave is 1.0 Mhz. Find the conductivity of the conducting medium.

4 M

8(a) Derive the expression for transmission co-efficient and reflection co-efficient.

8 M

8(b) Define standing wave ratio. What value of S results is reflection coefficient equals ±½?

6 M

8(c) Given γ = 0.5, η₁ = 100 (Ω), η₂ = 300 (Ω). E'_{x_{1 = 100 (V/m). Calculate values for the incident, reflected waves. Also show that the average power is conserved.}}

6 M

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