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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 Hϕ 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'x1 = 100 (V/m). Calculate values for the incident, reflected waves. Also show that the average power is conserved.
6 M

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