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Code No: NR211003

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II B.Tech I Semester Supplimentary Examinations, May/Jun 2009 ELECTROMAGNETIC THEORY ( Common to Electronics & Instrumentation Engineering and Electronics & Control Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

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1. (a) By applying Gauss’s law to an isolated point charge q, show that Coulomb’s law can be deduced from Guass’ law. [8M]

(b) Charge is uniformly distributed in the region −2 2. [8M]

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2. (a) A parallel plate capacitor consists of two plates each 30cm×30cm spaced 2 mm apart two dielectrics each 1mm thick having relative permittivities of 3 and 5. If the potential difference between the plates is 5000V, Calculate the voltage gradient in each dielectric. [10M] (b) A parallel plate capacitor is composed of thin metal sheets 25cm×25cm with glass as dielectric 6.25mm thick in between with relative dielectric constant=6. Find the capacitance. [6M]

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3. (a) A scalar function φ is given by the expression φ =x2 +y2 +z2 ,determine the vector F=∇φ and also ∇xF. (b) State and explain Ampere’s force Law. 4. (a) Explain the inconsistency of Ampere’s law in time-varying fields.

[8M]

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(b) The electric vector E of an electromagnetic wave in free space is given by the expressions Ex = Ez = 0 ; Ey = A cos ω(t - z/c). Using Maxwell’s equations for free-space conditions, determine expressions for the components of the magnetic vector H. [8M]

5. (a) Show that the intrinsic impedance of the free space is 120 π Ohms.

[6M]

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(b) A lossy dielectric is characterized by µr = 4, εr = 2.5, σ = 10−3 mhos/m. at ˆX V/m. find α, β, ν, λ, η and H . [10M] 10 MHz. Let E = 20e−γz a

6. (a) What is an isotropic and homogeneous medium?

[6M]

(b) For wave propagating in a good conductor find the velocity of the wave in the conductor and the intrinsic impedance of the conductor. [10M]

7. (a) Derive expressions for reflection and transmission coefficients for plane electromagnetic waves normally incident on a plane boundary separating two dielectric media. [8M] (b) Define the terms ‘Brewster Angle’ and ‘Critical Angle’. What is significance of these angles? [8M] 1 of 2

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Code No: NR211003 8. (a) Discuss the significance and applications of Poynting Theorem.

[8M]

(b) Explain the utility of Poynting vector. If the peak poynting vector in free space is 10w/m2 find the amplitudes of electric and magnetic fields. [8M]

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