Download AKTU B-Tech 4th Sem 2014-15 Electronic Field Theory Question Paper

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EC 402(MTU)

(Following Paper ID and Roll No. to be filled in your Answer Book)

PAPER ID: 130402

Roll No.

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B. Tech.

(SEM. IV) THEORY EXAMINATION, 2014-15

ELECTRONIC FIELD THEORY

Hours]

[Total Marks: 50

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Note: Attempt all questions.

1. Attempt any four questions : 3.5×4=14

(a) Prove the vector triple product identity

A×(B×C)= B(A.C) - C(A.B).

(b) What is the physical significance of gradient, divergence and curl.

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(c) Evaluate div (curl A) if

A = (sin ? / r²) a_r + (cos? / r) a_?

(d) State Divergence theorem and Stokes's theorem.

(e) Express the vector in Cartesian coordinates

A = r a_r + sin ? a_?

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2. Verify whether following vector field is solenoidal and irrotational

A = yza_x + zxa_y + xy a_z

3. Attempt any two questions : 6×2=12

(a) Given the potential V = r sin ? cos f. Find the electric flux density D at (2, p/2, 0).

(b) Enlist the properties of conductors, dielectrics and semiconductors.

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(c) Derive the expression for capacitance of spherical capacitor using Gauss's law. A spherical capacitor has radii a= 1.5 cm and b= 4cm has an inhomogeneous dielectric of e = 10e₀ / r. Calculate the capacitance of the capacitor.

4. Attempt any two questions: 6×2=12

(a) State Biot-Savart's law. Prove that the magnetic field due to infinite conductor carrying conductor I at a distance r is H = I / (2pr)

(b) State and explain Maxwell's equations. Discuss its physical significance.

(c) Derive an expression for energy in magnetic field.

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5. Attempt any two questions: 6×2=12

(a) Derive the expression of reflection and transmission coefficients. Derive the relation between the two.

(b) State and Explain Poynting Theorem

(c) A uniform plane wave propagating in medium has

E = 2e^-az sin (10⁸t-ßz)a_y V/m.

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If a medium is characterized by e_r=1, µ_r= 10 and s= 5S/m. Find :

(i) Attenuation constant

(ii) Phase constant

(iii) Velocity of propagation

(iv) Propagation constant

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(v) Intrinsic impedance.