Download GTU BE/B.Tech 2018 Winter 5th Sem Old 151002 Engineering Electromagnetics Question Paper

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GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER-V (OLD) EXAMINATION - WINTER 2018

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Subject Code:151002 Date: 16/11/2018

Subject Name: Engineering Electromagnetics

Time: 10:30 AM TO 01:00 PM Total Marks: 70

Instructions:

1. Attempt all questions.

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2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

Q.1 (a) Explain the concept of dot product and vector product with the help of proper equations and vector diagrams. 07

Q.1 (b) State Coulomb’s law. Derive the expression for following: 07

1. Scalar & Vector form of Coulomb’s law,

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2. Electric field intensity.

Q.2 (a) What do you mean by boundary conditions? Derive the boundary conditions at the interface between two dielectric materials with permittivities e₁ and e₂. 07

Q.2 (b) Write down point and integral forms of all four Maxwell’s equations for steady & time-varying electro-magnetic fields. 07

OR

Q.3 (a) An infinitely long coaxial cable is carrying current I by the inner conductor of radius ‘a’ and —I by the outer conductor of radii ‘b’ and ‘c’, where c>b. Derive the expressions for H at (i) ?c. 07

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Q.3 (b) Using del operator, explain the following in brief: 07

1. Gradient of a scalar
2. Curl of a vector

Q.4 (a) Write a detailed note on the divergence & its physical interpretation. 07

OR

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Q.4 (b) Derive the expression for the following: 07

1. The divergence theorem
2. Stoke’s theorem

Q.5 (a) Illustrate the concept of skin depth and skin effect in good conductors. Derive 07

1. Maxwell’s 1^st equation for electrostatics

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2. Maxwell’s 3^rd equation for electrostatics.

Q.5 (b) Given the potential field V=2x²y - 5z, and a point P(-4, 3, 6), find following at point P : the potential V, the electric field intensity E, the direction of E, the electric flux density D, and the volume charge density ?_v. 07

OR

Q.1 (a) Derive 07

1. Lorentz force equation

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2. Point form of Ohm’s law.

Q.1 (b) Three infinite uniform sheets of charges are located in the free space as follows: 3nC/m² at z=-4, 6 nC/m² at z= 1, and -8 nC/m² at z = 4. Determine E at the point P(2, 5, -5) & (0, 2, -3). 07

Q.2 (a) A current filament carrying 15 A in the a_z direction lies along the entire z axis. Find H in rectangular coordinates at: (i) P(v2, 0, 4). 07

Q.2 (b) Find the magnitude of current density in a sample of silver for which s = 6.17 x 10⁷ S/m and µ_e = 0.0056 m²/V-s if: (a) the drift velocity is 1.5 µm/s; (b) the electric field intensity is 1 mV/m; (c) the sample is a cube 2.5 mm on a side having a voltage of 0.4 mV between opposite faces; (d) the sample is a cube 2.5 mm on a side carrying a total current of 0.5 A. 07

OR

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Q.3 (a) Determine an expression for the volume charge density associated with each of the following D fields: 07

1. D = 4xy/z a_x + 2x²/z a_y — 2x²y/z² a_z;
2. D = z sinf a_? + z cosf a_f + ? sinf a_z;

Q.3 (b) A slab of dielectric material has a relative dielectric constant of 3.8 and contains a uniform electric flux density of 8 nC/m². If the material is lossless, find: (a) E; (b) P; (c) the average number of dipoles per cubic meter if the average dipole moment is 10^-29 C-m. 07

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