**GTU Last yaer question papers**

**GUJARAT TECHNOLOGICAL UNIVERSITY**

**B. E. Sem. – V – Examination – June- 2011**

**Subject code: 151002**

**Subject Name: Engineering Electromagnetics**

** **

**Instructions:**

**1. Attempt all questions.**

**2. Make suitable assumptions wherever necessary.**

**3. Figures to the right indicate full marks.**

**4. The symbols have the usual meaning.**

**Q.1 (a) **Define electric field intensity. Derive the expression for the intensity of electric field due a line charge along the Z direction with uniform charge density ρL c/m using Coulomb’s law and verify the same using Gauss’s law.

** ****(b) **Prove the following relations from the fundamental principle of electromagnetic theory :

(i)

*a*

*l*

*R*

ñ

= ohms

(ii) *F *= *Q*(*E *+ *v *× *B*)

** ****Q.2 (a) **What is an electric dipole?Derive the expression for the potential and electric field intensity due to a dipole at distances very large from the origin compared to the spacing d between the charges +Q and – Q .

** ****(b) **Given the Potential field in cylindrical coordinates V=1000 Φ+50 Volts.Calculate the value at P(0.4,30°,1) in air of (i)E (ii)D

(iii) ρv (iv) Energy density

** **

**OR**

**(b) **Given that ñ ñ *D a *4 10 3 = C/m2 in cylindrical coordinates. Evaluate both sides of the divergence theorem for the volume enclosed by ρ = 1m , ρ = 2m, z = 0 and z =10m

** ****Q.3 (a) **Assuming the potential function V varies as a function of ρ in cylindrical coordinates systems ,obtain the solution of Laplace equation and deduce the value of capacitance of a coaxial capacitor

** ****(b) **Curl free vector is an irrotational field, which is a conservative fieldalso.Justify

**(c) E **and **F **are vector fields given by **E **= 2xax + ay + yz az and

**F **= xy ax -y2ay+ xyz az .Determine

(a) | **E **| a t (l, 2, 3)

(b) The component of **E **along **F **at (1, 2, 3)

(c) A vector perpendicular to both **E **and **F **at (0, 1, – 3) whose magnitude is unity

**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.

(i)Deduce the expressions for H at

i)ρ < a (ii) a <ρ < b (iii) b < ρ < c (iv) ρ > c.Sketch the plot of H as a function of radius.(ii) Find the inductance of the coaxial cable

**(b) **Do as directed

(i) **D **= 8*ρ *sin *φ ***a***ρ *+ 4*ρ *cos *φ ***a***φ *C*/*m2. Find div **D**

(ii) Find the laplacian of the scalar *V e x y **z *sin 2 cosh − = .

** ****Q.4 (a) **Using Gauss’s law explain the concept of divergence. Prove Divergence theorem. Obtain Maxwell’s first equation

** ****(b) **(i) Express the vector field ( ) ( ) 2 2 1

*x y **D *= *x *+ *y xa *+ *ya *− in cylindrical components . Evaluate D at the point P ( 2, 60 , 5) 0 ñ = ö = *z *= . Express the result in cylindrical and Cartesian components.

(ii) Find ∇× *A *for the vector field è *A *= 10sinè*a *in spherical coordinates at P(2,Π/2,0).

** ****OR**

**Q.4 (a) **Deduce the boundary conditions with necessary derivations (i)at the interface between two dielectric materials with permittivities ε1 and ε2 and (ii) at the interface between two magnetic materials with permeabilities μ1 and μ2

** ****(b) **A circuit has 2000 turns enclosing a magnetic circuit of 30 sq cm in section.A current of 5A in the circuit produces a field of flux density 1 wb/cm2 and when the current is doubled, the flux density increases by 50%.Determine the value of the inductance of the circuit for the current varying between 5A and 10A.Also find the induced emf when the current increases from 5A to 10A in

0.1sec.

**Q.5 (a) **Using Faraday’s law and the concept of displacement current density, Ampere’s circuital law, divergence theorem, obtain all Maxwell’s equations for time varying fields in point and integral forms .Derive the necessary equations.

** ****(b) **A wave propagating in a lossless dielectric has the components *E t z a V m **x *500cos(10 ) / 7 = − â and *y **H *1.1cos(10 *t z*)*a *7 = − â A/m. If the wave is travelling with the velocity of υ =0.5C,find(i) μr (ii) εr (iii)β (iv) λ

(v) η

** ****OR**

**Q.5 (a) **State and prove Poynting theorem relating to the flow of energy at a point in space in an electromagnetic field.

** ****(b) **A certain signal generator produces a uniform plane wave in free space having a wavelength of 12 cm.When the propagates through a lossless material of unknown wavelength,its wavelength reduces to 8 cm.The E field amplitude is 50V/m and H field is 0.1 A/m. Find the generator frequency, μr, εr of unknown material..