**GTU question papers**

**GUJARAT TECHNOLOGICAL UNIVERSITY**

**B.E. Sem-V****th ****Examination December 2010**

**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.**

**Q.1 (a) **Answer the following in brief **08**

**(i) **‘The divergence of the curl of a vector is zero’-Justify the statement with one example.

**(ii) **Find the ay dot aɸ and ax dot aθ

**(iii) **Given 60 μC point charge located at the origin, find the total electric flux passing through that portion of the sphere r=26 cm bounded by 0˂θ˂π/2 and 0˂ɸ˂π/2.

**(iv) **For a coaxial cable find the electric field density inside the inner core, in between inner and outer core and outside the cable.

**(b) **Answer the following

**(i) **What is Gradient? with help of gradient prove that E= – V

**(ii) **Find the volume charge density that is associated with D = ρz2 sin2ɸ

ap + ρz2 sinɸcosɸ aɸ + ρ2z sin2ɸ az c/m2

**Q.2 (a) **Derive the electric field intensity and electric field density due to an infinite and uniform line charge density.

** ****(b) **In the space, a line charge ρL=80 nC/m lies along the entire Z-axis, while point charge of 100 nC each are located at (1,0,0) and (0,1,0). Find the potential difference VPQ given P (2,1,0) and Q (3,2,5).** **

**OR**

**(b) **Given the flux density D = (2cosθ/r3) ar + (sinθ/r3) aθ c/m2, evaluate both sides of the divergence theorem for the region defined by 1˂ r ˂ 2 , 0 ˂ θ ˂ π/2 , 0˂ ɸ˂ π/2

** ****Q.3 (a) **Describe the boundary condition between free space and conductor. What is an importance of boundary condition?

** ****(b) **Write Maxwell’s equations in point form and explain physical significance of equations.** **

**OR**

**Q.3 (a) **Derive Poisson’s and Laplace’s equations and states their applications. ** **

**(b) **Write Maxwell’s equations in integral form and explain their physical significance.

** ****Q.4 (a) **State and explain Ampere’s circuital law. Find the magnetic field intensity due to long straight conductor using Ampere’s circuital law.

** ****(b) **A charge of 10 nC is moving with a velocity of 1 (-0.5 ax + ay -0.71 az) m/s.

Determine the force exerted on the test charge when

(i) a magnetic induction B = ( ax + 2ay + 3 az) mWb/m2 is applied

(ii) an electric field E = (3ax + 2ay + az) kV/m is applied.

(iii) When B and E given above are applied simultaneously.

**OR**

**Q.4 (a) **What is curl? With help of curl meter explain the physical interpretation of curl and state its applications.

** ****(b) **A filamentary current of 10 A is directed in from infinity to the origin on the positive x axis, and then back to infinity along the positive y axis. Use the Biot- Savart law to find H at P (0,0,1)

**Q.5 (a) **Define and explain the following terms:

(i) Magnetization (ii) Polarization

(iii) Skin effect and (iv) Standing wave ratio

** **

**(b) **Write short note on:

(i) Wave motion in free space

(ii) Magnetic boundary condition

** **

**OR**

**Q.5 (a) **Define and explain the following terms:

(i) Poynting Vector (ii) The scalar and Vector magnetic potential

(iii)Hall effect (iv) Retarded Potential

** ****(b) **(i) Transform the 5ax vector to spherical coordinate at A(x = 2,y = 3, z = -1).

(ii) Given V = (10/r2 ) sinθcosɸ, Find the electric flux density at (2, π/2,0)

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