GUJARAT TECHNOLOGICAL UNIVERSITY
B.E. Sem-Vth Examination December 2010
Subject code: 151002
Subject Name: Engineering Electromagnetics
Date: 15 /12 /2010 Time: 03.00 pm – 05.30 pm
Total Marks: 70
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
|
|
Q.1 (a) Answer the following in brief
- ‘The divergence of the curl of a vector is zero’-Justify the statement with one example.
- Find the ay dot aɸ and ax dot aθ
- 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.
- For a coaxial cable find the electric field density inside the inner core, in between inner and outer core and outside the cable.
|
08 |
(b) Answer the following
- What is Gradient? with help of gradient prove that E= – V
- Find the volume charge density that is associated with D = ρz2 sin2ɸ ap + ρz2 sinɸcosɸ aɸ + ρ2z sin2ɸ az c/m2
|
06 |
| Q.2 (a) Derive the electric field intensity and electric field density due to an infinite and uniform line charge density. |
07 |
| (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).
|
07 |
| 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 |
07 |
| Q.3 (a) Describe the boundary condition between free space and conductor. What is an importance of boundary condition? |
07 |
| (b) Write Maxwell’s equations in point form and explain physical significance of equations. |
07 |
| OR
Q.3 (a) Derive Poisson’s and Laplace’s equations and states their applications. |
07 |
| (b) Write Maxwell’s equations in integral form and explain their physical significance. |
07 |
| 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. |
07 |
(b) A charge of 10 nC is moving with a velocity of 107(-0.5 ax + ay -0.71 az) m/s. Determine the force exerted on the test charge when
- a magnetic induction B = ( ax + 2ay + 3 az) mWb/m2 is applied
- an electric field E = (3ax + 2ay + az) kV/m is applied.
- When B and E given above are applied simultaneously.
|
07 |
| OR
Q.4 (a) What is curl? With help of curl meter explain the physical interpretation of curl and state its applications. |
07 |
| (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) |
07 |
Q.5 (a) Define and explain the following terms:
- Magnetization
- Polarization
- Skin effect and
- Standing wave ratio
|
07 |
(b) Write short note on:
- Wave motion in free space
- Magnetic boundary condition
|
07 |
| Or
Q.5 (a) Define and explain the following terms:
- Poynting Vector
- The scalar and Vector magnetic potential
- Hall effect
- Retarded Potential
|
07 |
| (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) |
07 |