# QP: Engineering Electromagnetics

## 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:

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

1. ‘The divergence of the curl of a vector is zero’-Justify the statement with one example.
2. Find the ay dot aɸ and ax dot aθ
3. 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.
4. For a coaxial cable find the electric field density inside the inner core, in between inner and outer core and outside the cable.
08

1. What is Gradient? with help of gradient prove that E= – V
2. 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

1. a magnetic induction B = ( ax + 2ay + 3 az) mWb/m2 is applied
2. an electric field E = (3ax + 2ay + az) kV/m is applied.
3. 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:

1. Magnetization
2. Polarization
3. Skin effect and
4. Standing wave ratio
07
(b) Write short note on:

1. Wave motion in free space
2. Magnetic boundary condition
07
Or

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

1. Poynting Vector
2. The scalar and Vector magnetic potential
3. Hall effect
4. 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