HOME WORK:3

School:LSTCA Department: ECE

Name of the faculty member: M.I.Anwar Course No: ECE207

Course Title: Electromagnetic Field Theory

Class: B.Tech Term: Section:E6912 Batch:

Max. Marks: 7 Date of Allotment:27/3/11 Date of Submission:05/4/11

Part A

Q1: A conductor of radius a carries a uniform current with
. Show that magnetic vector potential for
is

Q2: A current distribution gives rise to a vector magnetic potential
, calculate

1. 
   at(-1,2,5)

2. The flux through the surface defined by
   

Q3: A conducting bar can slide freely over two conducting rails as shown in Figure . Calculate the induced voltage in the bar

(a) If the bar is stationed at z =1 8 cm and B = 4 cos 10⁶t a_y mWb/m²

(b) If the bar slides at a velocity u = 20a_z, m/s and B = 4a_y mWb/m²

(c) If the bar slides at a velocity u = 20a_z m/s and B = 4 cos (10⁶ t— z) a_y mWb/m²

Take right direction to be z-axis.

Q4: A magnetic core of uniform cross section 4 cm² is connected to a 120V, 60Hz generator as shown in Figure. Calculate the induced emf V₂ in the secondary coil.

5. An EM field is said to be nonexistent or not Maxwellian if it fails to satisfy Maxwell's equations and the wave equations derived from them. Which of the following fields in free space are not Maxwellian?

(a) H = cos x cos 10⁶t a_x

(b) E = 100 cos cot ax

(c) D = e^-10ysin(10⁵ - 10y) az

(d) B = 0.4 sin 10⁴a_z

6. In free space, H = 0.1 cos (2 x10⁸t - kx) ay A/m. Calculate

(a) k, λ, and T

(b) The time t₁ it takes the wave to travel λ /8.

(c) Sketch the wave at time t₁.

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