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This is an assignment paper for the subject Electromagnetic Fields
( Telecommunication Engineering ), it concerns vectors in the analysis of electric and magnetic fields. The paper is pretty straight forward, direct questions and no need for references. Ideally it should be typed rather than written.

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  1. A vector field is specified by the expression:

Assuming two points in this vector field, P(1,2,-1) and Q(-2, 1, 3), find:

  1. at P; (4 Marks)
  2. Unit vector of at Q;                                                                                                              (6 Marks)
  • A unit vector directed from Q to P. (5 Marks)
  1. A point charge is located at (2,-1,3). Find the absolute potential at (1,0,1).

                                                                   (5 Marks)

  1. Determine the gradient of the scalar field: (7 Marks)
  2. A potential field is specified by the expression:in rectangular system of coordinates. For this field find the following:
  3. The Electric field intensity E; (6 Marks)
  4. The Electric flux density D; and (3 Marks)
  • The Volume charge density.                 (4 Marks)
  1. Using Divergence theorem, evaluate where   =   while S is the surface of the cube bounded by x = 0,x = 1; y = 0, y = 1; z = 0, z = 1.                                      (10 Marks)
  2. A point charge, Q = 30 nC, is located at the origin. Determine the electric flux density D at (1,3,-4) m. (10 Marks)
  3. Find the work done by a forcein giving a 1nC charge, a displacement                                                                                                                   (7 Marks)
  4. Find the unit vector specifying the direction of a force given by the expression:

(5 Marks)

  1. Point charge = 300μC located at (-1, 1, -3) m experiences a force (8 Marks)
  2. Calculate the capacitance of a parallel plate capacitor containing two dielectrics as illustrated in Figure 2. The interface of the two dielectrics is parallel to the plates of the capacitor. (12 Marks)                                            
A = 2 m2




1             1 mm


Figure 2

  1. Calculate the electric field intensity and the current density which correspond to a drift velocity of in silver. Suppose for silver and .                (8 Marks)


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