Electrical IComputer I Mechatronics

Department of Electrical and Computer Engineering

Module 0404215 Electromagnetic (I) First Exam 07/11/2005 Time allowed: 1 hour

Q1 Using your own words, explain the following terms: Scalar quantity, Dot product, Orthogonal coordinate system, Divergence operator?

(6 marks)

Q2 Derive the cosine formula cos2222 BCCBA ? (Hint: use the triangle shown in Figure 1 and the dot product )

(4 marks)

Figure 1

Q3 Calculate the gradient of xyzyxM 22 and the directional derivative dldM in the

direction zyx 1243 at (2,-1,0)? (4 marks)

Q4 Determine the flux of a vector filed K(r) )(210 zrrze out of the entire surface of the cylinder ,1r 10 z . Confirm the result using the divergence theorem?

(6 marks)

======================================================================

Some useful relations:

1- A . (B C) = B . (C A) = C . (A B)

2- .Az

AAr

rArr

zr

1)(1 (Cylindrical)

3- .Az

Ay

Ax

A zyx (Cartesian)

4- AzAz

yAy

xAx (Cartesian)

A

C B

Department of Electrical and Computer Engineering

Module: Bioelectromagnetic (I) First Exam 05/11/2006 Time: 1 hour Instructor: Dr. Omar Saraereh

Q1: If zyxA 6410 and yxB 2 , find:

i) The component of A along y

ii) The magnitude of BA3

iii) A unit vector along BA 2

iv) The angle between BandA

(4 points)

Q2: If sincos rrA , evaluate dlA. around the path shown below. Confirm this using Stokes's theorem.

(10 points)

Q3: Find the directional derivative of 2cos2rzM along the direction zrA 2 and evaluate it

at (1,2

, 2)?

(6 points)

Department of Electrical and Computer Engineering

Module: Electromagnetic (I) First Exam 29/10/2006 Time allowed: 1 hour

Instructor: Dr. Omar Saraereh

Q1: Point P(-4, 2, 5) and the two vectors, zyxA 101820 and zyxB 15810 , define a triangle. i) Find a unit vector perpendicular to the triangle.

ii) Find a unit vector in the plane of the triangle and perpendicular to B . iii) Find a unit vector in the plane of the triangle that bisects the interior angle at P. (6 marks)

Q2: The following coordinates, 60and20and,50and30,4and2r identify a closed surface. a) Find the enclosed volume.

b) Find the total area of the enclosing surface. c) Find the length of the twelve edges of the surface.

d) Find the length of the longest straight line that lies entirely within the surface. (8 marks)

Q3: A vector field 3rrD exists in the region between two concentric cylindrical surfaces defined by r = 1 and r = 2, with both cylinders extending between z = 0 and z = 5. Verify the divergence theorem.

(6 marks)

================================================================

Some useful relations:

1- VzVzV

rVr

2- . Az

AArr

rAr

zr 1)(1

3- TzAz

yAy

xAx

Department of Electrical and Computer Engineering

Module: Electromagnetic (I) First Exam 30/03/2006 Time: 1 hour Instructor: Dr. Omar Saraereh

Q1: If zyxA 6410 and yxB 2 , find:

i) The component of A along y

ii) The magnitude of BA3

iii) A unit vector along BA 2

iv) The angle between BandA (25 marks)

Q2: Find the directional derivative of 2cos2rzM along the direction zrA 2 and evaluate it

at (1,2

, 2)?

(35 marks)

Q3: Verify Stokes’s theorem for the vector field sincosrB using the path and the surface of the quarter section of a circle shown below? (40 marks)

================================================================Some useful relations:

1- VzVzV

rrVr 1

2- . Az

Ay

Ax

A zyx

3- TzAz

yAy

xAx

4- )(1)()1( rzrz ArArr

zr

Az

Az

AAr

rD

Q1: Find a vector G whose magnitude is 4 and whose direction is perpendicular to both vectors E

and F , where 23 zyxE and 63 zyF . (4 marks)

Q2: Consider the object shown in Figure 1. Calculate (a) The distance BC (b) The distance CD (c) The surface area ABCD (d) The surface area ABO (e) The surface area AOFD (f) The volume ABDCFO

(12 marks)

Q3: Find the directional derivative of 2cos2rzM along the direction zrA 2 and evaluate it at

(1,2

, 2)? (6 marks)

Q4: Using your own words, explain the following terms: Orthogonal coordinate system, Gradient operator? (3 marks)

Fig. 1

-----------------------------------------------------------------------------------------------------------

VzVzV

rrVr 1

. Az

Ay

Ax

A zyx

TzAz

yAy

xAx

)(1)()1( rzrz ArArr

zr

Az

Az

AAr

rD

The Hashemite University First Exam

Faculty of Engineering Electromagnetic I Electrical Engineering Department second Sem. 07/08 Instructors: Dr. Omar Saraereh Time: 1 hour