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Name _____________________________

Sept. 24, 2009

ECE 311 Exam 1 Fall 2009

Closed Text and Notes

1) Be sure you have 13 pages.

2) Write only on the question sheets. Show all your work. If you need more room for a particularproblem, use the reverse side of the same page.

3) Write neatly, if your writing is illegible then print.

4) The last 2 pages contain equations that may be of use to you.

5) This exam is worth 100 points.

6) No Calculators are allowed.

Signature_____________________________

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Problem ABET Outcome Points Score

1 10

2 10

3 10

4 (i) 10

5 10

6 (i) 12

7 (i) 10

8 (i) 10

9 (i) 10

10 (i) 8

total 100

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(10 pts) 1.

(a) Convert the vector x zA xya yza to the cylindrical coordinate system.

(b) Convert the point with spherical coordinates of (1, 45o, 45

o) to rectangular coordinates.

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(5 pts) 2. The angle between 2 ra and 2 cos 2 sina a is

a) 0ob) 30oc) 45od) 60o

e) 90o

f) 135o

g) Position dependent

h) None of the above

(5 pts) 3. The intersection of the surfaces defined by r= 5 and = 60 is a

a) a pointb) a circle

c) a straight line

d) a plane

e) a cone

f) a cylinder

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(10 pts). 4. Charge +Q is located at the origin, charge +3Q is located at (4, 0, 0) in a Cartesian coordinate

system. To keep the two charges at rest, the third charge is introduced. Which one of the

following is true?

(a)The third charge must be positive, closer to the origin than to point (4, 0, 0)(b)The third charge must be positive, closer to the (4, 0, 0) point than to the origin(c)

The third charge must be negative, closer to the origin than to point (4, 0, 0)

(d)The third charge must be negative, closer to the (4, 0, 0) point than to the origin(e) It is impossible to make the two charges at rest by introducing another charge(f)None of the above

(10 pts) 5. Which ones of the following are true? Your choice can be multiple.

(a) If 0S

sdD

, D

is 0.

(b) There is no electric charge in an air region having electric field 2 yE a .

(c)4

1

rE a

rV/m cannot be a vector denoting electric field intensity.

(d) The electric field at any point in space due to an infinitely long line charge placed along y-axis

does not have a y-component.

(e) In a static electric field, the work done by moving a point charge along a closed loop from a point

back to this point is always 0.

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(12 pts) 6. There are 2 point charges. A 1 C charge is placed at (1, 1, 0), another 1 C charge is placed at (-1,1, 0). Calculate the electric force received by a 2 C charge located at the origin.

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(10 pts) 7. An infinitely long line charge having density 1 C/m is located along the z-axis. Another infinite

sheet of charge having density 2 C/m2is positioned at y= 4. Find the electric field at point (0, 8,

0) in the rectangular coordinate system.

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(10 pts) 8. The electric potential at the origin is 1 V, and that at point (3, 4, 5) is 8 V when the referencepoint of the voltage is placed at infinity. Now the reference point is moved to the origin, calculate theelectric potential at point (3, 4, 5).

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(10 pts) 9. There are three concentric spherical shells having radius a, b, and crespectively as shown in thefigure below. Charges are uniformly distributed on the three shells. The charge density on the innermost shell(r= a) is /a

2(in Coulombs/meter

2). On the middle shell (r= b) the charge density is /b

2(C/m

2), and on

the outmost shell (r = c) the charge density is /c2(C/m

2).

(a)Calculate the electric field in the region of b r c.

(b)Calculate the electric field in the region of r > c.

a

b

c

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(8 pts) 10. A solid sphere of radius 2 m is located at the origin as shown in the figure below. The chargedensity inside the sphere is 1 (C/m

3). The charge density outside of the sphere is zero. Assuming that the

electric potential at infinity is zero, calculate the electric potential due to the solid sphere at any point outsideof the sphere, i.e. in the region of r> 2 m.

2 m

V = 1 C/m3

x

y

z

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