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Unformatted text preview: .h powoam DO NOT BEGIN THIS EXAM UNTIL TOLD TO START Name:
Student Number:
Instructor:
ECE 2317
Applied Electricity and Magnetism
Exam 1 February 16, 2002 . This exam is closed book and closed notes. A calculator and one crib sheet (one 8.5” X 11” piece of paper) are allowed. . Show all of your work. No credit will be given if the work required to obtain the solutions is not shown. . Perform all your work on the paper provided. . Write neatly. You will not be given credit for work that is not easily legible. . Leave answers in terms of the parameters given in the problem.
. Show units in all of your final answers. . Circle your ﬁnal answers. If you have any questions, ask the instructors. You will not be given
credit for work that is based on a wrong assumption. . You will have a total of 90 minutes to work the entire exam. l25 Prob. 1 /25 Prob. 3 /25 Prob. 2 /25 Prob. 4 TABLE OF INTEGRALS TABLE OF COORDINATE SYSTEM FORMULAS x=pcos¢ ii=sin600s¢=x/r
y=psin¢ f‘j)=sin6'sin¢=y/r
2:2 f~2=cos0=zlr x=rsin0cos¢
y =rsin05in¢
z=rcos¢9 P=Jx2+y2
¢=tan"(y/x)
2:2 p=rsin0
z=rcost9 Problem 1 (25 pts) A point charge having q = 1 [C] is at the origin. Find the vector force on this point charge due to
a line segment of uniform charge density ,0,0 [C/m] that is parallel to the x axis as shown below. The line segment has length L and is located at a height h above the x axis. I‘M
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.4 26/ W2“ *F“ L Problem 2 (25 pts) A circular disk of radius a centered at the coordinate origin, and lying in the xy plane, has a surface charge density p5: —(x2 + y 2“32) [C/m2.] a (a) Find the total charge on the disk. 3 . X rgzgfagtz
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5:3:(Xr2 +9 ‘74,?13“); P [Ofﬁ/C/e/ = ZW—ﬂ (912+32>3/Z(:>‘Ci€[ a.
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Totalcharge= ._____[C] 1 917 [/Q /‘ @22—49) i]
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(b)Findtheelectn;f1eldat(0,0,3). _ EC) L‘ = F g ) E, [if 2 32 ff ROOM FOR EXTRA WORK Problem 3 (25 pts) A surface charge density p: = ,030 cos¢ sm 6 [C/mz], where p30 is a constant, exists on the portion 0 < 0 < %, 0 < 4) <3? of a sphere of radius a as shown. Find the total charge on this part of the sphere. Total charge = + __ [C] ROOM FOR EXTRA WORK Problem 4 (25 pts) A point electrode is at the origin inside a large tank of saltwater. The electrode injects a total
current of 10 [A], which spreads equally in all directions. This produces a current density vector
in space that is described in spherical coordinates by ' J=f( 1°2][A/m2] 47rr Calculate the total current I that crosses the circular area S shown below, ﬂowing in the upward direction. Do this by performing an integration in cylindrical coordinates, over the area of the
circle. The circle lies in a plane that is parallel to the xy plane, and is centered on the z axis. The radius
of the circle is a, and it lies at a height h above the xy plane. 2 4(1" 3“ : r
— Lrnl'y electrode Total current = [A] 30 5» I l ROOM FOR EXTRA WORK II
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