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Unformatted text preview: Exam 1 PHYSICS 241 September 26, 2008 . I  "\
Firstname i Z 3 ﬂ . Lastname :gﬂl '1 g I i (2% Section # TA’s Name You must start all problems from the equations 0n the sheet.
You must show all work to get full credit for the problem. If you need more space, you may use the back of the sheet. If you do so, make sure that
you put an arrow indicating that. Do not get hung up on algebra. It is only worth a small fraction of the points. Do not Spend too much time on any one problem. The point values are listed for each
question so you can make efﬁcient use of your time. Some problems may involve several steps. Even if you can’t ﬁgure out all of them1 write
down what you do know. You can also explain in words what to do. For example “If I could
ﬁnd the time t (which I don’t know how to do) I would use it in this equation to ﬁnd blank. . .”.
The phrase “in terms of whatever variables...” certainly implies that you must use variables
given in the statement of the problem. You cannot have variables in the ﬁnal answer which
depend upon each other. For example, you can’t have a velocity 'u in your ﬁnal answer if it
can be expressed in terms of the time t which you also have in the ﬁnal answer. Lastly, you
answer can obviously include any needed constants. Please box your answers. Good Luck.
Page 2 Page 3
Page 4 Page 5 Total /100 1: Three charges are arranged at the corners of an equilateral triangle. The Xcomponent
of the net electric force on (221 IS zero. Determine Q3 in terms of Q3 (magnitude and Sign).
Calculate/ explain. 15 points. ‘ Q 3 0m Mimi armta (,1 195m (3 {A + '>( 04th Hr” 6va a —x cc, (031ij3 EM 0&156’53'!" Q22}? /"___.ia>.\®z[ L/‘fz' . , C0860
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WED 93 '1 we. [>1 (’ leg! 21692) 2: Four charges (Q) are placed in a perfect square and are held ﬁxed. You now bring a
5th charge —q in from inﬁnitely far away and place it perfectly in the center of the square.
What is the minimum work you had to do to bring in that 5th charge? 10 points. . . ”Hun “Jerk you; (90 Carreqmuaj +0 "Hm Clwxgci En
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D [‘3 LID/502* 6/502 =3: D/ﬁ chlwceh—f) G); lilniliclly Id UFE‘Acl : Wmm h' L} KITFéo‘ D/J:1 Wm EFF—60D 3: Four charges (Q) are in a perfect square as shown. Each has the same mass. Suddenly1
all four are released from rest. Describe the motion of each charge at that instant and in
the future. Tell me everything you can about their velocities and accelerations. Are they
changing? Keep in mind that vectors have magnitudes and directions. 15 points. . .. all Li charges W'UUC alonﬂﬂa Cg‘tgﬂmb away FmM W x D (Lolalet" 0'10 ‘Hxe Square, (see 1% do CQE'milmm )e .
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“I colt161+ WW E” Y” r” 1..., 7‘” (”to We 7] 4: Two imaginary” Gaussian spherical surfaces (shown as dashed lines) surround a point
charge Q. You calculate the electric ﬂux through each surface Is the ﬂux larger through
the small sphere or the large Sphere or are they the same? Explain. 10 points .4": ‘ @E 22; "3 Glam/Eld "Hal “in”? CQQPCmQF \‘L‘ x: X 00 Hm GFCLFJSCA] JV} ‘3?) HELL gFLﬂm 5: You have a solid insulating cylinder of inﬁnite length with radius R and constant volume
charge density pchmge. You measure the electric ﬁeld outside the cylinder at a radius of 2B.
At What radius inside the cylinder is the electric ﬁeld exactly the same size? Hint: Use
Gauss’ Law. 25 points. L/ EC?) )<Q7TPL):P CE W Ell/6f L rn'x 6: Charge is distributed on a circular disk of radius a. The charge density on the disk is
0' 2 out: where p is the cylindrical radius. 30 points total. :1: Determine the total charge on the disk in terms of Whatever variables are needed. b: Setup (but do not evaluate) the integral needed to determine the electric potential at
the indicated point on the z axis. Make certain that you have substituted for everything,
put in appropriate limits1 etc. The integral should be completely ready to evaluate. ‘ ' LC .
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