Unformatted text preview: PHYS 1 12  Test 1 ' Summer 2009
——————_—___________ Problems: In order to qualify for pom‘al credit you have to provide at least a logical start towards a solution,
even r'fr't may beﬂawed. Do not ﬂood the space with obviously useless information. ———————_—.—_.__________ P1: A charge Q= —3.4 uC is placed at a distance )1 = 0.1 l in above a
very long straight line of charge with uniform linear charge density It
= —5.5 pC/m as in the ﬁgure. A test point charge :1 = 1049 uC is “I"
placed in point A where it ﬂoats in static equilibrium at height hfZ T
above the line of charge.
a) [3] Sketch a cylindrical Gaussian of arbitrary radius r and length 
L, coaxial with the line of charge. Write out an expression for the E t h
electric ﬂux through its surface in terms of the ﬁeld E 4, r and L. a '
Recall that the area of the q
if, ﬂ curved surface of a cylinder A
i \(f/ \H 18 Its Circumference times it
. _ len .
, ‘13:; Eh'3\1trl:_ gm El K J éh  L. i
I,
b) 15] Use part (a) and Gauss’s Law to derive a symbolical $25
1 expression for the magnitude E; of the electric ﬁeld produced by
the line at distance r from it, in term of .2, so, and r.
E; E (l, in r L ’ Lh:
Q in @th E 1‘— it'b E 3’" :7‘ I” e) [4] Use vector arrows to represent the electric ﬁeld vectors EQ and EA created by the charge Q and the line
of charge it in point A. Then calculate the magnitude of each of the two ﬁelds in point A. l Kai 4343:; 'l«OllX0'3 EL 2 gig T5: ; Its1,205? X ’l
EA=L: _$_3J(:U"C— ': — N
m —»= to WW 4/ d) [4] Calculate the net electric ﬁeld in point A. .
x (Weir—75
a \,01 AWE ,2 e} [4] Use the equilibrium between the electric and gravitational forces to calculate the mass m of the test
charge q. l‘ @ if 7 ””56 , __ @
this :Wa 13E”, (’iﬁlélxlﬁcmﬁ) :
[2 WV" 3’ J ‘s—F 505 lit} '17.
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 Spring '08
 FREAMAT
 Physics

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