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Unformatted text preview: EEl W2010 Midterm Name: C ........... ‘
,9 u to :4 ID #: ......................... Tu. January 19, 2010, 2—3250 pm Solve all four problems! You are allowed to use a 3”x5” index card
as cheat sheet and a calculator. No books or lecture notes. You have 90 minutes. Problem 1 (6/22 points) [1] A hollow. spherical insulating cone is placed in a uniform electric ﬁeld E.
Consider the electric ﬂux through the conical surface A and the ﬂux through
the open crosssection B of the cone shown below. Which ﬂux is larger ? (a) ﬂux through A is larger
(b) ﬂux through B is larger
@ﬂux through A and B is exactly the same [2] A spherical mbber balloon has a charge uniformly distributed over its surface.
As the balloon is inﬂated (but remains spherical), how does the electric ﬁeld E
vary inside the ballon and outside, at some point well away from the surface 7 .the ﬁeld inside and outside stays the same (b) the ﬁeld changes inside but remains unchanged outside
(c) the field changes outside but remains unchanged inside (d) the ﬁeld changes both inside and outside [3] Which of the following geometries for light sources will produce the weakest
dependence on intensity with distance ? (a) A spherical light bulb (b) A 2 m long ﬂuorescent tube
@A large area lightning panel (larger than the tube)
(d) They will all produce the same intensity dependence. [4] An imaginary Gaussian surface encloses three charges as shown in the ﬁgure. If you add a forth charge as shown, what happens to the net ﬂux through the
Gaussian surface '? (a) increases (b) decreases @ stays the same [5] Order the four fundamental forces according to their strength (strongest to
weakest) (a) gravitation (lo) ((). —\ (A ) ._ (0‘)
(b) strong nuclear force
(c) electromagnetic force (d) weak nuclear force [6] Explain the meaning of Gauss’s law in your own words Total {lax over +146 waace ecouals +0 'H’IQ {Dbl
Claw“ QMdoSed lagHie suréqce, Problem 2 (4/22 points)
Given these products between unit vectors in different coordinate system:
d‘Iﬁ¢=—sin¢,é‘y.&‘¢=cos¢, (‘1‘,(’i¢=0,
calculate the ¢—component of the following vectors in cylindrical coordinates:
(a) A. = (3. 4, 2) in rectangular coordinates
(b) §=y&'I—z(Ty+ziiz (c) 1": 25,, + 225, ll Problem 3 (4/22 points)
Assume a volume charge density of
Mp) = 2 104;? C/m5 Calculate the total charge enclosed in the cylinder deﬁned by —1 m S 2 S 1 m,
OSpSO.5m, andOS¢S7L 701ml 0”;ng Q”: fv Pyoll/ 7x05
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(2'°’°')[%].', U]: [%P"]:'5 Problem 4 (8/22 points) Consider an arrangement of two conducting. concentric, inﬁnitely long cylinders
with a symmetry axis along the zaxis. The inner conductor is solid and has a
radius a. The outer conductor is inﬁnitely thin (sheet) and has a. radius b > a
(as illustrated in the ﬁgure). A section of this system of length L has a charge
+Q on the inner conductor and —Q on the outer conductor. (a) Use Gauss‘s law to derive an expression for the electric ﬁeld between the
inner and the outer conductor (a < p < b). (b) Use Gauss’s law to derive an expression for the ﬁeld outside the outer
cylinder (p > b). (c) How does the ﬁeld between the two conductors (a < p < b) change if you
double the charge on the outer conductor ? (d) What can you say about the electric ﬁeld inside the solid inner conductor
assuming that it has a constant volume charge density (p < a) ? a) angs' [aw b) 7—o‘f‘a) enclosed C anvbef Frsuon OApAa:
QM = {gig
[SB d§= a“;
L/z
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DP [ﬂ ”2 2m 02 02
DP: 8Q
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 Fall '08
 Joshi

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