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Name:
k~Je.
Vnid: _ _ _ _ _ _ _ _ _ _ _ __
1
Final Exam
Discussion TA: _ _ _ _ _ _ _ _ __
y
Show all work!! Report all numbers to three (3) significant figures.
A. Find an exact for the electric field E at a point P located at (x,y)=(O,a) from a dipole
consisting of a positive charge (+q) and negative charge (-q) at positions
(-a,0) and (+a,0) as shown. Vse the symbols ~(Coulomb constant), and unit
E-;: t J'-) t t ~ j
vectors t and j, as needed.
VectorE= _ _ _ _ _ __
-\-.!:h(J>~t;O
ZJ:\i.-
LEx ==
!:1L
2£A'2.
LEi;;::
~ &\\1\'\\0 - ~~l. )\V'\l\~o
C1»l.\\-
~ E= *,-~--=~T ~
--
B. !:&;
Cb> ,-\-t;" ::
()
= Q t-L\­
=-
t 1
----~--.-~~~-~--
A cloud of positive charge has a volume charge density of P = Po rlR where r is the
distance from the center of a sphere of radius R and Po is a constant. Find the magnitude of
the electric field E at a point inside the sphere at distance r < R.
Ii'J ::::'f:l t\V\ ~ l\ ~M ~.
~
C. ·9
e \'
Two protons are held at rest at a separation d = 2.2 x 10 m = 2.2 nm. If they are
released and fly apart to large (infinite) distance as a result of electric repulsion. what
is the final speed v of each proton?
v= _ _ _ _ _ _ _ __
=E~\j> H +e
+e
.11(----4.'--....""'--""'--.. .
d
Ph~sics
2220
Spring 2013 Name: All / G-b 6 -c./
Unid: _ _ _ _ _ _ _ _ _ _ _ __
Discussion TA:
Bt'n
2
Final Exam
---------------
Broml('~
Show all work!! Report all numbers to three (3) significant figures.
A. The strengtlrofthe magnetic flux through a curved open surface So (the "net"
2
part of the "butterfly net" shown) is $B B = 1.45 T·m. The radius of the net's hoop is r 0.24 m and the magnetic field B in the plane of the hoop is uniform and perpendicular to the plane ofthe hoop, as shown. Find the magnitude ofB. B=
<3.0(
T
---------------
For "'- c.loS1>oI s().,f,,(~ Iik-d')uY' nd Cfn c{ flo; f
Flu x t' (\
Ff() x C) cA- So cfs ~:::: 1::6
::: B., A
~ J
net
hoop
S/I'\ce &t/l or (S
f~rp-t'1 .'cvltfr to It
ihen CPs =8,4
a'lJ
&= Ji--=-~L - 23.0/T
I'S
B. A very long hollow
PiP~as inner [Jlihs a and outer radius b. A uniform current density J
J
flows vertically upward between the inner and outer radii as shown. Find B, the magnitude of the magn~e~tt~~1i)ce r> b from the pipe's axis. B(r) =
U C, /1'1 ~
k V­
-"
f/I (Y\
J g.J-f,
~7
c. pM ~ ':, t.. II W
VII(.
J-,... Ve
~ }{oIenc -t- ~/tfNen{.'''( c<#)m",t -Vl~(e
B2f rr- :::){o "Ie1l6 -=- )JO J AHI!(ur.n.t -'AoJ(J7b2,..T1~~ 13 2/1 (' ~ flo J n ~~~ B'" .Jja:Jlh7..« 2) 2Y'­
A square wire loop of length L to a side rotates on a central axis that is perpendicular to a magnetic field of strength 0.1 T. If the loop is rotating at an angular frequency of ro = 60 rad/s, what is the maximum EMF emax in the As.>(/
loop? 8max=
(YJ.(!.
6V U~e ~r",d qy~ JqW'
~B:::-
L ==.11'1
_/ -7
.
B# A =lgllA Icase
B
axis
I\nOWff =-cl'lf.::: -W/tB <;,hWt)
",~e" '7i~ (.u ~ )n=' /0(' -/ ', whE ·1-:::: {J.) L2-'6= (, V
\. R... wt ---; ~4 ·
M~A
fov- t)[/r
C~t;.{ I5A{c?5 wt). We.
tl'lf"'WA
'S
j
L--Mf
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