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(PHYS013)[2008](s)midterm~dli^_10535.pdf
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Midterm Exam
No.1
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No.1
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F=ke(2q2/r2 -q2/(r+s)2 -q2/(r-s)2)
=keq2/r2(2-1/(1+t)2 -1/(1-t)2) , t=s/r
=keq2/r2(2t4 -6t2)/(1-t2)2
F>0 if t>3, repulsive
F<0 if t<3, attractive
No.1
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F=keq2/r2(2t4 -6t2)/(1-t2)2 , t=s/r for t<<1
(1+x)-n1-nx if x<<1
1/(1-t2)2=(1-t2)-2 1+2t2
F=keq2/r2(2t4-6t2)(1+2t2)
=keq2/r2(-6t2)= -6keq2s2/r4
p=2qs, F=(-3/2)kep2/r4,attractive
No.1
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Electric Field
E(x)= keq/x2(1/(1+s/2x)2 -1/(1-s/2x)2)
=keq/x2(1/(1+t/2)2 -1/(1-t/2)2) , t=s/x
If t<<1, p=2qs
E(x) keq/x2(-2t)= -ke2qs/x3= -kep/x3
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Electric Potential E(x)=-dV(x)/dx
V(x)= keq(1/(x+s/2)-1/(x-s/2))
= keq/x(1/(1+t/2)-1/(1-t/2)) , t=s/x
keq/2x2, If t<<1
E(x) = -keqs/x3= -kep/x3,p=2qs
No.1
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E(x)=-kep/x3
F=qE(r-s/2)-qE(r+s/2)
=-kepq/r3(1/(1-t/2)3 -1/(1+t/2)3), s/r=t
-kepq/r3(1+3/2t)-(1-3/2t)), t<<1
=-3kepqs/r4=(-3/2)kep2/r4
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F=(3/2)kep2/r4, repulsive
No.1
23-22a
E=(1/2)kep/r3
E=kep/r3
E=kep/r3
E=(1/2)kep/r3
No.1
23-22a
+q
-q
Fy=0
Fx=qE(r+s/2)-qE(r-s/2)
=(1/2)kepq((r+s/2)-3 -(r-s/2)-3)
=(1/2)kepq/r3 (1-3s/2-1-3s/2)
=(-3/2)kep2/r4
E=(1/2)kep/r3
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Fy=0
Fx=2keq2/r2-2keq2/(r2+s2)r/(r2+s2)
if s/r<<1
Fx=2keq2/r2 (1-1/(1+s2/r2)3/2)
=2keq2/r2 (3/2s2/r2)
p=2qs, F=(3/4)kep2/r4,repulsive
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No.2
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No.2
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Should the bottom plate be charged positive or negative relative to the top plate to make the electron turn to right?
Positively
No.2
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Whatstrengthelectricfieldisneedediftheelectronistoemergefromanexithole1.0cmawayfromtheentrancehole,travelingatrightangletoitsoriginaldirection?Hint:choosethex,yvectorsshowninthefigure.
No.2
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KE=.mv2
vx=vy=v/2
vxt=s,2vy=at=tqE/m
E=2KE/(qs)=37500N/C
KE=.mv2
W=FL=(qE/2)(s/2)
W=KE
E=2KE/(qs)
No.2
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Whatminimumseparationdmustthecapacitorplateshave?
d=.a(t/2)2=.(qE/m)(s/2vx)2
=s/4=2.5mm
No.2
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Calculatethekineticenergyoftheexitelectron.
Nochange!
No.2
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Iftheangleischangedfrom45to30,whatistheanglebetweentheenterpathandtheexitpathoftheelectron.
120or60
No.2
No.3
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E1toE5?
atod?
No.3
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E2=E4=0
Eup=Q/(20A/2)=Q/(0A)
Edw=2Q/(20A/2)=2Q/(0A)
E1=-E5= Eup+Edw=3Q/(0A)
E3=Edw-Eup=Q/(0A)
A/2
Eup
Eup
Edw
Edw
No.3
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Ea=qa/(20A/2)=qa/(0A)
Eb=(Q-qa)/(20A/2)= (Q-qa)/(0A)