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GENERAL PHYSICS II
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1 Electro StaticsCoulomb
s law
rR
QkQF
2
21
1. 4 4 4
A.(3),(1),(2),(4) B.(4),(2),(1),(3)
C.(2),(3),(4),(1) D.(1),(4),(3),(2)
E.(3),(4),(1),(2)
3. 4 2
A.(a),(b),(v),(d) B.(a),(b),(c)
C.(a),(b) D.(a)
E.(b),(c),(d)
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2 Charge is Quantized
Q (C)N e
= -1.610-19C
3 The Electric Field
rR
kQE
2
Electric Dipole
Q = Ne
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4 Electric Field Continuous Charge
Distributionr
r
dqkE
2
Volume charge density:when a charge is distributed evenly throughouta volume
= Q/ V
Surface charge density:when a charge is distributed evenly over asurface area
= Q/A
Linear charge density:when a charge is distributed along a line
= Q/
EX. Line Charge
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EX Charged Disk
5 Gausss Law
Electric fluxis the product of the magnitude of the electric field and the
surface area,A, perpendicular to the field
AdE
Gauss lawrelates the net flux of an electric field through a closedsurface (a Gaussian surface) to the net charge q
encthat is enclosed by
that surface.
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0
encqAdE
EX Applying Gausss Law
Cylindrical Symmetry
Planar Symmetry
Spherically Symmetric
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4.
A. B.
C. D.
E.
6. 3
= 2.00 R= 100 cm
7. 1.50 m
= (3.00 4.00) 6.00 7.00
6 Electric Potentialand Potential EnergyConsider two charged particles. The potential energy of the system is
12
21
R
QkQU
The electric potential is
R
kQV
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1.
2.
7. Equipotential Surface A.B.C.D.E.
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Electric Field from Potential
In general, the electric potential is a function of all three dimensions
Given V(x,y,z) you can findEx
,Ey
andEz
as partial derivatives
V(x,y,z) =
1. = 3 2
E. A D ................................................. N/C
2. r = 3 2
A.2.51 10NB. 5.20 10NC. 7.53 10ND. 1.00 10NE. A D ................................................. N
3. + r = 3 2 r = 3 2 A.-1.85 10JB.1.85 10JC.-4.19 10JD.8.39 10JE. A D ................................................. J
x y z
V V VE E E
x y z
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4. r = 3 2 1A.628.3 CNm /2 B.-628.3 CNm /2 C.377.0 CNm /2 D.-377.0 CNm /2 E. A D ................................................. CNm /2
7
Capacitance
C (Farad;F)Q
V
(Combination of Capacitors)
1. (Series Combination) Q (Q1= Q2= Q3= Q) V
Ceq
V
QC
CVQ
...1111
321
CCCCeq
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2. (Parallel Combination) V (V1=V2= V3= V) Q
Ceq
1. C1=1.16 F C
2=3.22 F V=96.9 v
a c b d S1
S2 C
1,C
2 e f
1. C1= C
5= 8.4 C
2= C
3=C
4= 4.2 V
ab= 220
...321 CCCCeq
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A. a b 2.5
B. C1 5.5 x 10-4
C. V5= 66V voltage C5
D. A,B,C
E. A,B,C
Capacitors with Dielectrics
A dielectricis a nonconducting material that, when placed between the plates ofa capacitor, increases the capacitance
Dielectrics include rubber, plastic, and waxed paper
0CC The capacitance is multiplied by the factor when the dielectric completely fillsthe region between the plates.
W (J)V (Volt)
QVW2
1
2
2
1CVW
C
QW
2
2
1
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6. a,b =
Electric Circuits
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() (Q)
(C/s) (A)Q (C)t (s)
1 (Resistivity)
(R)
(Resistivity) (m)
(m)A (m2)
4. 6 3
A.54
B.55
C.56
D.57
E.58
tQI
AR
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2 Kirchhoffs Rules1 Junction rule
321 III
2 Loop rule
A B(VAB= VA VB)
1. 2. A B 3. A B
I = I
Loop Loop
IRE
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4.
A. Vad
6.58 V
B. Vad
4.58 V
C. 4.00 V 3.983 V
D. 4.00 V 4.00 VE.
3. A
RE
RD
RC
RB
RA
12
10.
9
8.
7.
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5. P 100 V Q
A. -10V
B.+10VC.-20V
D.+20V
E.+30V
3 RC Circuits:
Charging
The charge on the capacitor varies with time
q(t)= C (1 e-t/RC
) =Q(1 e-t/RC
)
The current can be found
RCteRdt
dqti /)(
is the time constant = RC
Discharging
q(t)= Qe-t/RC
2. RC t= 0 s 100 V,
1.06 V 10 s t=17s A.2.2 , 44
B.3.3 , 66
C.4.4 , 88D.5.5 ,100
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E.6.6 ,110
Magnetic Fields
1Magnetic Force
F
(N)
q (C)v (m/s)B
(T)
v B
2. 50 cm 2.0 N/C
A. 5.5610-11 B. 5.5610-7
C. 1.3910-11
E. 2.2210-11
BvqF
sinBvqF
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5. 75.0 cm 0.860 T x
a b c d e f 6.58 A f N
A.
-4.24 B.-4.24 C. 4.24 D. 4.24 E. 4.24 -4.24
B.
(T)
(Helical Path)
qB
mvR
qB
mT
2
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1.
2.
3.
14. 22.5 B=455 T 65.5
A.75.6 ,1.2
B.76.6 ,1.2
C.77.6 ,2.2
D.78.6 ,3.2
E.79.9 ,3.2
7.K d
m e
qB
mvR
sin
qB
mT
2
S
qB
mv
2
cos
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(Magnetic Force Acting on a Current Carrying Conductor)
F
(N)I (A)
(m)
B
(T)
B
BIF
sinBIF
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7. AB I CD AB
C D CD
I AB CD CD
h
AB
2
E (Volt)L (m)v (m/s) v B
E Bv
E = LvBsin
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10.
11. = 262 = 12.7 = 13 477
A.1.33A
B.1.44A
C.1.55A
D.1.66A
E.1.78A
3 Amperes Law
enciSdB 0
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Solenoids and Toroids
r
iNB
2
0
inB0
4 Faradays Law of Induction
dt
dN B
AdBB
Induced Electric Fields
dt
dSdE B
12.
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13. = 12, = 16
emf = 3A.300 B.400
C.500
D.600
E.660
9.
b
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12. AB di/dt
a)
b) emf
c) emf
a=12.0 cm b=36.0 cm L=24.0 cm di/dt=9.60 A/s
10. 4.00 cm 0.0280A 1.00 cm
A.7.5 x 10-7T B. 6.5 x 10-7T C.5.5 x 10-7T
D. 4.5 x 10-7T E.3.5 x 10-7T