CIE IGCSE Physics Turning Forces Circular Motion and Gravitational attraction.
Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and...
Transcript of Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and...
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Benjamin Franklin
Two type of charges: positive and negative.
Like charges repel one another.
Unlike charges attract one another.
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++
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4
++
w=mg
F T
F E
Static Equilibrium
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5
++
w=mg
F T
F E
FT cos
FT sin
∑ F y=F T cos−mg=0F T cos=mg
∑ F x=F E−F T sin =0F E=FT sin
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++
w=mg
F T
F E
FT cos
FT sin
∑ F y=FT cos−mg=0F T cos=mg
F T=mg
cos
∑ F x=F E−F T sin=0F E=F T sin
F E= mgcos sin=mg tan
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--
w=mg
F T
F E
FT cos
FT sin
∑ F y=FT cos−mg=0F T cos=mg
F T=mg
cos
∑ F x=F E−F T sin=0F E=F T sin
F E= mgcos sin=mg tan
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““Two Type of Charges.”Two Type of Charges.”
Electron
Protron
Neutron
−1.6 X 10−19C
1.6 X 10−19C
0C
9.11 X 10−31kg
1.67 X 10−27kg
1.67 X 10−27kg
Particle Charge Mass
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6 electrons 6 protons
6 X −1.6 X 10−19C 6 X 1.6 X 10−19C
0C
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16 electrons 6 protons
16 X −1.6 X 10−19C 6 X 1.6 X 10−19C
10 X −1.6 X 10−19C =−1.6 X 10−18C
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4 electrons 6 protons
4 X −1.6 X 10−19C 6 X 1.6 X 10−19C
2 X 1.6 X 10−19C =3.2 X 10−18C
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ConductorConductor – Materials in which charges move freely.
InsulatorInsulator – Materials in which charges cannot move freely.
Semi-ConductorSemi-Conductor - Materials in which charges move freely under certain conditions.
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Charging by InductionCharging by Induction
+ - + - +- + - + -+ - + - +- + - + -
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Charging by InductionCharging by Induction
+ - + - +- + - + -+ - + - +- + - + -
+ + + + + + +
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Charging by InductionCharging by Induction
- -- - -- - - - -
+ + + + + + +
+ + + + ++ + ++ +
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Charging by InductionCharging by Induction
+ - + - +- + - + -+ - + - +- + - + -
+ + + + + + +
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Charging by InductionCharging by Induction
- -- - -- - - - -
+ + + + + + +
+ + + + ++ + ++ +
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Charging by InductionCharging by Induction
- -- - -- - - - -
+ + + + + + +
+ + + + ++ + ++ +
“Ground”
“Switch”
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Charging by InductionCharging by Induction
- -- - -- - - - -
+ + + + + + +
- - - - -- - -- -
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Charging by InductionCharging by Induction
- -- - -- - - - -
+ + + + + + +
- - - - -- - -- -
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Charging by InductionCharging by Induction
- -- - -- - - - -
- - - - -- - -- -
Negatively Charged.
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q1
q2
F 21
F 12
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q1
q2
F 21
F 12
r12
r 21
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q1
q2
F 21
F 12
r12
r 21
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q1
q2
F 21 F 12
r12
r 21
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F e=k∣q1∣∣q2∣r12
2 r12
k= 14o
=9 X 109 N m2
C 2
o=8.85 X 10−12 C 2
N m2
o=Permittivity of Free Space
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Charles Coulomb
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Charles Coulomb
● Electric Force between two stationary particles:– inversely proportional to the square of the the
distance ( r ) between the two particles and directly along the line connecting them.
– proportional to the product of the charges ( q1 and q2 )
– Attractive if the charges are of opposite signs and repulsive if the charges are of like signs.
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Charles Coulomb
2
212
2
29
221
108542.8
1098.84
1
NmCX
CNmXkk
rqq
kF
o
oe
ee
−=
===
=
ε
π ε
permittivity of free space
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Gravitational vs. Electrical
Consider two electrons 2 angstrom apart. What is thegravitational and electrical forces between them?
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Gravitational vs. Electrical
2rmGmF ee
G =
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Gravitational vs. Electrical
( )( )( )
=
=
−
−−−
210
3131
2
211
2
1000.21011.91011.9107.6
mXkgXkgX
kgNmX
rmGmF ee
G
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Gravitational vs. Electrical
( )( )( )
NX
mXkgXkgX
kgNmX
rmGmF ee
G
51
210
3131
2
211
2
1039.1
1000.21011.91011.9107.6
−
−
−−−
=
=
=
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Gravitational vs. Electrical
221
rqqk
Fe =
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Gravitational vs. Electrical
( )( )( )
=
=
−
−−
210
1919
2
29
221
1000.21060.11060.11099.8
mXCXCX
CNmX
rqqk
Fe
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Gravitational vs. Electrical
( )( )( )
NX
mXCXCX
CNmX
rqqk
Fe
27
210
1919
2
29
221
1075.5
1000.21060.11060.11099.8
−
−
−−
=
=
=
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Gravitational vs. Electrical
2451
27
101039.11075.5 ≈= −
−
NXNX
FF
G
e
The electrical force is much greater than the gravitational force at this distance.
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Don’t forget force is a vector!
rrqqkF e ˆ2
2112 =
Force exerted by charge 1 on charge 2, with a unitvector that points from charge 1 to charge 2.
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Forces obey Newton’s third law!
2112 FF −=
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4.0m
3.0m
q1=10C
Find the net force on qo.
q2=−10C
q0=10C
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4.0m
3.0m
q1=10C
Find the net force on qo.
q2=−10C
q0=10C
∣F 10∣
∣F 20∣
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4.0m
3.0m
q1=10C
Find the net force on qo.
q2=−10C
q0=10C
∣F 10∣
∣F 20∣ ∣F 0∣
0
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F 0=F 0x
iF 0 y
j=0.056 N i−0.10 N j
∣F 0∣=F 0 x
2 F 0 y
2 =0.11N
0= tan−1F 0 y
F 0x=−60.75o
F 0 x=∣F 10∣=k
q1q0
r102 =0.056 N
F 0 y=−∣F 20∣=k
q2q0
r202 =−0.10 N
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4.0m
3.0m
q1=10mC
q2=20mC
q0=10mC
Find the net force on qo.
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4.0m
3.0m
q1=10mC
q2=20mC
q0=10mC
F 20
F 10
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4.0m
3.0m
q1=10mC
q2=20mC
q0=10mC
F 20
F 10
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∣F 10∣=kq1q0
r102 =2.25 X 107N
∣F 20∣=kq2q0
r202 =1.125 X 105N
F 0x=F 10 cos=1.35 X 107N
F 0 y=F 10 sinF 20=1.81 X 107N
F 0=F 0x
2 F 0 y
2 =2.258 X 107N
o=tan−1F 0 y
F 0x=53.28o
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q1
q2q
0
q1=20C q2=50Cq0=10C
5.0 m
F 10F 20
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49
q1
q2q
0
q1=20C q2=50Cq0=10C
5.0 m
F 10 F 20
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50
q1
q2q
0
q1=20C q2=50Cq0=10C
5.0 m
Find place where the net force on charge qo is equal to zero.
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q1
q2q
0
q1=20C q2=50Cq0=10C
5.0 m
Find place where the net force on charge qo is equal to zero.
F 10F 20
F 0= F 20− F 10=0F 20=F 10
k∣q2∣∣q0∣r20
2 =k ∣q1∣∣q0∣r10
2
∣q2∣r20
2 =∣q1∣r10
2
![Page 52: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/52.jpg)
52
q1
q2q
0
q1=20C q2=50Cq0=10C
5.0 m
Find place where the net force on charge qo is equal to zero.
F10F 20
F 0= F 20− F 10=0F 20=F 10
k∣q2∣∣q0∣r20
2 =k ∣q1∣∣q0∣r10
2
∣q2∣r20
2 =∣q1∣r10
2
∣q2∣5m−x 2
=∣q1∣x2
5.0 m - xx
![Page 53: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/53.jpg)
53
q1
q2q
0
q1=20C q2=50Cq0=10C
5.0 m
Find place where the net force on charge qo is equal to zero.
F10F 20
F 0= F 20− F 10=0F 20=F 10
k∣q2∣∣q0∣r20
2 =k ∣q1∣∣q0∣r10
2
∣q2∣r20
2 =∣q1∣r10
2
∣q2∣5m−x 2
=∣q1∣x2
5.0 m - xx
x2
5m−x 2=∣q1∣∣q2∣
x5m− x
=∣q1∣∣q2∣
x=∣q1∣∣q2∣
5m−x
x=5m∣q1∣∣q2∣
−x∣q1∣∣q2∣
![Page 54: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/54.jpg)
54
q1
q2q
0
q1=20C q2=50Cq0=10C
5.0 m
Find place where the net force on charge qo is equal to zero.
F10F 20
F 0= F 20− F 10=0F 20=F 10
k∣q2∣∣q0∣r20
2 =k ∣q1∣∣q0∣r10
2
∣q2∣r20
2 =∣q1∣r10
2
∣q2∣5m−x 2
=∣q1∣x2
5.0 m - xx
x 2
5m−x 2=∣q1∣∣q2∣
x5m−x
=∣q1∣∣q2∣
x=∣q1∣∣q2∣
5m−x
x=5m∣q1∣∣q2∣
− x∣q1∣∣q2∣
xx∣q1∣∣q2∣
=5m∣q1∣∣q2∣
x 1∣q1∣∣q2∣=5m∣q1∣
∣q2∣
x=5m ∣q1∣∣q2∣
1∣q1∣∣q2∣
![Page 55: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/55.jpg)
55
q1
q2q
0
q1=20C q2=50Cq0=10C
5.0 m
Find place where the net force on charge qo is equal to zero.
F10F 20
5.0 m - xx
x=5m ∣q1∣∣q2∣
1∣q1∣∣q2∣
x=5m ∣20C∣∣50C∣
1∣20C∣∣50C∣
x=1.94m
![Page 56: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/56.jpg)
56
q1
q2
q0
Find net force on charge q0.
xa
a
![Page 57: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/57.jpg)
57
q1
q2
q0
Find net force on charge q0.
r10
r20
xa
a
F 20
F 10
q1=q2=qr10=r20=r
![Page 58: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/58.jpg)
58
Find net force on charge q0.
F 20 y
F 10 y
F 10x, F 20x
Y components cancel. X-components have equal magnitude.
q1=q2=qr10=r20=r
![Page 59: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/59.jpg)
59
q1
q2
q0
Find net force on charge q0.
r10
r20
xa
a
F 20
F 10
F 10=F 20=kq qor2
F o=2F 10 x=2F 10 cos=2k
qq0
r2 xr =2kxq q0
r3 =2kxq q0
x2a2 3 /2
F o=2kxq q0
x2a2 3 /2i
q1=q2=qr10=r20=r
![Page 60: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/60.jpg)
60
Electric Field – The force per charge. Use a small test charge to determine the pattern of the force.
+
+
q
qoSmall Test Charge
![Page 61: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/61.jpg)
61
Electric Field – The force per charge. Use a small test charge to determine the pattern of the force.
+
+
q
qo
E=Fqo
![Page 62: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/62.jpg)
62
Electric Field – The force per charge. Use a small test charge to determine the pattern of the force.
+
+
q
qo
E=Fqo
![Page 63: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/63.jpg)
63
Electric Field – The force per charge. Use a small test charge to determine the pattern of the force.
+q qo
E=Fqo
+
![Page 64: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/64.jpg)
64
Electric Field – The force per charge. Use a small test charge to determine the pattern of the force.
+q
qo
E=Fqo
+
![Page 65: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/65.jpg)
65
Electric Field – The force per charge. Use a small test charge to determine the pattern of the force.
+q
qo
E=Fqo+
![Page 66: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/66.jpg)
66
Electric Field – The force per charge. Use a small test charge to determine the pattern of the force.
+q
qo
E=Fqo+
![Page 67: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/67.jpg)
67
Electric Field – The force per charge. Use a small test charge to determine the pattern of the force.
+q
![Page 68: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/68.jpg)
68
Electric Field – The force per charge. Use a small test charge to determine the pattern of the force.
+q
-Symmetrical
- Points away from positive charges.
![Page 69: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/69.jpg)
69
Electric Field – The force per charge. Use a small test charge to determine the pattern of the force.
-q
-Symmetrical
- Points towards negative charges.
![Page 70: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/70.jpg)
70
Electric Field – The force per charge. Use a small test charge to determine the pattern of the force.
- ++
![Page 71: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/71.jpg)
71
Electric Field – The force per charge. Use a small test charge to determine the pattern of the force.
- ++
![Page 72: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/72.jpg)
72
Electric Field – The force per charge. Use a small test charge to determine the pattern of the force.
- +
+
![Page 73: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/73.jpg)
73
Electric Field – The force per charge. Use a small test charge to determine the pattern of the force.
- +
+
![Page 74: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/74.jpg)
74
Electric Field – The force per charge. Use a small test charge to determine the pattern of the force.
- ++
![Page 75: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/75.jpg)
75
1. Number of lines proportional to the charge.
2. Lines leave the charge perpendicular to the surface of the charge.
3. Lines point in the direction of the Electrical Force felt by a positive charge (i.e. away from positive charges and towards negative charges).
4. Lines NEVER cross one another.
5. Lines are symmetric around the charge.
6. Density of lines is proportional to the Electric Field in that area.
Drawing Electric Field Lines.Drawing Electric Field Lines.
![Page 76: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/76.jpg)
76
- +32C−32C
1 line per 4C
![Page 77: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/77.jpg)
77
- +32C−32C
1 line per 4C
![Page 78: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/78.jpg)
78
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79
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80
q1 q2
![Page 81: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/81.jpg)
81q1 q2
![Page 82: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/82.jpg)
82q1 q2
![Page 83: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/83.jpg)
83q1 q2
![Page 84: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/84.jpg)
84
E=Fq0
E point charge =kqr2 r
E=k∑i
qir i
2 r i
Electric Field
![Page 85: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/85.jpg)
85
http://physics.weber.edu/schroeder/software/EField/
http://www.its.caltech.edu/~phys1/java/phys1/EField/EField.htmlhttp://hibp.ecse.rpi.edu/~crowley/java/Efield/App.htmhttp://web.mit.edu/jbelcher/www/java/vecnodyncirc/vecnodyncirc.html
![Page 86: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/86.jpg)
86
q1
q2
Find net force on charge q0.
r10
r20
xa
a
E20
E10
F o=2kxqq0
x2a2 3 /2i
E=2kx qx2a2 3 /2
i
q1=q2=qr10=r20=r
![Page 87: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/87.jpg)
87
E=k∫ dqr 2 r
Volume Charge Density =QV= dqdV
Surface Charge Density =QA= dqdA
Linear Charge Density =Ql=dqdl
Electric Field
![Page 88: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/88.jpg)
E=k∫ dqr 2 r
Volume Charge Density =QV= dqdV
Surface Charge Density =QA= dqdA
Linear Charge Density =Ql=dqdl
Electric Field
![Page 89: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/89.jpg)
Electric Field of a ring of charge:
R
P
![Page 90: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/90.jpg)
Electric Field of a ring of charge:
R
P
dq
d E
![Page 91: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/91.jpg)
Electric Field of a ring of charge:
R
P
dq
d E
dq
Y – components cancel.
![Page 92: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/92.jpg)
Electric Field of a ring of charge:
dE=k dqr2
dE x=kdqr2 cos=k dq
r2xr= kxr3 dq
E x=∫dE x=∫ kxr3 dq=
kxr3∫dq=Q total
kxr 3 =
kxQx 2R2 3 /2
![Page 93: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/93.jpg)
Electric Field of a ring of charge:
E x=kxQ
x2R2 3 /2R=0.1mx=1.2mQ=8 nC
E= kxQx2R2 3 /2
i
E=9 X 109 Nm2
C2 1.2m 8 X 10−9C
1.2m 20.1m 23 /2i=49.48 N
Ci
![Page 94: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/94.jpg)
Electric Field of a ring of charge:
E x=kxQ
x2R2 3 /2R=0.1mx=1.2mQ=8nC
E= kxQx2R2 3 /2
i
E=9 X 109 Nm2
C2 1.2m 8 X 10−9C
1.2m 20.1m 23 /2i=49.48 N
Ci
F 0=q0E=−5C 49.48 N
Ci=−247.4 N i
qo=−5C
![Page 95: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/95.jpg)
Electric Field of a charged sheet ( another look ):
R
![Page 96: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/96.jpg)
Electric Field of a charged sheet ( another look ):
RP
=QA= dqdA
xr
dq
dr E x=kxQ
x2R2 3 /2
dE= kxx2R2 3 /2
dq
Recall for a ring:
![Page 97: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/97.jpg)
Electric Field of a charged sheet ( another look ):
RP
=QA= dqdA
xr
dq
drE x=
kxQx2R2 3 /2
dE= kxx2R2 3 /2
dq
Recall for a ring:
dq= dA= 2r dr
d E
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Electric Field of a charged sheet ( another look ):
=QA= dqdA
dE= kxx2r2 3/2
2 r dr
E=∫ kxx2r23/2
2 r dr
E=2 x k ∫ x2r2 −3 /2r dr
![Page 99: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/99.jpg)
∫2 x2r2 −3 /2r dr
u=x2r2
du=2r dr
∫u−3 /2du=[ u−1 /2
−1/2 ]=[−2 x2r2 −1 /2]oR
![Page 100: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/100.jpg)
Electric Field of a charged sheet ( another look ):
=QA= dqdA
dE= kxx2r2 3 /2
2 r dr
E=∫ kxx2r23 /2
2 r dr
E=2 x k ∫ x2r2 −3 /2r dr
E=−2 x k [x 2r2 −1 /2]oR
E=2 x k [ 1∣x∣
− 1xR2 ]
![Page 101: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/101.jpg)
Electric Field of a charged sheet ( another look ):
=QA= dqdA
E=2 x k [ 1∣x∣
− 1xR2 ]
What if R ∞ ?
E=2k =2 14o =
2o
![Page 102: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/102.jpg)
=2 nCm2
=−2 nCm2 E=
2o
2o=o
![Page 103: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/103.jpg)
=2 nCm2
=−2 nCm2 E=
2o
2o=o
q0
![Page 104: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/104.jpg)
=2 nCm2
=−2 nCm2 E=
2o
2o=o
q0
w=mg
FT
F E=q0E
![Page 105: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/105.jpg)
=2 nCm2
=−2 nCm2 E=
2o
2o=o
q0
w=mg
FT
F E=q0E
∑ F y=F T cos−mg
F T=mg
cos
![Page 106: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/106.jpg)
=2 nCm2
=−2 nCm2 E=
2o
2o=o
q0
w=mg
FT
F E=q0E
∑ F y=FT cos−mg=0
F T=mg
cos
∑ F x=q0E−F T sin =0
q0=F T sinE
q0=mg tan /o
![Page 107: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/107.jpg)
107
Gauss's Law
![Page 108: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/108.jpg)
108
Flux:
=Electrical Field X Area=E A
A=5m2
E=100 NC
=100 NC 5m2
=500 N m2
C
![Page 109: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/109.jpg)
109
Flux:
=Electrical Field X Area
A=5m2
E=100 NC
=100 NC 5m2
=500 N m2
C
![Page 110: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/110.jpg)
110
Flux:
=Electrical Field X Area
E
A
![Page 111: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/111.jpg)
111
Flux:
=E⋅A
E
A
A cos
![Page 112: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/112.jpg)
112
Flux:
=E⋅A=∣E∣∣A∣cos
E
A
A cos
![Page 113: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/113.jpg)
113
Flux:
=E⋅A=∣E∣∣A∣cos=10 NC
5m2 cos 30o=43.30 N m2
C
E=10 NC
A=5m2
=30o
A cos
![Page 114: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/114.jpg)
114
q1
2
![Page 115: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/115.jpg)
115
E=Q inside
o
Gauss's Law
![Page 116: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/116.jpg)
116
q
r
Gauss's LawGauss's Law
E=E A
E=k qr2 AE= 1
4o
qr2 A
![Page 117: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/117.jpg)
117
q
r
Gauss's LawGauss's Law
E=E A
E=k qr2 AE= 1
4o
qr2 A
E= 14o
qr2 4 r2
E=qo=Q inside
o
![Page 118: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/118.jpg)
118
q
r
Gauss's LawGauss's Law
E=Qinside
o
![Page 119: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/119.jpg)
119
q
r
Gauss's LawGauss's Law
=∫ E⋅ dA
∫ E⋅dA
![Page 120: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/120.jpg)
120
q r
Gauss's LawGauss's Law
=∫ E⋅ dA
∫ E⋅dA=∫∣E∣∣dA∣cos
A
![Page 121: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/121.jpg)
121
q r
Gauss's LawGauss's Law
=∫ E⋅ dA
∫ E⋅dA=∫∣E∣∣dA∣cos
∫ E⋅dA=∫∣E∣∣dA∣cos 0o
∫ E⋅dA=∫∣E∣∣dA∣∫ E⋅dA=∣E∣∫∣dA∣∫ E⋅dA=k q
r 2 4 r2
A
![Page 122: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/122.jpg)
122
q r
Gauss's LawGauss's Law
=∫ E⋅ dA
∫ E⋅dA=k qr2 4r 2
∫ E⋅dA= 14o qr2 4 r2
∫ E⋅dA= qo
A
![Page 123: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/123.jpg)
123
q r
Gauss's LawGauss's Law
=∫ E⋅ dA=qenco
A
![Page 124: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/124.jpg)
124
E=Qinside
o
Volume Charge Density =QV=
qV
Surface Charge Density =QA=
q A
Linear Charge Density =Ql=q l
![Page 125: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/125.jpg)
125
Infinite Line of Charge
q
EE
![Page 126: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/126.jpg)
126
Infinite Line of ChargeE
=Ql=q l
= constant
l
A1
A2
No electrical field passes through A1 or A2 .
![Page 127: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/127.jpg)
127
Infinite Line of ChargeE
l
r
l
2r
A=2 r l
=Ql=q l
= constant
![Page 128: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/128.jpg)
128
Infinite Line of ChargeE
l
r
l
2r
A=2 r lqinside= l
=Ql=q l
= constant
![Page 129: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/129.jpg)
129
Infinite Line of ChargeE
l
r
l
2r
A=2 r l
=Ql=q l
= constant
qinside= l
E=q insideo
E A= lE 2 r l = l
E=
2o r
![Page 130: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/130.jpg)
130
Infinite Line of ChargeE
l
r
l
2r
A=2 r l
=Ql=q l
= constant
qinside= l
E=qinsideo
E A= lE 2 r l = l
E=
2o r
E=22
2o r
E=2
4o r=2k
r
![Page 131: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/131.jpg)
131
+ + ++ + ++ + ++ + +
Infinite Sheet of Charge
![Page 132: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/132.jpg)
132
+ + ++ + ++ + ++ + +
Infinite Sheet of Charge
AA
qenc=A
![Page 133: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/133.jpg)
133
+ + ++ + ++ + ++ + +
Infinite Sheet of Charge
AA
EAE A= Ao
2EA=Ao
E=
2o
E=Qinside
o
![Page 134: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/134.jpg)
134
=2 nCm2
=−2 nCm2 E=
2o
2o=o
![Page 135: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/135.jpg)
135
=2 nCm2
=−2 nCm2 E=
2o
2o=o
q0
![Page 136: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/136.jpg)
136
=2 nCm2
=−2 nCm2 E=
2o
2o=o
q0
w=mg
FT
F E=q0E
![Page 137: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/137.jpg)
137
=2 nCm2
=−2 nCm2 E=
2o
2o=o
q0
w=mg
FT
F E=q0E
∑ F y=F T cos−mg
F T=mg
cos
![Page 138: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/138.jpg)
138
=2 nCm2
=−2 nCm2 E=
2o
2o=o
q0
w=mg
FT
F E=q0E
∑ F y=FT cos−mg=0
F T=mg
cos
∑ F x=q0E−F T sin =0
q0=F T sinE
q0=mg tan /o
![Page 139: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/139.jpg)
139
Hollow Sphere with total charge Q.
E=Qinside
oE A=Q
o
E 4 r2=Qo
E= Q4r2o
=k Qr2
![Page 140: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/140.jpg)
140
Solid Conducting Sphere with total charge Q.
E=Qinside
o
+ +
![Page 141: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/141.jpg)
141
Solid Conducting Sphere with total charge Q.
E=Qinside
o
+ +
![Page 142: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/142.jpg)
142
Solid Conducting Sphere with total charge Q.
E=Qinside
o
+ ++ +
![Page 143: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/143.jpg)
143
Solid Conducting Sphere with total charge Q.
E=Qinside
o
+ +
+
+
![Page 144: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/144.jpg)
144
Solid Conducting Sphere with total charge Q.
E=Qinside
o
+ +
+
+
+ +
![Page 145: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/145.jpg)
145
Solid Conducting Sphere with total charge Q.
E=Qinside
o
+ +
+
+
+
+
![Page 146: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/146.jpg)
146
Solid Conducting Sphere with total charge Q.
E=Qinside
o
+ +
+
+
+
+
+
+
+
+
+
+
All charge will lie on the surface of the conducting sphere.
E A=Qo
E 4 r2=Qo
E= Q4 r2o
=k Qr2
r >= R
R
r
![Page 147: Electrical Forces and Fields - Drexel Universityjoetrout/phys102/electric_forces...gravitational and electrical forces between them? Gravitational vs. Electrical r2 Gmm F e e G = Gravitational](https://reader035.fdocuments.net/reader035/viewer/2022063021/5fe5a55eae60b1320c4c8e2d/html5/thumbnails/147.jpg)
147
Solid Conducting Sphere with total charge Q.
E=Qinside
o
+ +
+
+
+
+
+
+
+
+
+
+
All charge will lie on the surface of the conducting sphere.
E A=Qo
E 4 r2 =0E=0
r < R
Rr