Agenda • Today Continuous Charge Distribution • Tuesday – lab 5 & Quiz • Wed&Fri – Chapter 24 • Today – Continuous Charge Distribution • Gravity Equivalent • Complex Layers • HMWK CH. 22 Up Today • HMWK Due Thurs.
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Agenda
• Today Continuous Charge Distribution• Tuesday – lab 5 & Quiz• Wed&Fri – Chapter 24• Today
– Continuous Charge Distribution• Gravity Equivalent• Complex Layers
• HMWK CH. 22 Up Today• HMWK Due Thurs.
Fields & Potential In a SolidGravity First
EarthM=ME
R=RE
V=(4/3)RE3
SA=4RE2
=M/V=3ME/(4rE3)
Even Distribution?
Solid ObjectsDensityVolumeSurface AreaMass
Electrical ObjectsCharge & Charge Density
Find the ZeroesUse reference 0 at infinity (Usual)
EarthM=ME
R=RE
V=(4/3)RE3
SA=4RE2
=M/V=3ME/(4rE3)
Even Distribution
Where is FG=0?Where is PEG = 0?
Gauss’s LawField then Force?
EarthM=ME
R=RE
V=(4/3)RE3
SA=4RE2
=M/V=3ME/(4rE3)
Even Distribution
Flux = Field x Area= EA
0
4
4
1
E dA
qkq
Gm
Gauss’s LawField at a point r?
EarthM=ME
R=RE
V=(4/3)RE3
SA=4RE2
=M/V=3ME/(4rE3)
Even Distribution
0
4
4
1
E dA
qkq
Gm
Choose Surface so E Perp to it.Also, E constant across surfaceFor point charge/sphere Sphere
Gauss’s LawField at a point r?
EarthM=ME
R=RE
V=(4/3)RE3
SA=4RE2
=M/V=3ME/(4rE3)
Even Distribution
0
2 2
4
4
14 1
1
4
4
E dA EA
qkq
Gm
GmE
A
Gm GmE
r r
What if “Surface” inside Earth?What is m in equation?
Gauss’s LawField at a point r?
EarthM=ME
R=RE
V=(4/3)RE3
SA=4RE2
=M/V=3ME/(4rE3)
Even Distribution
0
2 2
4
4
14 1
1
4
4
E dA EA
qkq
Gm
GmE
A
Gm GmE
r r
What if “Surface” inside Earth?What is m in equation?
Gauss’s LawField at a point r?
EarthM=ME
R=RE
V=(4/3)RE3
SA=4RE2
=M/V=3ME/(4rE3)
Even Distribution
2encl
encl
GmE
rm V
Vencl=(4/3)r3
Gauss’s LawField at a point r?
EarthM=ME
R=RE
V=(4/3)RE3
SA=4RE2
=M/V=3ME/(4rE3)
Even Distribution
2
32
, is constant
4
3
4
3
encl
encl
GmE
rm V
GE r
r
E G r
Where (r) is field zero?
EarthM=ME
R=RE
V=(4/3)RE3
SA=4RE2
=M/V=3ME/(4rE3)
Even Distribution
2
32
3
3
, is constant
4
3
4
3
34
3 4
encl
encl
E
E
E
E
GmE
rm V
GE r
r
E G r
ME G r
r
ME Gr
r
Where (r) is field zero?
Inside: E=Gr(ME/rE3)
Outside: E=GME/r2
Two SituationsWhere is “Special Point”Where r = rE
Both must have same valueWorks: Both E=GME/rE
2 Inside zero: at center of earthGravitational pull cancels outOutside only zero at infinityCase similar for small - q & big + qWhat can be different for Elect?Material Dependence!
Interesting Graph3D Charge Distribution
E
r
r r=rE
Linear Inside1/r2 outside
DiscontinuityValue Same
What if charged conductor?
MetalCharge = +Q
Where is field zero?Everywhere inside metalOutside, E=kQ/r2
Outside is just air
+ ++
+
++
+
+
+
+
+
+
++
+
++
+
+
++
++
+ +
Interesting Graph3D Metal
E
r
r r=rE
Zero Inside
1/r2 outside
DiscontinuityValue Not Same?
Real Graph3D Metal
E
r
r r=rE
Zero Inside
1/r2 outside
DiscontinuityValue Same
Exponential Decay Near SurfaceNanoScale
Potential of Charged Conductor?
MetalCharge = +QR=rE, etc..
What is potential in a metal?ConstantWhere can we find a value?At edge, r=rE V=kQ/r outsideV=kQ/rE at edgeV=kQ/rE throughout
Outside is just air
+ ++
+
++
+
+
+
+
+
+
++
+
++
+
+
++
++
+ +
Interesting Graph3D Metal
V
r
r r=rE
Constant Inside
1/r outside
DiscontinuityValue Same
What if charged Insulator?
InsulatorCharge = +Q
=1R=RE, etc…
Where is field zero?At center & InfinityOutside, E=kQ/r2 Inside, E=(k/)(Qr/rE
3)See can make life interestingFor now, = 1.E=(k)(Qr/rE
3)
Outside is just air [ = 1]
+ ++
+
++
+
+
+
+
+
+
++
+
++
+
+
++
++
+ +
3E
E
ME Gr
r
Interesting Graph3D Insulating Charge
E
r
r r=rE
Linear Inside1/r2 outside
DiscontinuityValue Same
What if >1?
Interesting Graph3D Insulating Charge
E
r
r r=rE
Linear Inside1/r2 outside
DiscontinuityValue Not Same?
What if >1? Field becomes smaller inside
Interesting Graph3D Insulating Charge
E
r
r r=rE
Linear Inside1/r2 outside
DiscontinuityValue Always Same!
What if >1? Field becomes smaller insideIn transition region from inside to outside, k changes value.
ExponentialBridge
What if charged Insulator?Potential, = 1
InsulatorCharge = +Q
=1R=RE, etc…
Outside is just air [ = 1]
+ ++
+
++
+
+
+
+
+
+
++
+
++
+
+
++
++
+ +
3
2
23
23
, is constant
4
3
4
3
4 3
3 4
encl
encl
E
E
kQV
rm Vol
kV r
r
V k r
QV k r
r
QV kr
r
Potential Graph3D Insulating Charge
V
r
r r=rE
Quadratic1/r outside
DiscontinuityValue Always Same!
What if >1?
What now? Metal Shell
InsulatorCharge = +Q
=1R=RE, etc…
Outside is just air [ = 1]
+ ++
+
++
+
+
+
+
+
+
++
+
++
+
+
++
++
+ +
What now? Metal Shell
InsulatorCharge = +Q
=1R=RE, etc…
Outside is just air [ = 1]
+ ++
+
++
+
+
+
+
+
+
++
+
++
+
+
++
++
+ +What does chargeOn shell look like?
What now? Metal Shell
InsulatorCharge = +Q
=1R=RE, etc…
Outside is just air [ = 1]
+ ++
+
++
+
+
+
+
+
+
++
+
++
+
+
++
++
+ +What does chargeOn shell look like?
-
-
-
-
--
-
-
-
-
+
+
+
+
+
++
+
Metal Shell
InsulatorCharge = +Q
=1R=RE, etc…
+ ++
+
++
+
+
+
+
+
+
++
+
++
+
+
++
++
+ +
How much –q on shell?|+q|=|-q|=Q
-
-
-
-
--
-
-
-
-
+
+
+
+
+
++
+
E = 0 in shellE=Qencl/A E=0 Qencl=0
Agenda
• Today Continuous Charge Distribution• Tuesday – lab 5 & Quiz• Wed&Fri – Chapter 24• Today
– Continuous Charge Distribution (if Time)• Gravity Equivalent• Complex Layers
• HMWK CH. 22 Up Today• HMWK Due Thurs.
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