gauss's law · rod example: charge density changes according to the function... ρ = a/r2...
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Gauss's Law
Deriving Gauss's law using Coulombs Law
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Gauss's Law
φE = ∮E dA = εo
• qin
![Page 3: Gauss's Law · Rod Example: Charge density changes according to the function... ρ = a/r2 where a is a constant. R φ E = ∮E dA = ε o • q in Then sub into Gauss's Law and proceed](https://reader033.vdocuments.mx/reader033/viewer/2022050104/5f431e7b0a9b0370e4512c18/html5/thumbnails/3.jpg)
Deriving Coulomb's Law using Gauss's Law
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What the flux is going on inside a chaaaged insulator?
R
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ERF
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Finding Efield in and Around a Hollow Metal Sphere
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Finding E field near the middle of a long charged rod...
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Finding E Field near middle of a charged sheet...
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Does your G
aussian surface contain a net charge?
NO
YES*Strength of Efield can not be determ
ined, but if you are given E then could find a value for the flux entering or leaving one face of the surface using...
What type of m
aterialdoes your G
aussian surface contain?
CONDUCTORINSULATOR
Is your Gaussian
surface inside the m
aterial?
Is your Gaussian
surface inside the m
aterial?
YES
NO
YESIs the charge
uniformly distributed
through the material?
NO
NO
YES
THEN
THEN
The Lee Swindell Inspired G
aussian Flow Chart D
eluxe
This chart is a fluxing good idea!
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What the flux is up with nonuniform charge densities?
• They require that you perform an extra "shell" method integration just to find the enclosed charge.
• They only show up in two places...rods and spheres made of nonconducting material.
• You will be given a function for how the charge density changes as you move through the object.
Spherical Example:
Charge density changes according to the function...ρ = a/r where a is a constant.
R
φE = ∮E dA = εo
• qin
Then sub into Gauss's Lawand proceed as per usual.
![Page 11: Gauss's Law · Rod Example: Charge density changes according to the function... ρ = a/r2 where a is a constant. R φ E = ∮E dA = ε o • q in Then sub into Gauss's Law and proceed](https://reader033.vdocuments.mx/reader033/viewer/2022050104/5f431e7b0a9b0370e4512c18/html5/thumbnails/11.jpg)
Rod Example:Charge density changes according to the function...ρ = a/r2 where a is a constant.
R
φE = ∮E dA = εo
• qin
Then sub into Gauss's Lawand proceed as per usual.
![Page 12: Gauss's Law · Rod Example: Charge density changes according to the function... ρ = a/r2 where a is a constant. R φ E = ∮E dA = ε o • q in Then sub into Gauss's Law and proceed](https://reader033.vdocuments.mx/reader033/viewer/2022050104/5f431e7b0a9b0370e4512c18/html5/thumbnails/12.jpg)
What the flux is up with a charged ball bearing inside a charged metal spherical shell?
+3 Q
+12 Q
Find the Efield everywhere and the charge on all surfaces.
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The Shadow Trick!
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R
r
Integrate to find enclosed charge.
Use Gauss's Law for Sphere
Shell Method: Surface area of shells "bleeds" into third dimension giving you volume.
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r
rs
rc
P
Find the Efield at point P which is the midpoint of the center to center distance r. Use only the variables given, and known constants. Both objects are insulators with a negative charge and a uniform volume charge density ρ.
sphere
cylinder
WTF(What the Flux)
First Find EField @ P from sphere using Gaussian sphere of radius r/2...
Finally superimpose the two Efields
*Note that because both objects are negativethe fields would be pointing opposite directions.
*Note that without knowing a value for r c and rs we have no way to know if E tot would be pointing up or down.
Next find Efield from cylinder @ P using Gaussian can of radius r/2...
That answer is notfluxing pretty!