Gauss's Law · Rod Example: Charge density changes according to the function... ρ = a/r2 where a...

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Gauss's Law Deriving Gauss's law using Coulombs Law

Transcript of Gauss's Law · Rod Example: Charge density changes according to the function... ρ = a/r2 where a...

Page 1: 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

Gauss's Law

Deriving Gauss's law using Coulombs Law

Page 2: 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

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

Deriving Coulomb's Law using Gauss's Law

Page 4: 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

What the flux is going on inside a chaaaged insulator?

R

Page 5: 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

ERF

Page 6: 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

Finding E­field in and Around a Hollow Metal Sphere

Page 7: 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

Finding E field near the middle of a long charged rod...

Page 8: 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

Finding E Field near middle of a charged sheet...

Page 9: 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

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!

Page 10: 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

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

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

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.

Page 13: 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
Page 14: 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

The Shadow Trick!

Page 15: 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
Page 16: 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

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.

Page 17: 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

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!


Target Boards, JEE Main & Advanced (IIT), NEET 2015 ...vidyadrishti.com/gauss's law boards 2015 notes.pdf · Gauss’ Law Author: Pranjal K. Bharti (IIT Kharagpur) Mb: 7488044834

Target Boards, JEE Main & Advanced (IIT), NEET 2015 ...vidyadrishti.com/gauss's law boards 2015 notes.pdf · Gauss’ Law Author: Pranjal K. Bharti (IIT Kharagpur) Mb: 7488044834

B.Sc. (GENERAL) PROGRAMME PHYSICS (PHYG)dcbgirlscollegejorhat.org/Syllabus/Physics.pdf · Gauss's law and its application to calculation of fields due to hollow and solid sphere ,energy

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