l5 ch24 gauss law - cpb-us-w2.wpmucdn.com€¦ · chapter 24: section 24.4: gauss’s law....
TRANSCRIPT
DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture5 A.Danylov
Lecture 5
Chapter 24
Gauss’s Law
95.144
Physics II
What? Surface integration?He must be kidding!
Course website:https://sites.uml.edu/andriy-danylov/teaching/physics-ii/
DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture5 A.Danylov
Today we are going to discuss:Chapter 24:
Section24.4:Gauss’s Law
DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture5 A.Danylov
Φ ∙
Gauss’s Law
ForanyclosedsurfaceenclosingtotalchargeQin,thenetelectricfluxthroughthesurfaceis:
This result for the electric flux is known as Gauss’s Law.
q1
q3
q2
Gaussian surface
q5
q4
1)ItworksforanyclosedsurfacecalledGaussian
2)QinisthenetchargeenclosedbytheGaussiansurface(chargesoutsidemustnotbeincluded)
3)DistributionofQindoesn'tmatter
(AGaussiansurfaceisanimaginary,mathematicalsurface)
Gaussian surface
Both, Gauss’s law and Coulomb’s law, help to find electric fields based on distribution of charges.
Properties:
dA
E
DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture5 A.Danylov
Gauss’s Law/Symmetry
Evaluationofthissurfaceintegralisoftendifficult.However,whenthechargedistributionhassufficientsymmetry(spherical,cylindrical,planar),evaluationof
theintegralbecomessimple.
Φ ∙Gaussian surface
DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture5 A.Danylov
Notice a remarkable feature of this result:The field outside the sphere isexactly the same as it would have beenif all the charge had beenconcentrated at the center.
A total charge Q is spread uniformly throughout a dielectric sphere of radius R. What is the electric field outside the sphere (r>R)?
Example E field outside of a charged dielectric sphere
Example 24.3
DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture5 A.Danylov
A total charge Q is spread uniformlythroughout a dielectric sphere ofradius R. What is the electric fieldinside the sphere (r<R)?
ELet’s plot it
Example E field inside of a charged dielectric sphere
Example 24.4
DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture5 A.Danylov
Suppose the nonconducting sphere hasa spherical cavity of radius a centeredat the sphere’s center. Assuming thecharge Q is distributed uniformly inthe “shell” (between r = b and r = a),determine the electric field as afunction of r fora) r < ab) a < r < bc) b < r
Example E field created by a sphere with a spherical cavity
DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture5 A.Danylov
Findtheelectricfieldofaninfinitelylonglineofchargewithlinearcharge
densityλ (C/m).
Example 24.4
Example E field outside of a long, charged wire
DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture5 A.Danylov
Find the electric field of an infinitely long line of charge with volume charge density ρ (C/m).
Problem 24.50(b)
Example E field inside of a long, charged wire
DepartmentofPhysicsandAppliedPhysicsPHYS.1440Lecture5 A.Danylov
Thank you