L4 Ch24 Gauss Law - Faculty Server...
Transcript of L4 Ch24 Gauss Law - Faculty Server...
Department of Physics and Applied PhysicsPHYS.1440 Lecture 3 Danylov
Course website:http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII
Lecture 3
Chapter 24
Gauss’s Law
95.144
Physics II
Department of Physics and Applied PhysicsPHYS.1440 Lecture 3 Danylov
Today we are going to discuss:
Chapter 24:
Section 24.4 Gauss’s Law
Department of Physics and Applied PhysicsPHYS.1440 Lecture 3 Danylov
Φ ∙
Gauss’s LawFor any closed surface enclosing total charge Qin,
the net electric flux through the surface is:
This result for the electric flux is known as Gauss’s Law.
q1
q3
q2
Gaussian surface
q5
q4
1) It works for any closed surface called Gaussian
2) Qin is the net charge enclosed by the Gaussian surface (charges outside must not be included)
3) Distribution of Qin doesn't matter
(A Gaussian surface is an imaginary, mathematical surface)
Gaussian surface
Both, Gauss’s law and Coulomb’s law, help to find electric fields based on distribution of charges.
Properties:
dA
E
Department of Physics and Applied PhysicsPHYS.1440 Lecture 3 Danylov
Gauss’s Law/Symmetry
Evaluation of this surface integral is often difficult. However, when the charge distribution has sufficient symmetry (spherical, cylindrical, planar),
evaluation of the integral becomes simple.
Φ ∙Gaussian surface
Which spherical Gaussian surface has the larger electric flux?
ConcepTest Gauss’s LawA) Surface AB) Surface BC) They have the same fluxD) Not enough information to tell
Flux depends only on the enclosed charge, not the radius.
Determine the electric flux through each surface
Example Electric Flux
Flux depends only on the enclosed charge, not the radius.
Φ ∙
S1: Φ=(+Q-3Q)/ε0
S2: Φ=(+Q+2Q-3Q)/ε0
S3: Φ=(+2Q-3Q)/ε0
S4: Φ=0 (no charge inside)S5: Φ=(+2Q)/ε0
Department of Physics and Applied PhysicsPHYS.1440 Lecture 3 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
Department of Physics and Applied PhysicsPHYS.1440 Lecture 3 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
Department of Physics and Applied PhysicsPHYS.1440 Lecture 3 Danylov
Find the electric field of an infinitely long line of charge with
linear charge density λ (C/m).
Example 24.4
Example E field outside of a long, charged wire
Department of Physics and Applied PhysicsPHYS.1440 Lecture 3 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
Department of Physics and Applied PhysicsPHYS.1440 Lecture 3 Danylov
Thank you