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