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Lecture 3.1 :!Electric Flux

Lecture Outline:!Motion in a Uniform Electric Field !

Symmetry and Electric Fields!Electric Flux!Gauss’s Law!

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Jan. 27, 2015

Textbook Reading:!Ch. 26.6 - 27.3

Announcements

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•Quiz #2 in class Thu. (Jan. 29) covers Ch. 26 material (through 26.5).!

•HW3 due next Tue. (2/3) at 9am on Mastering Physics. Are the “Hints” working for everyone? !

•Read through Ch. 27 this week, preferably before your recitations.!

•Note: I will be out of town next week. Prof. Gianfranco Vidali will substitute for me.!

•Please let me know if you are having any difficulties with the material in the course.

Last Lecture...

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E-field of an infinite plane of charge:

as R → ∞

Last Lecture...

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Clicker Question #1

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Three points inside a parallel-plate capacitor are marked. Which is true?

A.  E1 > E2 > E3 B.  E1 < E2 < E3 C.  E1 = E2 = E3

D.  E1 = E3 > E2

Clicker Question #1

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Three points inside a parallel-plate capacitor are marked. Which is true?

A.  E1 > E2 > E3 B.  E1 < E2 < E3 C.  E1 = E2 = E3

D.  E1 = E3 > E2

Last Lecture...

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Parallel-plate capacitor has plates which are much larger than the separation between the plates (d). As long as this is true, electric-field has no dependence on plate spacing.

Last Lecture...

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I create a capacitor by moving 1011 electrons from one side to the other.

If d=5.0mm, and the plates have radius = 3.0cm, What’s the E-field

inside?

Motion in a Uniform Electric Field

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A charged object placed in an electric field experiences a force.

Motion in a Uniform Electric Field

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Infinite planes, and parallel plate capacitors, create electric fields that are uniform (same magnitude and direction at all points in

space)

F=ma=qE

Motion in a Uniform Electric Field

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You’ve already studied motion of objects subject to a constant acceleration in another class...gravitational acceleration!

Projectile Motion due to gravity

Motion in a Uniform Electric Field

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You’ve already studied motion of objects subject to a constant acceleration in another class...gravitational acceleration!

Projectile Motion due to gravity

Motion of an electron beam (“cathode ray”) in a TV

Motion in a Uniform Electric Field

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I place an Electron inside the capacitor I made earlier, next to the negative side. How long does it take to cross? What’s its speed when it reaches the positive side?

Clicker Question #2

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Which Electric Field is responsible for the proton’s trajectory?

Clicker Question #2

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Which Electric Field is responsible for the proton’s trajectory?

Clicker Question #2

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Which Electric Field is responsible for the proton’s trajectory?

Which answer would be correct if the proton were replaced by an electron in the diagram?

Motion in a Uniform Electric Field

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Dipole in a Uniform Electric Field

Dipole in a Non-Uniform Electric Field

Dipoles in a non-uniform Electric Field

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Dipoles in a non-uniform Electric Field

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Changing Gears

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You now have a basic understanding of what an Electric Field is, and how to determine it for an arbitrary

distribution of charge. !In Ch. 27, we learn an important technique that greatly

simplifies the process for charge distributions with special symmetries.

Symmetry and Electric Fields

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Fiddler Crab (male of the species)Snowflake

Symmetry (or the lack thereof) is an important concept that physicists (and other scientists) like to identify in things they are studying.

Symmetry and Electric Fields

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We can often say a lot about electric fields and charge distributions using arguments of symmetry.

Symmetry and Electric Fields

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We can often say a lot about electric fields and charge distributions using arguments of symmetry.

Symmetry and Electric Fields

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We can often say a lot about electric fields and charge distributions using arguments of symmetry.

Symmetry and Electric Fields

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We can often say a lot about electric fields and charge distributions using arguments of symmetry.

Symmetry and Electric Fields

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Electric Flux

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Given some unknown charge distribution (hidden inside a box, for example), we can

study its character based on the E-field lines passing in/out of the box.

The box in these examples is just an imaginary surface!

Electric Flux

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Given some unknown charge distribution (hidden inside a box, for example), we can

study its character based on the E-field lines passing in/out of the box.

The box in these examples is just an imaginary surface!

Electric Flux

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Given some unknown charge distribution (hidden inside a box, for example), we can

study its character based on the E-field lines passing in/out of the box.

The box in these examples is just an imaginary surface!

Electric Flux

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Electric Flux = The amount of electric field passing through a surface.

Electric Flux

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Given an arbitrary surface (not necessarily a nice flat one), in an E-field (not necessarily a nice uniform one):

Clicker Question #3

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A.  Surface A has more flux.

B.  Surface B has more flux.

C.  The fluxes are equal.

D.  It�s impossible to say without knowing more about the electric field.

Surfaces A and B have the same shape and the same area. Which has the larger electric flux?

Clicker Question #3

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A.  Surface A has more flux.

B.  Surface B has more flux.

C.  The fluxes are equal.

D.  It�s impossible to say without knowing more about the electric field.

Surfaces A and B have the same shape and the same area. Which has the larger electric flux?

Electric Flux

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If the surface is closed (like the earlier box example), we need to integrate over the whole surface.

Gauss’s Law

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Gauss’s Law

Gauss’s Law

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How about the flux of numerous point charges?

Gauss’s Law

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How about the flux of numerous point charges?

Gauss’s Law

Reminders

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•Take advantage of office hours (Tue., 3-5pm) and physics clinic.!

•ALL questions assigned in recitation are fair game for use on exams and quizzes!!

•Please put in the time/effort on your homeworks/recitation…it will pay off at exam/quiz time!!

•Quiz #2 on Thursday.