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Transcript
```Lecture 3.1 :!
Electric Flux
Lecture Outline:!
Motion in a Uniform Electric Field !
Symmetry and Electric Fields!
Electric Flux!
Gauss’s Law!
!
Ch. 26.6 - 27.3
Jan. 27, 2015
1
Announcements
•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? !
•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.
2
Last Lecture...
E-field of an infinite plane of charge:
as R → ∞
3
Last Lecture...
4
Clicker Question #1
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
5
Clicker Question #1
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
5
Last Lecture...
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.
6
Last Lecture...
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?
7
Motion in a Uniform Electric Field
A charged object placed in an electric field experiences a force.
8
Motion in a Uniform Electric Field
Infinite planes, and parallel plate capacitors, create electric fields
that are uniform (same magnitude and direction at all points in
space)
F=ma=qE
9
Motion in a Uniform Electric Field
You’ve already studied motion of objects subject to a constant
acceleration in another class...gravitational acceleration!
Projectile Motion
due to gravity
10
Motion in a Uniform Electric Field
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
10
Motion in a Uniform Electric Field
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?
11
Clicker Question #2
Which Electric Field is responsible for the proton’s trajectory?
12
Clicker Question #2
Which Electric Field is responsible for the proton’s trajectory?
12
Clicker Question #2
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?
12
Motion in a Uniform Electric Field
Dipole in a Uniform
Electric Field
Dipole in a Non-Uniform
Electric Field
13
Dipoles in a non-uniform Electric Field
14
Dipoles in a non-uniform Electric Field
14
Changing Gears
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.
15
Symmetry and Electric Fields
Symmetry (or the lack thereof) is an important concept that physicists
(and other scientists) like to identify in things they are studying.
Fiddler Crab (male of the
species)
Snowflake
16
Symmetry and Electric Fields
We can often say a lot about electric fields and charge
distributions using arguments of symmetry.
17
Symmetry and Electric Fields
We can often say a lot about electric fields and charge
distributions using arguments of symmetry.
17
Symmetry and Electric Fields
We can often say a lot about electric fields and charge
distributions using arguments of symmetry.
17
Symmetry and Electric Fields
We can often say a lot about electric fields and charge
distributions using arguments of symmetry.
17
Symmetry and Electric Fields
18
Electric Flux
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!
19
Electric Flux
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!
19
Electric Flux
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!
19
Electric Flux
Electric Flux = The amount of electric field passing
through a surface.
20
Electric Flux
Given an arbitrary surface (not necessarily a nice flat
one), in an E-field (not necessarily a nice uniform one):
21
Clicker Question #3
Surfaces A and B have
the same shape and the
same area. Which has
the larger electric flux?
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
22
Clicker Question #3
Surfaces A and B have
the same shape and the
same area. Which has
the larger electric flux?
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
22
Electric Flux
If the surface is closed (like the earlier box example), we
need to integrate over the whole surface.
23
Gauss’s Law
Gauss’s Law
24
Gauss’s Law
numerous point charges?
25
Gauss’s Law
numerous point charges?
Gauss’s Law
25
Reminders
!
•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!!