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1
Physics 202, Lecture 2
Today’s Topics
Announcements
Electric Fields More on the Electric Force (Coulomb’s Law) The Electric Field Motion of Charged Particles in an Electric Field
Announcements Homework Assignment #1:
WebAssign (corresponds to Ch. 23 #5,10,12,15,19,26,42)
Due Friday, Sept 14 at 10PMFuture assignments will be due Mondays at 10 PM.
IMPORTANT: Exam policy revisionIf you have an evening class conflict, let us know
right away (now!) and we will accommodate it. Recall exam dates: 10/1, 10/29, 11/26, 5:30-7 PM.
2
Coulomb’s Law (Point Charges)
!F21= !ke
q1q2
r2r̂
Force on q2 by q1:
Force on q1 by q2:
r
!F12= ke
q1q2
r2r̂
Vector direction of F: more explicitly
!r1
!r2
q1
q2
!r2!!r1
!F12= ke
q1q2
|!r2!!r1|2
(!r2!!r1)
|!r2!!r1|= ke
q1q2(!r2!!r1)
|!r2!!r1|3
in the above language: r =|!r2!!r1|
r̂ =
!r2!!r1
|!r2!!r1|
Force on q2 by q1:
Coulomb’s Law: Multiple charges
Many point charges: linear superposition
!F1=
!Fi1
i
! = keq1qi
ri12r̂i1
i
!
!r1
!r2
q1
q2
!r1!!r2
!F1= ke
q1qi
|!r1!!ri |
2
i
"(!r1!!ri )
|!r1!!ri |
= keq1qi (!r1!!ri )
|!r1!!ri |
3
i
"
q3
!r3
Force on charge 1:
More explicitly:
Important: vector sum!
3
Coulomb’s Law: DistributionsContinuous distributions of charge: divide into
!qii
" # dq$
Line segment (1 dimension): dq = !dx
!qi
Surface (2 dimensions): dq = !dA
Volume (3 dimensions): dq = !dV
more about this shortly!
Interaction of point charge with continuous distribution:
!F1= keq1
dq
r2r̂!
One of four fundamental forces: Strong >Electromagnetic > weak >> gravity Magnitude: Proportional to 1/r2 : r doubled ¼ F Direction: repulsive for like signs, attractive for opposite signs
A conservative force (work independent of path):
A potential energy can be defined. (Topic of Ch. 25)
Properties of the Electric Force
r
qqkU e 21
=
)()(2121if
i
e
f
er
rUU
r
qqk
r
qqkrdFW
f
i
!!!=+!=•= "!!
4
The Electric Field
Original (Coulomb’s) view of electric force q applies electric force on q0 (action at a distance)
Force on charge always proportionalto strength of that charge!
“Modern” view of electric force: q is the source of an electric field E
The electric field E applies a force on q0
!F = ke
q0q
r2r̂
!F = q
0keq
r2r̂ = q
0
!E
E
q: source chargeq0: “test charge”E independent of q0!
q0
qF
Aside: Vector and Scalar Fields
What is a field?•A field represents some physical quantity
(e.g., temperature, wind speed, force)•It can be a scalar field (e.g., temperature field)•It can be a vector field (e.g., electric field)•It can be a “tensor” field (e.g., spacetime curvature)
The field concept is extremely useful in physics,both conceptually and for practical purposes
Using the concept of the electric field,one can map the electric field anywhere in spaceproduced by any arbitrary charge distribution
5
A Scalar Field
7782
83685566
8375 8090 91
757180
72
84
73
82
8892
7788
887364
These isolated temperatures sample the scalar field(you only learn the temperature at the point you choose,
but T is defined everywhere (x, y)
A Vector Field
7782
83685566
8375 809091
7571
80
72
84
73
57
8892
77
5688
7364
That would require a vector field(you learn both wind speed and direction)
Perhaps more interesting to know which way the wind is blowing…
6
The Electric Field, Recap Charge q sources an electric field E
(charge at origin) More generally,
Multiple sources:
Continuous distributions:
!!r
!r
q
!E(!r ) = ke
q
r2r̂
!r
q
P
P
!E(!r ) = ke
q
|!r !!"r |2
(!r !!"r )
|!r !!"r |= ke
q(!r !!"r )
|!r !!"r |3
!r !!"r
!E(!r ) = ke
qi
ri2r̂i
i
!
!E(!r ) = ke
qi (!r !!"ri )
|!r !!"ri |3
i
#
!E(!r ) = ke
dq(!r !!"r )
|!r !!"r |3#
!E(!r ) = ke
dq
r2r̂!
(more general)
Visualizing the Electric Field
+
+ chg
field lines
+ charge
vector map map
+
Consider the electric field of a positive point charge at the origin:
Magnitude: length of arrows Magnitude: local density of lines
7
Rules for Field Lines
Field lines can start or terminate only on charges, never empty space.
Property 1.
Property 2.Field lines of point charge go off to infinity.(true for any localized distribution with nonzero net charge)
Property 3.Field lines originate on positive charges, terminate on negative charges.
Property 4.
No two field lines ever cross, even when multiple charges present.
Example: Point-Like Charges
+q -q
!E(!r ) = ke
q
r2r̂
!E(!r ) = ke
q
r2r̂
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