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Physics 202, Lecture 2
Today’s Topics
Electric Fields (Ch 21.6-21.11) Determining the Electric Field of given charge
distribution (discrete and continuous) Electric Field Lines Motion of Charged Particles in External Electric Fields
Announcements: No honors lecture tomorrow
Coulomb’s Law: Vector Form
!F21= ke
q1q2
r2r̂ = !
!F12
2 charges: force on q2 by q1
12r̂
principle of linear superposition
Multiple charges: force on charge i
F12
F21
F12
F21
Examples (board): 21.18, 21.20
!Fi =
!Fij
j
! = kqiqj
rij2r̂ij
i
!
2
The Electric Field
Original (Coulomb’s) view: q applies electric force on q0 (action at a distance)
Force on charge always proportionalto strength of that charge!
“Modern” view:q is source of electric field E, which fills all of space.
Interaction with the field leads to a force on q0
!F = k
q0q
r2r̂
!F = q
0kq
r2r̂ = q
0
!E q: source charge
E independent of q0!
q0
qF
F
(q0 often called the “test charge”: take the limit as )q0! 0
Aside: Vector and Scalar Fields
What is a field?
A physical quantity which has a value at each pointin space (for example: temperature, wind speed,…)
Here we will consider only scalar fields (e.g., temperature, electricpotential,…) and vector fields (e.g., windspeed, electric fields,…)
Concept of the electric field (and the magnetic field) is the most useful way to describe the physics of electromagnetism.
3
A Scalar Field
77 82
83685566
8375 809091
757180
72
84
73
8288
92
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
757180
72
84
73
57
8892
77
5688
7364
This is a vector field(specify both wind speed and direction)
Example: the way the wind is blowing…
4
Calculating the Electric Field for aGiven Charge Distribution
E field of point charge q:
Multiple point charge sources
Continuous distributions:
!E = k
q
r2r̂
!E =
!Ei
i
! = kqi
ri2r̂i
i
!
d!E = k
dq
r2r̂
!r
q
P
(observation point)
!E = d
!E!
!r
dq
P
Examples: 21.41, 21.40 (ring), line charge, disk
Visualizing the Electric Field: Field Lines
+
+ chg
Field lines
Visualize the electric field of a positive point charge:
Magnitude: local density of linesDirection: direction of arrows
Rules for Field Lines:
Field lines start or end only on charges (never empty space). They start on positive and end on negative charges.
Field lines of point charges extend toinfinity (true for any localized distributionwith nonzero net charge).
Field lines can never cross.
5
Example: Point-Like Charges
+q -q
!E(!r ) = k
q
r2r̂
!E(!r ) = k
q
r2r̂
Examples: Two Charged Particles
+q and +q +q and -q(dipole)
6
Two Charged Particles
Motion Of Charged Particle In Uniform Electric Field
Fundamental Formulas:
F=qE
a=F/m = qE/m v= vi +at
E
+q
-q
If initially at rest (vi =0) then v= at = (qE/m) t
Motion of +q:Same dir. as E
Motion of - q:
Opposite dir. as E
Examples: 21.56, 2d example (next slide)
7
Exercise: An Electron in a Uniform E. Field
Find out vertical displacement after the electronpasses through a downward uniform electric field E
Answer: y= - ½ (e/m)E (l/vi)2