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Physics 202, Lecture 2
Today’s
Today
s Topics
„
Electric Force and Electric Fields
„ Electric Charges and Electric Forces
„ Coulomb's Law
„ Physical Field
„ The Electric Field
„ Electric Field Lines
„ Motion
M ti off Charged
Ch
d Particle
P ti l in
i Electric
El t i Field
Fi ld
A Reminder
Lectures supplement but do not substitute for reading !
Lecture Effectiveness =
Preview + Lectures + Review
Properties of Electric Charges
ƒ
ƒ
ƒ
ƒ
2+1 types: positive, negative (+neutral).
Unit: Coulomb (C). 1 C= charge of 6.24x1018 protons.
19 C
El
Electric
i charge
h
is
i quantized:
i d q=±Ne,
N
e=1.602x10
1 602 10-19
Building blocks of matters:
Charge (C)
Electron
Proton
Neutron
-e=-1.602x10-19
+e=+1
+e
+1.602x10
602x10-19
0
Mass (kg)
9.11x10-31
1 673x10-27
1.673x10
1.675x10-27
ƒ Electric charge is conserved: charges can be moved
around, but the total charge remains the same.
‰ For deep thinkers: Why electrons and protons have
th same electric
the
l t i charge?
h
?
Electric Force And Coulomb’s Law
‰ Electric forces exist between two charged particles
‰ The direction of electric force depends on the signs of
the charges:
ƒ forces between opposite sign charges are attractive
ƒ forces between like sign
g charges
g are repulsive
p
+
-
-
+
+
+
-
-
‰ The
Th magnitude
it d off the
th electric
l t i forces
f
for
f point
i t charges
h
q1 q2
F12 = F21 = ke 2
r
(Coulomb’s
(Coulomb
s Law)
Coulomb Constant: ke = 8.987x109Nm2/C2 = 1/(4πε0)
ε0: permitivity of free space
Numeric Examples: Electric Force Is Huge
‰ Electric force between two 1C charges 1 meter apart:
F=8.99x109N
‰ Proton and electron in a hydrogen atom:
qelectron= -1.6x10-19 C, qproton= 1.6x10-19 C, r=5.3x10-11m
Æ Electric force F= 8
8.2
2 x10-8 N.
N
¾ This force is huge:
ƒ Compared to the mass of proton: 1.673x10
1 673x10-27 kg
ƒ Compared to the gravitational forces between them:
FG= 3.6x10-47N ((recall: FG=Gm1m2/r2)
™ Four fundamental forces:
Strong > Electromagnetic > Weak >> Gravitational
Coulomb’s Law in Vector Form
r
q1q2
E. Force on q2 by q1: F12 = Ke 2 r̂12
r
r
r
q1q2
E. Force on q1 by q2: F21 = Ke 2 rˆ21 = −F12
r
ƒ Exercise:
Use this vector form to verify
the attractive/repulsive feature
ƒ Note:
Multiple particles on charge i,
Fi= F1i+F2i+ F3i +….
r
r̂12
Exercise:
Electric Forces Due to Two Charged
g Particles
‰ Find the electric force on q3.
Solution: See board.
board
Properties of the Electric Force
‰ It is one of four fundamental forces:
Strong >Electromagnetic > weak >> gravity
‰ It is proportional to 1/r2 : double r Æ ¼ F
‰ Its direction is charge sign dependent:
like signÆ repulsive, opposite sign Æ attractive
‰ It is a conservative force. (Work independent of path)
W =∫
rf
ri
r r
ke q1q2 ke q1q2
F • dr = −
+
= ( −U f ) − ( −U i )
rf
ri
ÎA potential energy can be defined. (Ch. 25)
ke q1q2
U=
r
A Very Important Concept: Field
‰What is a “field” ?
Field: A physical quantity which has a physical value*
at each point in space (i.e. a distribution).
Examples of physical fields:
temperature,
p
, wind speed,
p
, electric field,, magnetic
g
field,, …
™ In this course, we consider only scalar and vector physical
quantities.
Example of Scalar and Vector Fields
Temperature (scalar)
Wind speed (vector)
Measurement can be made at any point on the map.
The Coulomb’s Law Revisited
‰ Original (Coulomb’s) view of electric force:
q1 directly applies an electric force on q2
r
q1q2
F12 = Ke 2 r̂12
r
‰ “Modern” view of electric force:
ƒ q1 creates an electric field E around it
ƒ The electric field E applies a force on q2
r
r
q1
F2 = Ke 2 rˆ12 q2 = E q2
r
E
In this modern view:
q1: source charge
q2: test charge
E independent of q2!
Electric Field and Electric Force
r
r
q0
F = E q = Ke 2 rˆ q
q
r
q0
E = Ke 2 rˆ
r
q0
q0: source charge
E: field by q0
q: test charge
F = qE
E force
f
on q b
by E
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Visualization of Electric Field: Field Lines
‰ Use of field lines is a convenient way to visualize electric fields
‰ Simple rules for drawing field lines:
ƒ line direction
direction: direction of E vector
ector
ƒ line density: relative strength of E. (denser = larger)
Field Lines e.g.: Point-Like Charges
Magnitude E=ke q/r2
+
+q
Magnitude E=ke q/r2
-q
q
Example 2: Two Charged Particles
+ and
+q
d +q
+
+ and
+q
d - q (dipole)
(di l )
Each field line always starts from a + q and end at a -q (or ∞)
Motion Of Charged Particle
In The Electric Field
‰ Fundamental Formulas:
ƒ F=qE
ƒ a=F/m = qE/m
ƒ v= vi +at
If initially rest (vi =0)
th
then
v= att = (qE/m)
( E/ ) t
Motion of +q:
Same dir.
dir as E
+q
-q
E
Motion of - q:
Opposite dir
dir. as E
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Exercise: An Electron in a Uniform E. Field
‰ Find out vertical displacement after the electron
pass through a downward uniform electric field E
‰ Solution: Exercise with your TAs
Answer: dy= - ½ (e/m)E (l/vi)2
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Cathode Ray Tube (CRT)
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