Physics 202, Lecture 2
Demo: Two Types of Electric Charges
Today s Topics
  Electric Force and Electric Fields
  Electric Charges and Electric Forces
  Coulomb's Law
  Physical Field
  The Electric Field
  Electric Field Lines
Opposite signs attract Like signs repel
  Motion of Charged Particle in Electric Field
Properties of Electric Charges




2+1 types: positive, negative (+neutral).
Unit: Coulomb (C). 1 C= charge of 6.24x1018 protons.
Electric charge is quantized: q=±Ne, e=1.602x10-19 C
Building blocks of matters:
Charge (C)
Electron
-e=-1.602x10-19
Proton
Neutron
+e=+1.602x10-19
0
Mass (kg)
9.11x10-31
1.673x10-27
1.675x10-27
  Electric charge is conserved: charges can be moved
around, but the total charge remains the same.
 For deep thinkers: Why electrons and protons have
the same electric charge?
Numeric Examples: Electric Force Is Strong
  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
à Electric force F= 8.2 x10-8 N.
  This force is large:
  Compared to the mass of proton: 1.673x10-27 kg
  Compared to the gravitational forces between them:
FG= 3.6x10-47N (recall: FG=Gm1m2/r2)
  Four fundamental forces:
Strong > Electromagnetic > Weak >> Gravitational
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:
  forces between opposite sign charges are attractive
  forces between like sign charges are repulsive
+
-
-
+
+
+
-
-
 The magnitude of the electric forces for point charges
F12 = F21 = ke
q1 q2
r2
(Coulomb s Law)
Coulomb Constant: ke = 8.987x109Nm2/C2 = 1/(4πε0)
ε0: permitivity of free space
Coulomb s Law in Vector Form

E. Force on q2 by q1: F12 = K e

E. Force on q1 by q2: F21 = K e
q1q2
rˆ12
r2

q1q2
rˆ21 = − F12
r2
r
r̂12
  Exercise:
Use this vector form to verify
the attractive/repulsive feature
  Note:
Multiple particles on charge i,
Fi= F1i+F2i+ F3i +….
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Quick Quiz
Properties of the Electric Force
  Two charges, q1=0.1C and q2=5q1 (i.e.0.5C), are separated by a
distance r=1m. Let F2 denotes the force on q2 (exerted by q1),
and F1 denotes the force on q1 (exerted by q2). Which of the
following relationship is true?
  F1=5F2
  F1=-5F2
  F2=-5F1
  F1=-F2
  It is one of four fundamental forces:
Strong >Electromagnetic > weak >> gravity
  It is proportional to 1/r2 : double r à ¼ F
 Its direction is charge sign dependent:
like signà repulsive, opposite sign à attractive
  It is a conservative force. (Work independent of path)
rf 

k qq k qq
W = ∫ F • dr = − e 1 2 + e 1 2 = ( −U f ) − ( −Ui )
ri
rf
ri
 A potential energy can be defined. (chapter 23)
U=
A Very Important Concept: Field
ke q1q2
r
Note the similarities and
differences to gravity
Example of Scalar and Vector Fields
 What is a physical field ?
Field: A physical quantity which has a physical value*
at each point in space (i.e. a distribution).
Examples of physical fields:
temperature, wind speed, electric field, magnetic field, …
Wind speed (vector)
Temperature (scalar)
  In this course, we consider only scalar and vector forms of
physical quantities.
Measurement can be made at any point on the map.
The Coulomb s Law Revisited
Electric Field and Electric Force
  Original (Coulomb s) view of electric force:
q1 directly applies an electric force on q2

qq
F12 = Ke 1 2 2 r̂12
r
r
 Field view of electric force:
  q1 creates an electric field E around it
  The electric field E applies a force on q2


q
F2 = Ke 21 rˆ12 q2 = E q2
r
E
In this field view:
q1: source charge
q2: test charge
E independent of q2
q

q
F = E q = Ke 20 rˆ q
r
E = Ke
q0
rˆ
r2
q0
q0: source charge
E: field by q0
q: test charge
F = qE force on q by E
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2
Visualization of Electric Field: Field Lines
Field Lines e.g.: Point-Like Charges
  Use of field lines is a convenient way to visualize electric fields
  Simple rules for drawing field lines:
  line direction: direction of E vector
  line density: relative strength of E. (denser = larger)
Magnitude E=ke q/r2
Magnitude E=ke q/r2
-q
+q
Motion Of Charged Particle
In The Electric Field
Example 2: Two Charged Particles
  Fundamental Formulas:
  F=qE
  a=F/m = qE/m
  v= vi +at
If initially rest (vi =0)
then v= at = (qE/m) t
Motion of +q:
Same dir. as E
+q
-q
+q and +q
E
Motion of - q:
Opposite dir. as E
+q and - q (dipole)
Each field line always starts from a + q and end at a -q (or ∞)
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Exercise:
Electric Forces Due to Two Charged Particles
Exercise: An Electron in a Uniform E. Field
 Find out vertical displacement after the electron
pass through a downward uniform electric field E
 For an electron charge e and mass m
 Answer: dy = - ½at2 = = - ½(F/m) (t)2 =- ½(eE/m) (l/vi)2
  Find the electric force on q3.
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