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Physics 202, Lecture 2
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 of Charged Particle in Electric Field
Demo: Two Types of Electric Charges
Opposite signs attract Like signs repel
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
Proton
Neutron
-e=-1.602x10-19
+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?
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
q1 q2
F12 = F21 = ke 2
r
(Coulomb s Law)
Coulomb Constant: ke = 8.987x109Nm2/C2 = 1/(4πε0)
ε0: permitivity of free space
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
Coulomb s Law in Vector Form

q1q2
E. Force on q2 by q1: F12 = K e 2 rˆ12
r


q1q2
E. Force on q1 by q2: F21 = K e 2 rˆ21 = − F12
r
  Exercise:
Use this vector form to verify
the attractive/repulsive feature
  Note:
Multiple particles on charge i,
Fi= F1i+F2i+ F3i +….
r
r̂12
Quick Quiz
  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
Properties of the Electric Force
  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)
W =∫
rf
ri
 
ke q1q2 ke q1q2
F • dr = −
+
= ( −U f ) − ( −Ui )
rf
ri
 A potential energy can be defined. (chapter 23)
ke q1q2
U=
r
Note the similarities and
differences to gravity
A Very Important Concept: Field
 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, …
  In this course, we consider only scalar and vector forms of
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

q1q2
F12 = Ke 2 r̂12
r
 Field view of electric force:
  q1 creates an electric field E around it
  The electric field E applies a force on q2


q1
F2 = Ke 2 rˆ12 q2 = E q2
r
E
In this field view:
q1: source charge
q2: test charge
E independent of q2
Electric Field and Electric Force
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 force on q 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:
  line direction: direction of E vector
  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
Example 2: Two Charged Particles
+q and +q
+q and - q (dipole)
Each field line always starts from a + q and end at a -q (or ∞)
Motion Of Charged Particle
In The Electric Field
  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
E
Motion of - q:
Opposite 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
 For an electron charge e and mass m
 Answer: dy = - ½at2 = = - ½(F/m) (t)2 =- ½(eE/m) (l/vi)2
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Exercise:
Electric Forces Due to Two Charged Particles
  Find the electric force on q3.