Electrostatics
The study of electric charges
Introduction
• Did you ever run a comb through your hair? What do
you notice.
• What causes the paper holes to jump onto the comb?
• There are electrical forces that are in place due to the
presence of charge on the comb.
The Atom
• An atom consists of
various charged and
uncharged particles.
• The central region is
called the nucleus.
• Protons (+) and
neutrons make up
the nucleus.
• Electrons (-) move
around the nucleus
in an orbital path.

 Nucleus

Neutrons
Protons (+)
Electrons (-)
The Significance of Charge
• An atom with balanced
charges is considered neutral.
• The overall charge can be
changed by adding or
removing electrons. This
makes the atom an ion.
Add e-
Take eOverall Charge: 1
01
(Negative
(Neutral
Ion)
(PositiveAtom)
Ion)
Sample Problem (Atomic Charge)
•
•
•
•
-19
An helium atom has a net electric charge of -8.0x10 C.
Is it neutral or an ion?
Are there extra electrons or a shortage of them?
How many extra electrons are there?
– Charge Per e-: -1.60*10-19C
19

8.0

10
C

#e 
1.6 1019 C
qNet
#e 
qe


#e  5
Sample Problem (Atomic Charge)
•
•
•
•
-19
An atom has a net electric charge of 4.8x10 C.
Are there extra electrons or a shortage of them?
How many electrons short is this atom?
Draw this atom given it is Boron.
Electrostatic Demo’s
• Tape
• Electroscope
Electric Forces
• Charges exert a force on other charges
Like Charges
Repel
Opposites
Attract
Actual Charge of Protons/Electrons
• Recall, charge is measured in Coulombs (C).
• Even though protons and electrons are very
small, they still have charge.
• Let us use q as a variable for charge.
Electron
qelectron  1.60 1019 C
Proton
q proton  1.60 1019 C
How do atoms get charged?
• Work can remove electrons from the atom.
– Results in a positively charged atom
• The free Electron can be transferred to
another atom.
– Results in negatively charged atoms
Separating Charge
• Charges are balanced in neutral objects.
• Work must be done to separate charge (free electrons).
• Once charge is separated, it can be used in
experiments.
Separation of Charge
• Bring a charge rod near a neutral conductor
• Un-like charges are attracted
• Like charges are repelled
Charge by conduction
• A charge rod touches a neutral conductor
• Like charges are repelled and uniformly
distribute
Charge by Induction
The
charges
oncharge
the
spheres
redistribute
to
A
Separation
charge
object
of
isthe
placed
takes
near
place
neutral
conductors
charge
object
is
removed
Contact
between
conducting
sphere
is maximum
broken
Result:
Two
spheres
charged
by
induction
separation
A
B
B
Charging by Polarization
• Certain substances, such as the one below, have polar
molecules. These molecules have opposite charges at
each end.
• Charging by polarization takes place when a charged
object is brought near, realigning the molecules in the
substance.
Magnification
Conductors and Insulators
• Electrical Conductors are similar to Heat
conductors.
• Electrical Conductors allow charge to
move easily.
• Electrical Insulators do not allow charge to
move easily
Conductors and Insulators
• Electrical Conductors all electrons to move
easily.
– Metals
– Graphite
• Electrical Insulators do not allow electrons
to move easily
– Glass
– Plastic
– Rubber
Coulomb’s Law
• The electrostatic force one charged object exerts
on an other
• The force is related to the amount of charge
– i.e more charge – more force
• The force is proportional to 1/d2
– i.e. the further apart the charges, the smaller
the force
Coulomb’s Law
F
Symbol
F
q1
q2
d
K
Kq1 q 2
Force
Charge
Charge
Distance
constant
d2
Unit
N
C
C
m
N m2 / C2
Electro-static Applications
Electrostatic filter
Coulomb’s Law in 2-D
•
•
•
•
To find Fnet with 3 or more charges
Calculate each Force vector.
It helps to have a grid system on which to work.
Use vector addition to find the resultant Fnet
q2
q3
F13
q1
F14
F12
FNet
q4
Coulomb’s Law in 2-D (cont.)
kq1q2
F12 
d12 2
Charge (C)
q1
3.0 X 10-4
q2
-2.6 X 10-5
q3
7.2 X 10-6
F12


9.0 10
9 Nm2
C2

4
5
3.0

10
C

2.6

10
C



13m

2
F12  5.4 N
q2 F12
20
q3
13
F13
q1
kq1q3
F13 
d132
F13


9.0 109
Nm2
C2
 3.0 10 C  7.2 10 C 
4

20m

6
2
F13  0.972 N
Coulomb’s Law in 2-D Sample
• Determine the direction of each of the forces prior to
vector addition.
opp
tan  
adj
F12
 2 
  tan  
 3 
2
  tan  
4
  33.7
  26.6
Quad II Adjust
Quad III Adjust
  33.7 180
  26.6  180
  146.3
  206.6
1
opp
q2
5.4N
hyp
adj
0.972N
hyp
q3
F13
1
opp
q1
adj
Coulomb’s Law in 2-D Sample
• The remaining
task is to use
analytical
vector addition.
Mag
Ang
X
Y
Q
F12
5.4N
146.3°
-4.49
3.00
II
F13
0.972N
206.6°
-0.87 -0.44
III
FNet
5.94N
154.5°
-5.36
II
F12 x  F12 cos 
F12 x   5.4 N  cos 146.3
F12 x  4.49 N
F12 y  F12 sin 
F12 y   5.4 N  sin 146.3
F12 y  3.00 N
F13 x  F13 cos 
F13x   0.972 N  cos  206.6
FNet
F13 x  0.87 N
F13 y  F13 sin 
F13 y   0.972 N  sin  206.6 FNet
F13 y  0.44 N
FNet
 YTot 
tan   

X
 Tot 
Y 
  tan 1  Tot 
 X Tot 
1  2.56 N 
  tan 

 5.36 N 
  25.5
X Tot  F12 x  F13 x
X Tot  4.49 N  0.87 N
X Tot  5.36 N
YTot  F12 y  F13 y
YTot  2.56 N
 X Tot 2  YTot 2

 5.36 N    2.56 N 
 5.94 N
2
2.56
Quad II Adjust
2
  25.5 180
  154.5
FNet  5.94 N @154.5
Electric Field lines
• Electric Field lines indicate the direction of the force due
to the given field.
• The lines point radially outward from a positive charge.
• The lines point radially inward from a positive charge.
Electric Field lines
• Electric Field lines can bend if there is more than one
charged particle.
Use symmetry to help.