Chapter 21: Electric Charge and Electric Field
• The nature of electric charge
Understanding conservation of electric charge.
• How objects become electrically charged.
• Coulomb’s law to calculate the electric force between charges.
• The distinction between electric force and electric field.
• Electric field due to a collection of charges.
• How to use the idea of electric field lines to visualize and interpret electric fields.
Electric Charge
Back in 600 BC, the ancient Greeks has discovered the electric properties of matter.
They found that rubbing an amber with a wool makes amber attractive.
In this process, the amber acquires an electric charge. We call it is charged. Amber is called “elektron” in Greek language. This is where “electric” word comes from.
Electric Charge and Electrostatics
The interaction between steady (at rest) charges is called electrostatics.
Experiments in Electrostatics
Benjamin Franklin (1706‐1790) has called these charges + and – charges.
Like charges repel each other, opposite charges attracts each other. Electric Charge and the Structure of Matter
All materials are made up of atoms – building blocks of matter ‐
Atoms are consist of neutrons, protons and electrons
Electron mass ~2000 times smaller than proton.
Electric Charge and the Structure of Matter
Because the electron is very weak and loosely bound to the nucleus.
In charging process the electrons are being exchanged. The net charge is being conserved.
Classification of Atoms according to their charges:
Matters are made of atoms – usually found neutral in the nature–
Conservation of Electric Charge
During any process/reaction in an isolated system, charge remains the same. Only moves from one to another. – usually electrons transferred ‐
One can transfer charge from one matter to another •Transfer with contact – direct– direct charging
•Transfer without contact –induction‐ charging with induction
•Note: Unit for charge is C (Coulomb) Charge of electron ‐e = ‐1.602 x 10‐19 C Charging with contact / direct charging
Glass and Silk
Rubber and Fur
‐
‐
‐
• During these processes, charges (electrons) are transferred from one to another – charge conserved‐
• This is one way of charging an object – charging with contact ‐
Electrical classification of materials
• Materials are classified in three groups according to their electrical properties
• Classified in terms of the ability of electrons move through the material
– Insulators – rubber, glass, silk, fur, dry wood, etc.
• Electrons are bounded to atoms, can not move freely
– Conductors –metals: copper, aluminum, silver, iron, etc. • Some fraction of electrons can move freely – Semiconductor – materials between these two categories‐
• Germanium and silicon are most common semiconductors
• In a electrified/charged insulator, the charges stays in the charged region.
• In a charged conductors, exceeding charges distributed at the surface, remember same charges repel one another.
Induction: Charging a Conductor
• Consider an uncharged/neutral conducting sphere
– Equal amount of + and – charges q=0.
• Bring a negatively charged rod near the sphere?
– + charges will be attracted and – ones will be repelled
• Connect sphere to the ground by using a conducting wire.
– One may consider earth as a huge sphere that can provide and give electrons as much as desired.
– Some number of the electrons will transferred to the earth.
• Now disconnect the sphere from the earth then take the charged rod away.
Finally
• Conductor becomes positively charged. More protons then the electrons. This process is known as charging by induction. Example Question
Question: How many electrons in ‐1.00 C charge?
– Charge of electron: e=‐1.602x10‐19 C.
# of electrons / C = ‐1.00 C /‐1.602x10‐19 C =6.24x1018.
Guess how many electrons in a matter (copper) of volume 1cm3
– Size of atom ≈10‐10m. 29 electron in a copper atom.
#of electrons = 29 x (10‐2m )3 /(10‐10m)3 ≈ 1025
Note: Only approximately 1023 of them moves freely.
• In a glass‐silk or rubber‐fur experiments only 10‐6 C charge is obtained ≈1012 electrons << 1025
Coulomb’s Law: Force between charged particles
• Charles Coulomb (French physicists 1736‐1806) first measured magnitude of electric force between charged particles. (sometimes called also Coulomb force) – Used a fiber wire with a torsion constant similar to Cavendish’s experiment to determine the G.
q1q2
F k 2
r
9
2 2
• ke=8.9876x10 N.m /C ~ 9.0 N.m2/C2 ‐ Coulomb constant‐
• This constant also written in the form 1
k

–
4 o
–  o  8.8542 1012 C /N.m
permittivity of free space
• For Multiple forces, one may use the superposition principle. 2
2
Similarities between Electric / Coulomb and Gravitational Forces
q1q2
F k 2
r
Coulomb Force
q is + or F is attractive or
repulsive
m1m2
Fg  G 2
r
Gravitational Force
m is only +
F is always attractive
• Both varies as inverse square of the separation
• Experimentally shown that Fe is also a conservative force.
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Example: The Hydrogen Atom ‐1/2
Example: The electron and proton of a hydrogen atom are
separated (on average) by a distance of approximately
5.3x10‐11m. Find the magnitude of the electric force and the
gravitational force between the two particles.
Fe  ke
qe q p
r
2
k e  8.9876x10 N.m / C
9
Fg  G
2
2
qe  q p =-1.602x10-19 C
Fe  8.2 108 N
me m p
r
2
G  6.67x10-11 N.m 2 / kg 2
m e  9.111031 kg
m p  1.67  1027 kg
Fg  3.6 1047 N
Example: The Hydrogen Atom 2/2
Example: The electron and proton of a hydrogen atom are separated (on
average) by a distance of approximately 5.3x10‐11m. Estimate the
required force to keep electron in an orbit around the proton in an
hydrogen atom. Take the mean speed of electron approximately as
1/137th of the speed of light. Speed of light 3.00x108m/s. Compare this
value with the results of previous examples.
me  9.11 1031 kg
2
v
Fc  me
r
3.00  10 m/s/137 

kg
8
 9.11 10
31
2
5.3 1010 m
Required centripetal/central force: Fc  8.24 108 N
8
From Previous problem: Fe  8.2  10 N
Fg  3.6 1047 N
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Definition of Electric Field
We know that charged particles are interact.
Repulsive or attractive depends on the charges.
How do a charge know other charge is there?
How do they communicate?
In order to answer these problems, we define the
concept of “electric field”.
Any charge in the space creates a field around it that effects other charges.
We define the electric field as the force acting on unit
charge.
It is a vector quantity.
It’s unit is N/C.
Pictorial Representation of Electric Field ‐ A Point Charge ‐
In order to determine the electric field due to a point
charge particle, we can take a test charge of 1C and scan
the region where the charge is located.
Positive Charge
Negative Charge
Mathematical Representation of Electric Field ‐ A Point Charge ‐
Using Coulomb’s Law, we can mathematically determine the force
on the unit charge. First define a r unit vector
Let’s use the Coulomb’s law now:
Direction of the E is in the same direction of r if q is positive.
Direction of the E is in opposite direction of r if q is negative.
where
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Electric Field due a Charge Distribution
For multiple charges, the electric field at a point is the summation
of electric field due each fields (Superposition of Fields of each charges).
Example: Field of two charges at point P
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Calculations of Electric Field due to a Continuous Charge Distribution
For the point charges it is easy to apply superposition principle
For the continuous charge distributions story is a little bit different
We need to use integral to count for each charge pieces in the system
Charges along a line
Charges on a ring or a line
Define charge per unit length:
Use line integration: ds
Charges on an area
Charges on a circular or rectangular (plate) area
Define charge per unit area :
Use area (surface) integration: dA
Charges throughout a volume
Charges in a sphere or a cylinder
Define charge per unit area :
Use volume integration: dV
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Example: Electric Field due to a Charged rod
A rod of length l has uniform positive charge per unit length  and a
total charge Q. Calculate the electric field at a point P that is located
along axis of the rod and a distance a from one end as shown in the
figure.

E
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Note: Comment on getting electric field for infinitely large plate using this result!
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Electric Field Lines
The concept of “electric field” can be understood better with the electric field lines.
Electric field lines are imaginary lines drawn in a region that helps us to visualize the electric field in the region
Electric field lines tells us about the direction and magnitude (qualitatively) of the electric field in a point.
Direction:
Example: 
direction is tangent to the line
Magnitude: Depends on the density of field lines in a region.
Denser field lines means stronger electric field at the particular point.
Electric Field Lines: Multiple Charges
For multiple charges the electric field lines are the superposition field lines from all charges
Grass Seeds on a Fluid in an Electric Field
Experiment:
Grass seeds are floating on a insulating fluid (like transformer oils)
Two positively charged wires are inserted into fluid.
Results and Conclusion:
Normally, the grasses are neutral. Grass seeds are insulator like woods.
So what happens?
Electric field due to charged wires will induce a charge separation (polarization) in the grass seeds – induction ‐
As a consequence, they will line up with the electric fields.
Example:
Rank the magnitudes of the electric field at points A, B, and C shown in figure below (greatest magnitude first).
Example:
Field lines around opposite charges
Number of field lines from 2q is twice the ‐q
Same number of field lines
because amount of charges are same
Example:
Electric Field lines due to infinitely large plate or plates. *
+ plate alone
‐ plate alone
plates to gather
Note: Case is similar for infinitely long charged wires.
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You may use any of the followings if needed.
e = 1.602x10‐19 C
+e
‐e
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Note: First answer the question what would it be if the circle were complete.
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Electric Dipoles
• An electric dipole is pair of charges they have the same magnitude but different signs separated by a distance. • Many physical systems (especially molecules) in the nature has dipole character (e.g. water)
This dipole properties are important for many crucial chemical reactions
• TV antennas are also form a dipole.
• Even though net charge is zero in a dipole, they still may interact with the external E. Fields.
Remember the grass seeds placed in an electric field – they also act like dipoles –
or individually • We will study the following in this section:
Dipoles in an electric field. How do a dipole response to an electric field?
Electric fields produced/due to a dipole.
Electric Dipoles
• For an electric dipole, we define a vector quantity called electric dipole moment P.
magnitude of a dipole moment dipole is P=qd ‐ SI Unit = C.m
Direction of a dipole is directed from negative charge to positive charge.
P
• Example: Water
Water is made up of water molecules. – a molecule consist of atoms –
Chemical formula for water is H2O ‐ contains two hydrogen atom and one oxygen –
The following figure shows a H2O molecule
Covalent bonding keeps O and H atoms together‐
Because of the charge separation, H2O is a dipole
Because of this dipole properties, water is capable of interacting with other molecules. This interaction is called as reaction between molecules in chemistry. H2O molecule undergoes reaction with NaCl (sodium chloride – salt) and solves them into ions. This solving power increases when the P (dipole moment of the H2O) increases. An Electric Dipole in an External Electric Field
• What happens when we place a dipole on an electric field?
There will be a force acting on the + and – charges. Let’s call these forces F+ (force on + charge) and F‐ (force on + charge)
• The net force on the dipole is zero. F+ + F‐ = 0
• But there will be a torque on it – force of rotation – Remember: Reminder for Torque: Example of torque on a bolt
Figures below shows the torque produced by a force on a bolt
Magnitude of the torque
  rF sin( )
Direction:
Right‐hand‐rule gives the direction
Torque on an Electric Dipole
• Let’s now study the torque on a dipole in details.
Axis of rotation for a dipole can be considered as center

d
d
qE sin   qE sin   qdE sin 
2
2
Direction of torque in this example is “into the page”.
This expression can be written as   PE sin 
In most general form, this results yields to Some Cases: Let’s look at the some of the possible cases between P and E
P
 
 0
Unstable Equilibrium P
 
  P E

 
 0
Stable Equilibrium Torque always tends to turn the direction of dipole to line up with the external Electric Field. Potential Energy of an Electric Dipole
• We have seen that an electric field applies a torque on a dipole
• The torque will make it rotate such that the P will line up with E.
• While it is rotating, the torque will do some work so changing it’s energy
Let’s calculate the work done when P is rotated from 1 to 2
Because, the torque is changing while angle changing, we need to use integral …
Electric forces are also conservative forces as like the gravitation, so we can define a potential.
When you throw a + charge in opposite to a field, it goes slow down and comes back with the same speed. Just like a ball.
From Chapter 7: Negative of the change in the potential equals to work done on it.
W  U  (U 2  U1 )  U1  U 2
 U     PE cos 
In most general form: Potential Energy of a dipole in an Electric field
 
U  P  E
Some cases:  = 0 minimum potential energy stable equilibrium point. P // E
 =  maximum potential energy unstable equilibrium point. P anti // E
Conclusion, dipole tends to move to minimum energy as like a ball falling down.
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 

E  E  E
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RECOMMENDED END OF CHAPTER‐21
QUESTIONS AND PROBLEMS
2,3,5,6,7,8,12,13,14,15,16,18,20, and 21
1,2,6,9,14,15,16,19,21,22,25,26,28,30,31,33,37
40,41,44,47,49,50,52,53,55,57,58, and 59
62,63,64,66,68,69,72,75,77,84,89,102, and 104