### Topic 6.2 Electric Force and Field

```Topic 6.2
Electric Force and Field
(3 hours)
Electric Charge
• There are two types of electric charge,
positive charge and negative charge.
• It was not until the late 1890s through the work of J.J.
Thomson that the true nature of electrons was
discovered through experiments with cathode ray
tubes.
• We now know that
– charge is conserved
– charge is quantised
– the force between two point charges varies as the inverse
square law of the distance between the two charges.
Electrostatics:
The study of stationary charges.
• Unlike protons which are strongly bound in the
nucleus, the electrons in a material are relatively free
to move, and some electrons, given the right
conditions, can move from one material to another.
The materials can become electrically charged.
• Materials can either have an excess of electrons or a
deficiency of electrons.
– substances with an excess of electrons are negatively
charged.
– substances with a deficiency of electrons are positively
charged.
• When a perspex rod is rubbed with a piece of
silk, the perspex rod becomes positively
charged and the silk becomes negatively
charged as demonstrated in the figure.
Law of Conservation of Charge
• When charging objects by friction, charge is not
created but rather redistributed on the two surfaces.
This can be stated according to the Law of
Conservation of Electric Charge that states that in a
closed system, the amount of charge is constant.
• If you examine the previous figure more closely – there
is a total of 16 positive charges and a total of 16
negative charges on the perspex rod and the silk before
rubbing. After the process of “ electrification ” by
friction, the charge is redistributed but the same
number of positive and negative charges exist. In other
words, charge is conserved.
Electrostatic Force
• Like charges repel each other
• Unlike charges attract each other
Measuring Charge
• The coulomb (symbol: C) is the SI derived unit of electric
charge. It is defined as the charge transported by a steady
current of one ampere in one second.
1C=1A∙s
• The elementary charge, usually denoted as e, is the electric
charge carried by a single proton, or equivalently, the
absolute value of the electric charge carried by a single
electron. This elementary charge is a fundamental physical
constant. To avoid confusion over its sign, e is sometimes
called the elementary positive charge.
• This charge has a measured value of approximately 1.602 ×
10−19 C.
• Conversely, one coulomb is the charge carried by 6.25 ×
1018 electrons or protons.
Conductors
• Metals consist of positive ions surrounded by
a ‘sea’ of delocalized electrons (electrons that
are not all attached to a specific atom). Hence
there are many electrons available for
conduction. Solutions that conduct
(electrolytes) contain electrons and positive
and negative ions that are free to move.
Therefore, conductors have a low electrical
resistance.
• If a conductor is held in the hand, any excess
of electron charge that forms on the
conductor will be transferred to the earth
through the body of the person holding the
conductor. Conversely, any deficiency of
electron charge that forms on the conductor
will be transferred from the earth through the
body of the person holding the conductor. It is
said that the conductor is earthed or
grounded.
Insulators
• In an insulator, the electrons are held tightly
by the atomic nuclei and are not as free to
move through a material. They can
accumulate on the surface of the insulator but
they are not conducting.
Band Gap Theory
• According to the energy band theory that is used
to explain the properties of conductors,
semiconductors (such as germanium and silicon),
and insulators, the valence or outer-shell
electrons are held in the valence band that is full
or partially filled with electrons. When there are
many atoms in close proximity (as there is with all
materials), there also exists an upper energy
band known as the conduction band. The
conduction band is empty. A forbidden energy
gap exists between the valence and conduction
bands.
• For conductors such as metals, the valence
and conduction bands overlap. However, in
insulators, the energy gap between the
valence band and the conduction band is
large. Therefore, electrons cannot move
across the forbidden energy gap. Insulators
thus have a high electrical resistance and
when an insulating material is held, the
electrons remain on the surface of the
insulator and are not able to be conducted
through the person. The charge on an
insulator will remain for a short period of time
until it leaks off the surface or is discharged.
The Electroscope
• http://www.shep.net/resources/curricular/ph
ysics/p30/unit2/electroscope.html
Coulomb’s Law
• The French physicist, Charles
Augustin Coulomb (1738-1806),
using a torsion balance of his own
invention, confirmed the existence of
an inverse square law of electric
charge.
Coulomb’s Law
• On the basis of his experiments, he concluded
that
– the force F between two point charges q1 and q2
was directly proportional to the product of the
two point charges.
– the force between the two point charges was
inversely proportional to the square of the
distance between them r2.
• Together this gives:
Coulomb’s Law
• When F is measured in newtons (N), q1 and q2 in
coulombs (C), and r in metres (m), the quantitative
statement of k is the constant of proportionality called
the Coulomb Constant. Its value is 8.99 × 109 N m2 C-2.
• Note that it is not necessary to include the sign of the
charge when carrying out the calculations. Simply use
the magnitude of the point charges and then draw a
diagram with the signs of each point charge shown,
this will also indicate whether the force is attractive or
repulsive.
Alternate Coulomb’s Law
• You may also see Coulomb’s Law written as
• where k is replaced by 1 / 4πε0. The part of the
constant ε0 is called the permittivity constant of
free space. On its own, it has a value of
8.95 × 10 -12 N m2 C -2 , and this value applies if
the experiment is carried out in air or in a
vacuum. If the experiment is carried out in
another medium, the value of ε0 will need to be
substituted with another value.
Example:
• Two charges, q1 = 4.00 mC and q2 = 6.00 mC,
are placed in a straight line separated by a
distance of 2.00 cm as shown below. Find the
force exerted on each charge.
1
2
• If another charge, q3 = - 2.5 mC is placed 3.00
cm above q2 (as shown below) then what is
the net force experienced by q2?
3
1
2
Homework:
• Tsokos, Pages 287 and 288, Questions 1 to 15
Electric Field
reasoned that just as Newton had
developed the gravitational field
concept, so too the concept of
electric field could be an analogy of
this. Faraday argued that an electric
field is a region of influence around a
point charge or group of point
charges.
Electric Field
• If an electric field is present at a
particular place, when a second
point charge is placed near it, it feels
a force. The stronger the field, the
stronger the electric force will be.
The electric field has direction
because the force on the charged
particle has direction. The direction
of the electric field is defined as the
direction of the force it causes to act
on a small positive test charge.
Electric Field Lines
• Faraday introduced the concept of electric
field lines to show the direction that an
isolated charge would follow if placed in the
field.
Rules for Electric Field Lines
1. they start on a positive charge and end on a
negative charge
2. they meet electrostatically charged objects at
right angles
3. they never cross over one another
4. their density is an indication of the strength of
the electric field
5. there is no electric field in a hollow conductor
6. the electric field is uniform between two
oppositely charged parallel conducting plates.
Electric Fields For Some Common Charge Distributions
Electric Field Strength
• The electric field strength or electric field
intensity at any point in space, E is equal to
the force per unit charge exerted on a positive
test charge.
• Electric field strength is a vector quantity and
it is measured in N C -1
Now throw in Coulomb’s Law…
and
become
Where k is Coulomb’s constant, q1 is the point
charge producing the electric field, q2 is the small
test charge, and r is the distance from q to the
particular point in space.
(Recall that the units for E are N C-1)
Example:
• The electric field between two parallel plates
is 100.0 N C-1. What acceleration would a
charge of 2.0 mC and mass 1.00 x 10-3kg
experience if placed in this field. (Ignore its
weight)
Charges and Potential Energy
• Consider a fixed positive charge Q and a
positive test charge q that is infinitely far away
from Q. If the test charge q is moved close to
Q, work must be done to overcome the
repulsive force between the two charges.
Because of the work done to overcome this
repulsive force, there is now an equal amount
of potential energy stored is this system.
Q
q
q
Electric Potential
• We define the electric potential (V) at a point as
the work per unit charge that must be done to
bring a small positive test charge from far away to
the point of interest.
W
V
q
or
V
Ep
q
where V is the potential in volts (1 V = 1 J/C), W is
the work done (in J) which equals the potential
energy, and q is the magnitude of the test charge
(in C).
Electric Potential Difference
• Now consider an arrangement of charges that
creates an electric potential in the space
around it. Suppose you now move a charge
from one potential to another, the work that
must be done is given by
W  E p  E p final  E p initial  qVfinal  qVinitial
or
W  qV and, consequently Ep  qV
Energy in Electronvolts
• The relationship W = qV allows us to define a
new unit of energy, the electronvolt.
• One electron volt is the work done when one
elementary charge (e) is taken across a
potential difference of 1 V.
19
19
1 eV  1.60210 C 1V  1.60210
NOTE: 1 C∙V = 1 J
J
Example:
• A charge of 5.0 mC and mass of 2.0 x 10-8 kg is
shot with a speed of 300. m/s between two
parallel plates kept at a potential of 200. V and
300. V respectively. What speed will the
charge have when it reaches the 300. V plate?
• Two parallel plates have a potential difference
between them of 250 V. What work must be
done to move a charge of 5.0 mC from the
negative (low) plate to the positive (high)
plate.
• What is the speed of a proton whose kinetic
energy is 5000. eV?
Homework
• Tsokos, Pages 296 to 298, Questions 1 to 15
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