Ch. 15
Electric Force and
Electric Field
Concept questions #2, 4, 7, 9
Problems #1, 3, 4, 10, 11, 12, 15, 19,
21, 25, 27, 29, 38, 40, 42, 50
Primary goal of physics class.
• Study how the universe works
• Learn how the laws of nature affect us
• How to take advantage of these laws.
• Physics 1, studied mechanics and thermodynamics
• Physics 2, study properties of electricity, magnetism
and their properties.
• Will also look at waves, sound optics, and will see
how these are related to each other and electricity
and magnetism
Electricity is used almost everywhere
• Understanding and using electricity may be
the most important finding by man since fire.
• Without electricity, there would be no
computers, phones, television, radio,
microwaves…
• We would revert back to the 19th century.
In chapter 15 we will cover the electric charge
and electric force and then study electric
fields.
Chapter 16 cover electric energy.
Later we will discuss circuits, which are an
application of other chapters.
Ch. 15
Electric charge – physical observable that
allows a material to have electrical properties.
Easy way to see evidence of charge is to rub 2
nonconductors together. After doing so, you
can exert a force on another nonconductor.
• Simple experiments can show that there are two
types of charge.
• Benjamin Franklin named them positive and
negative.
– Rub a rubber or plastic rod against some fur. Then rub
a glass rod against silk. The two rods will attract each
other.
– Repeat with two rubber or two glass rods and there will
be a repulsive force.
Franklin’s convention was that the charge on the glass
is positive. The charge on the rubber is negative.
Conclusion ‘Like charges repel, unlike charges attract’
Atomic description of charge
The basic carriers of positive charge are
protons, which are located in a nucleus. The
nucleus is surrounded by electrons, which
carry negative charges.
In most matter, there are just as many protons
as there are electrons. The net charge is zero.
The matter is neutral.
• In a solid the nucleus of each atom is held in
place, so the protons don’t move.
• Electrons are much lighter than protons
mp = 1836 me
Electrons are much more easily accelerated by
forces. (They have less inertia)
Therefore, electrons are more easily
transferred from one material to another.
Objects become charged by gaining or losing
electrons.
Charge transfers readily from one object to
another when the objects come in contact with
each other.
Rubbing two materials together increases the
contact area and thus makes it easier for
electrons to move.
This is analogous to water moving down a pipe.
The wider the pipe, the easier it was for the
water to go through it.
Important rules for charges.
• The total electric charge is a conserved quantity.
• Neutral objects have an even number of positive
and negative charges.
• Charge is not created
• When an object is charged, it either gives or
takes an electron to another object, therefore
changing the charge of the object.
– When you rub a plastic rod with fur, the rod becomes
negatively charged when electrons move from the fur
to the rod.
Properties of charge
• In 1909 Robert Millikan discovered the
quantization of charge.
• The charge of an object is always a multiple of
some fundamental value that can’t be further
subdivided. Call this value ‘e’.
Objects only have charges of integer multiples of e.
Can’t have a charge of 0.2e or 0.5e.
Unit of charge
• e, the fundamental unit of charge, has a value
of: 1.60219 x 10-19 C
(round to 1.6 x 10-19 C)
• The SI unit of electric charge is the coulomb (C)
Conductors and insulator
We used the term nonconductor earlier.
The text definition: In a conductor, electric
charge moves freely in response to an electric
force. All other materials are insulators.
An insulator (glass, rubber)is a nonconductor.
Conductors
• Metals are conductors. In a conductor it is
easy for the electrons to move around in the
material.
• Since the electrons can move easily, the
material conducts charge.
• The charge can move around the entire
surface of the material.
• Copper is a good conductor. That is why it is
commonly chosen for wiring.
Insulators
• When an insulator becomes charged, the charge
doesn’t move into other regions of the material.
• The transferred electrons can’t move around very
far.
• When I charge up my pen, I can only pick up the
pieces of paper with the end that was rubbed
with the hair. Since the charges stay locally
concentrated, the charge at the end, is strong
enough to pick up the paper.
Charge by Conduction
First you have a negatively charged rod and a neutral
insulated conducting sphere. (The sphere is not
touching any other conductors.)
1) When the rod is placed near the sphere, a net
positive charge moves near the rod, a net negative
charge moves to the opposite side.
2) Upon contact, electrons from the rod move onto
the sphere and neutralize the positive charges.
3) Taking away the rod, the sphere is left with a
negative net charge.
Charge by Conduction
The sphere now has a negative charge.
The sphere still has the same amount of protons,
but now there are more electrons.
The object being charged by conduction will be
left with the same type of charge as the object
doing the charging.
We can repeat this with a positively charged rod.
Charge by Induction
• Using conduction, the two materials came in
contact with each other.
• Charging by induction does not require
physical contact.
• Idea of being grounded.
– Any object connected to a conductor that is
buried in the Earth is grounded. The Earth can
accept or supply an unlimited amount of
electrons.
Charge by Induction
• First you have a negatively charged rod and a neutral
insulated conducting sphere.
• When the rod is brought near the sphere, the
charges separate out.(as in the first step in
conduction)
• Now the grounding wire is attached to the sphere.
The repulsive force from the negatively charged rod
will push some of the electrons off the sphere and
down the wire.
• After removing the wire , the sphere has an excess of
positive charges.
Charge by Induction
The sphere will still have the same number of
protons (positive charges) but now has a smaller
amount of electrons (negative charges).
The sphere has an induced positive charge.
Also the negatively charged rod didn’t lose any of its
charge, because it never came in contact with the
sphere.
When charging by induction, the charged object
(sphere) obtains a charge opposite of the charge of
the charging object (rod).
Electric Force
Properties of the electric force exerted between
two stationary particles
1) directed along a line joining the two particles and
is inversely proportional to the square of the
distance separating the particles ( 1/r2)
2) proportional to the product of the magnitudes of
the charges of the particles.
3) It is attractive if the charges have opposite signs.
Repulsive if the charges have the same signs.
Electric Force and Coulomb’s Law
Coulomb’s law mathematically describes the
force between the two charges.
q1 q2
F k
r2
k (Coulomb constant) = 9x109 N m2/C2
This applies to point charges and to spherical
distributions, where r is the separation of the two
centers of charge.
Important values
Electron
Proton
Neutron
Charge(C)
-1.6x10-19
1.6x10-19
0
Mass (kg)
9.11x10-31
1.67x10-27
1.67x10-27
1 C of charge requires about 6.3x1018 protons
or electrons. 1 C is a lot of charge.
You would typically deal with magnitudes of
charges around 10-6 C.
Electric Force
• Remember that force is a vector quantity.
• All forces obey Newton’s 3rd Law of equal and
opposite reactions.
Even if two charges have different
magnitudes, they exert equal and opposite
forces on each other.
Example of electric force
Find the force the two protons separated by
10-9 meters exert on each other. Is the force
attractive or repulsive.
F
k
(1.6 x10
19
C )(1.6 x10
9
10 m
2
The force is repulsive.
19
C)
2.3x10
10
N
Superposition principle
• What to do when there are more than 2
charges.
• When more than 1 charges act on the charge
of interest, you need to compute the force
from each charge individually and then add up
the forces using vectors.
The Electric Field
• The electric force behaves much like the
gravitational force, in that it can act through
space. The two charges don’t have to be in
contact. These are examples of field forces.
• An electric field is produced by a charged
object and surrounds the object. The field
then exerts a force on any other charged
object.
Electric Field
• The electric field that is produced by a charge
Q at the location of a ‘test charge’ q0 is efined
as the force exerted by Q on q0, divided by the
test charge q0.
E = F/q0
SI units of electric field are N/C
Electric field is a vector
Electric Field
The Force exerted by an electric field depends on
the field strength (E) and the charge (q) that the
field is exerted on.
F = qE
Lets look at the force that Q exerts on q
F = k Qq/r2
The magnitude of the electric field the Q
produces at q is
E = k Q/r2
Electric Field
The magnitude of the electric field produced by a
single charge is:
E
k
q
r2
Electric field is a vector. The direction will be
from the location of the charge to the point
where the field is being measured.
The superposition principle is used here if more
than one charge is present. Need to add up the
individual electric fields from each charge.
Direction of Electric Field
The electric field acts along what are called
field lines.
For a point charge, the electric field lines will
spread out in a radial direction from the
charge.
If the charge is positive, the field lines radiate
outward. If the charge is negative, they
radiate inward.
Electric Field Lines
The electric field vector, E, is always tangent to
the field lines at each point.
The number of lines per unit area, through a
perpendicular surface is proportional to the
field strength.
If the lines are close together, the field is
strong.
Field Lines
Field lines begin on positive charges and end
on negative charges. Some lines will begin or
end infinitely far away.
The number of lines leaving a positive charge
or ending at a negative charge is proportional
to the magnitude of the charge.
Field lines can never cross each other.
see examples on pg 510,511.
Conductors in Electrostatic Equilibrium
• Electrostatic Equilibrium occurs when there is
no net motion of charge.
– Properties of isolated conductor
1 The electric field is zero everywhere inside the
conducting material
2 All excess charge is on the surface
3 The electric field just outside the conductor is
perpendicular to the surface
4 Charge accumulates at sharp points, where the
surface is most sharply curved.
Will talk about Van de Graaf generator at end
of chapter.
Electric Flux and Gauss’s Law
Gauss’s law is a second technique for
calculating electric fields, that when applied to
situations where there are specific
symmetries, is much more efficient than
Coulomb’s law.
Will introduce the concept of electric flux.
Electric Flux
When electric field lines pass through a given
surface, we say there is flux through the
surface.
For example, if the field lines are tangent to
the surface, they don’t penetrate at all and
there is no flux.
Electric Flux
Take a uniform electric field passing through a
surface of area A. The surface A is
perpendicular to the field lines.
The number of field lines per area is related to
the strength of the field. E N/A, where N is
the number of lines.
N EA, so the number of field lines is
proportional to the product of the field
strength times the area. This product is the
electric flux ( e)
e =EA
Flux
• e=EA
• This works when the electric field has a
constant magnitude over the area and the
field lines are normal to the surface.
• If the surface is slanted the flux becomes:
• e = E A cos
• Only the component of the electric field that
passes through the surface produces any flux.
When using Gauss’s law we will make use of a
‘Gaussian surface’ which is an imaginary
surface that located where we want to
calculate the electric field.
To use Gauss’s Law the electric field must be
constant on all points of a surface.
example: a point charge
Gauss’s Law applied to a point charge
e=EA
The electric field from a point charge is E = k Q/r2
Surround the point charge with a Gaussian
sphere of radius r.
e = E A = (k Q/r2)(4 r2)=4 k Q
relate the Coulomb constant to the permittivity
of free space ( 0)
-12 C2/(N m2)
=
1/(4
k)
=
8.85x10
0
e = Q/ 0
The flux through the surface is equal to the
charge the surface surrounds divided by 0.
This can be proven, via calculus, to work for
any closed surface.
Gauss’s Law relates the flux though a closed
surface to the charge the surface encloses.
e = Qenc/ 0
Flux
• when describing flux though through the
boundary of a closed surface, lines that enter
the enclosed volume have negative flux
• lines that exit the enclosed volume produce
positive flux.
• the sign of the net flux indicates whether the
enclosed charge is positive or negative.
• Gauss’s law is very useful when there is a
charge distribution that has a high degree of
symmetry. Otherwise, producing a Gaussian
surface where the electric field is uniform is
not practical.
• useful for point charges, spheres, long
cylinders and line charges, or planes.
• Need to pick a Gaussian surface that has all
points equidistant from the charge
• Using Gauss’s law to find the electric field of a
point charge. Use Gaussian sphere.
e = E A = E (4 r2) and e = Q/ 0
setting the two definitions of flux equal to
each other, we get E (4 r2) = Q/ 0
Q
2
E=
or
E
=
k
Q/r
2
4
o
r
This was the same expression we found using
Coulomb’s law earlier.
Look at a line of charge
Suppose you have a cable with a charge Q and
a length L. We can use Gauss’s Law to find the
electric field a distance r from the cable.
we assume the cable is very long to negate the end effects.
Our Gaussian surface is going to be a cylinder
whose axis is located on the cable.
e = E A = E (2 rL) = Q/ o
Q
E= 2 L r
The field strength is proportional to 1/r
(quite often we will call Q/L the linear charge
density )
0
Infinite sheet of charge
need the sheet of charge to be infinite to neglect the edge effects.
Let the sheet have a surface charge density:
= charge/area = Q/A
or Q = A
For a plane the Gaussian surface needs sides
that are perpendicular and parallel to the
plane. A box or upright cylinder will do.
e = E A and e = Q/ o
the is flux coming out/in through both ends of
the Gaussian box
• e = E A = E (2A) = Q/
• E = Q/(2A o)
• remember
o
= charge/area = Q/A
• E = /(2 o)
• Note that the electric field is constant.
• If you have an infinite sheet of charge, the
electric field would have a constant
magnitude wherever you measured.