Transcript Electrical Charge

Electric Charge
• Recall the 4 fundamental forces:
– Strong, EM, Weak, Gravity
• In order for the electromagnetic force to
affect bodies the presence of charge is
necessary.
• Electric charge is an intrinsic characteristic
of the particles that make up all matter.
• Electrostatics is the study of stationary, or
bound, charges. Moving charge is known
as “current” and will be discussed later.
• There are two known types of electric charge:
– Positive charge and Negative charge
• As a general rule, charges interact with one
another by means of the electromagnetic force.
• Like charges repel other like charges while
opposite charges attract one another.
Electric Charge
• The fundamental unit of charge is called the
Coulomb. Abbreviation: C
• A particle carrying a single charge (positive
or negative) carries a charge of
1.60 x 10-19 C
• In physics, the variable used to signify
charge is the lower-case letter q.
Practice
1) A tennis ball is rubbed on the carpet. How many
excess electrons are on the ball with a charge of
-3.25 x 10-17 C?
2) A lightning bolt transfers about 9.7 x 1020 electrons
to the earth. How much charge, in Coulombs, is
transferred?
Neutral Objects
• Charge is a fundamental characteristic of all
matter.
• In the macro-scale world most objects are
made of many atoms, each atom having
multiple charge particles.
• Like a single atom that has all its valence
electrons  same number of protons in
nucleus as electrons in the outer shells, most
large objects are considered neutral, having
the same amount of positive and negative
charge.
Charging Objects
(more on this later)
• Objects can become “charged” by creating an
imbalance of positive and negative charges on
the objects.
• While we often may describe an object as
“positively charged,” please be aware that the
presence of a positive charge is actually
indicative of a lack of electrons, the absence of
negative charges. Check out the three
examples below.
Conservation of Charge
• Like energy, charge is always conserved despite
changes to a system. This means if we start out
with 3 positive charges and 2 negative in a closed
system we must end up with the same amount of
charge present in the system after any changes
have occurred and been accounted for.
• An object can only have a charge that is an integer
multiple of the charge of an electron.
• The only known exception to the rule above is for
quarks, tiny sub-nucleonic particles that make up
protons and neutrons.
Extension
• If a proton has a charge of 1+ and is made
up of 3 quarks (2 identical “up” quarks and
1 “down” quark), why must quarks
necessarily have fractional charges?
• If a neutron has a net charge of zero and is
made up of 2 down quarks and 1 up quark,
can you figure out the charges on the up and
down quarks?
The material on this slide is an extension and will not be on
your test. DON’T FREAK OUT!
Conductors and Insulators
• In the same manner as heat transfer, an
electrical conductor is an object or material
that can transfer electrical charge easily
from one point to another.
• An electrical insulator is an object or
material that prevents the flow of electric
charge.
• Despite their inability to easily transfer
charge from place to place, insulators can
often become positively charged by
stripping off electrons (or collect charge by
accepting electrons).
What kinds of materials are good
electrical conductors?
(in normal conditions)
WHY???
1) Metals
2) The metallic bond/crystal
Conductors
METALS
Graphite
impure water (contains ions)
human body
nerves
plasma (hot ionized gas)
Insulators
pure water
glass and ceramics
plastic and rubber
leather and fur
paint and varnish
paper and cardboard
DRY gasses, including air
vacuum
stone and rock
dry wood
wax
sulfur
cloth
Can you name some other conductors/insulators?
Just b/c an object is made of insulating material does not mean that
charge will not move through it, only that it is less likely.
Metallic Bonds
• Metallic bonds form by individual atoms of
metallic substances which share all of their
valence electrons. This phenomena creates
what is called a “sea of electrons” in the
material.
• It is technically possible for an electron (a
charged particle) to move from one end of an
infinitely long strip of conductive material to
the other end with no resistance.
• There are few, if any, “conduction electrons”
in the valence shell of an insulator.
Charging by Conduction
• Friction: We can utilize frictional forces to
either deposit or removed electrons from
different surfaces.
– Rubbing a rubber rod with wool will result in
the rod gaining a negative charge as the rubber
has a tendency to “tear” electrons out of the
wool.
– Rubbing a glass rod with silk will result in the
formation of a positive charge on the glass as
the silk can actually remove electrons from the
surface of the rod.
Charging by Conduction
• When a charged object (like a rubber rod) is
placed in contact with a neutral conductor, the
charges on the surface of the object are forced off
onto the conductor. What do you think causes this
to occur?
hint: the answer has something to do with the electrostatic
force!!!
Conduct yourself well!
––
–
– –
–
––
– + –
+ – +
– + +–
+ –
+
– + + –
–
Net charge rod after = ???
Net charge block after = ???
Charging by Induction
• A charge is said to be induced when...
• When a neutral object is brought into proximity
(but not touching!) a charged object, the charges
on the neutral object will spread out such that
opposite charges will be attracted to the charge
source and like charges will be repelled away
from the source of charge.
• If we can siphon off some of the repelled
charges and then isolate the originally neutral
body, the body now has a distinct charge.
• One way to to this is with a “ground”
Induced Polarization
––
–
– –––
–
– + –
+ – +
– + +–
+ –
+
– + + –
–
Grounding
• To “ground” an object is simply to touch the
object, either directly or by means of a conductive
surface like a wire, to the earth.
• The Earth, being infinitesimally large in
comparison to all made made things, acts as an
infinite repository of extra charge.
• Thus if an object is highly negatively charged, the
like charges on the object will repel each other,
running through the grounding wire to the earth
until a charge equilibrium (neutrality) is
established on the object.
Induction with grounding
––
–
– –––
–
– + –
+ – +
– + +–
+ –
+
– + + –
–
What causes the attraction &
repulsion?
• While modern science has some theories, they are
young, relatively untested and well-beyond the
scope of this course.
• What we do know is that all charged bodies
produce an electric field. This field is a type of
force field (no joke!) that allows other charged
particles to “feel” the presence of the charge
producing the field.
• Technically a “field” of any type is a potential to
have a force, in this case, an electrostatic force.
• The intensity of the electric field is given by the
equation
kq
E 2
r
where E is the intensity of the electric field, k is a
constant, q is the size of the charge producing the
field and r is the radial, or straight line, distance
between the charge and the test point.
• The intensity of the field is normalized
(standardized) to measure the effect of the field per
a single unit charge, also called a test charge.
Electric Field Due To A Point Charge
To draw an E-Field, select a point in nearby space to the charged
Object. Mentally place a “test charge” at this point. Ask yourself,
“How would this charge move due to the presence of the other
charged body?”
Field of an Electric Dipole
Note the directions of the field lines. The E-Field variable is a vector
quantity, since it is measured as reference to a test charge,
which is always positive.
The E-Field Variable
• The E-Field variable measures the intensity of an
electric field at some point in proximity to the field.
• Symbol: E
Units: C/m
• The constant k
– This value has to do with an Electric field’s ability to
pass through space. For the problems we will work, it
has a constant value of 8.99 x 109 Nm2/C2
• The amount of force is quantified by
Coulomb’s Law of Electrostatic Force
which we will discuss later.
Quantifying the E-Static Force
• Another way to define the electric field is by measuring the
field’s effect, or force, on any concentration of charge, qo,
placed in the field. This way we define the field as
kq F
E 2 
r
qo
Where qo is the charge placed into the field and q is the charge
creating the field. If we algebraically arrange this formula
to solve for force, we see that F = Eqo. Expanding this
equation, we end up with Coulomb’s Law for electrostatic
forces.
Coulomb’s Law
Charge 1
F k
Charge 2
q1 q 2
r
2
electrostatic constant
2
m
k
 8.99109 N 2
4 o
C
1
2
C
 o  8.85109
Nm 2
distance of separation
LOOK FAMILIAR?
Recall Newton’s Law of Universal Gravitation:
m1m2
F G 2
r
It’s really weird, yet fascinating and elegant how the universe works
out such that two very different phenomena of nature are so similar
at the most fundamental levels…this is one of many cases in physics
where this symmetry stands out.
BUT WAIT! They are NOT the same at all, and have no
apparent relationship. One of the biggest failures of modern
Physics is the inability to reconcile the 4 fundamental forces
into a single causality.
• Some consequences of Coulomb’s Law:
– A shell of uniform charge attracts or repels a
charged particle that is outside the shell as if the
shell’s charge were concentrated at its center.
– A shell of uniform charge exerts no
electrostatic force on a charged particle that is
located inside the shell.
– On a conductor, any net, unbalanced charge
will be found on the outside surface as a result
of the electrostatic repulsion.
*We will prove the top two statements in AP Physics C by means
of the Gauss’s Law for electric fields.
**The top two statements have corollaries in gravitation!
Practice
1) A negative charge of -2.0 x 10-4 C and a positive
charge of 8.0 x 10-4 C are separated by a distance of
0.30 m. What is the force between the charges? What
direction will they move?
2) A negative charge of -6.0 x 10-6 C exerts an attractive
force of 65 N on a second charge 0.050 m away. What
is the magnitude of the second charge?
3) An object with charge +7.5 x 10-7 C is placed at the
origin. The position of a second charge +1.5 x 10-7 C
is varied continuously from 1.0 cm to 5.0 cm along the
x-axis. Draw a graph of the force on the first charge.
Wait, there’s more!
4) An object with charge +7.5 x 10-7 C is anchored
at the origin. A second charge of -7.5 x 10-7 C is
placed at coordinates (4,3) and allowed to move.
Calculate the magnitude and direction (specify the
angle) of the force on the second particle.
5) An object with charge +7.5 x 10-7 C is placed at
the origin (it can move). Two charges, both of
+1.4 x 10-3 C are anchored at x = +3 and x = -3
respectively. Find the force on the first charge.
6) What would happen if all three charges in 5) were
allowed to move? What would happen if you
revered the sign on the two outer particles to be
negative?
Storing Charge
• A capacitor is a device which stores charge
by using an unbalanced charge’s own
electric field against it to hold it in place.
• Capacitors are generally two pieces of
conductive material placed close together
but separated by an insulator.
A CAPACITOR is two conductors separated by
an insulator. If charges are placed on the conductors,
then it stores electricity. It is important to note that the
two conductors have EQUAL BUT OPPOSITE charges!
In its simplest form, a capacitor is two parallel plate
conductors separated by an air gap insulator.
Capacitance Defined…
• A capacitor stores charge by producing an electric
field between the surfaces. This electric field
“traps” charges on the plates of the capacitor.
• The dimensions and material that comprises the
capacitor will determine how much charge can be
stored by the capacitor.
• The variable C, or capacitance, defines how much
charge can be stored on the capacitor.
Charge stored on the
capacitor
Capacitance
q
C
V
Units: charge per electric potential
or Coulomb per Volt, C/V.
Electric Potential between
the opposing surfaces of
the capacitor.
Uh oh…another variable…
• Every E-Field has an electric potential
associated with it. The electric potential is
the sum of all electric fields through a
particular area. Defined another way, the Efield is the rate which the electric potential
changes across space. For you calculus
people that’s
E = dV/dx
Electric Field inside a capacitor
(or other area of uniform field)
• Using the equation from the previous slide,
if the field is changing at a uniform rate this
equation becomes a very useful and easy
one:
V = Ed
For many capacitors this equation describes
the electric field in between the metal
surfaces.
• Generally, we speak of just the electric
potential (V) of an E-Field. It can be
conceptually defined as the amount of work
that the field does on a particular amount of
charge, qo.
• This would be kind of like defining GPE
without mass. (i.e., mgh/m, meaning GPE
per unit of mass).
Electric Potential
W
V
qo
• Symbol: V
Units: Volts (V)
• Electric potential of a point charge q:
kq
V 
r
For many point charges in an array
kq
V 
r
However, the sign of the charge must be taken into
account when calculating the electric potential. So
it is possible to have a positive potential or a
negative potential overall, or even a net zero
potential.
Other topics you need to know:
(a.k.a. you should look these things up on the interwebs)
• Faraday Cage
• Lyden (or Leyden) Jar
• Miliken’s Oil Drop Experiment
– What was the main idea and setup? What did Miliken
accomplish?
• Lightning rods and building up charge on a point
on a conductor
– Since charge accumulates on the outside of all
conductors, any sharp corner will have a large
concentration of charge (and a higher absolute V) than
any smooth surface.