Download Electric potential

Electrostatics
• Electrical Forces
• Electric Charges
– conservation; Coulomb’s Law
• Electrical Conductors and Insulators
– semiconductors and superconductors
• Charging
• Electric Field
• Electric Potential
Electrostatics
• Electrostatics is the study of stationary
charges
• Electric Force
– follows inverse-square law like gravity
– Two varieties: attractive and repulsive
• Electric force is produced by electric
charge, just as gravitational force is
produced by gravitational mass.
Electric Charges
• Assume two types of charges, positive (+)
and negative (–).
• Like charges repel (+) ↔ (+) or (–) ↔ (–)
• Opposite charges attract (+)––> <––(–)
• Protons are positive (+)
• Electrons are negative (–)
• Neutrons have no net charge.
• Every atom has protons and electrons
32.2 Conservation of Charge
• Conservation of
Charge
Law of Conservation of Electric ChargeDuring any process, the net electric
charge of an isolated system remains
constant ( is conserved).
Total charge before= Total charge after.
•
An object that has unequal numbers of
electrons and protons is electrically
charged.
•
An atom with a net positive charge is a
positive ion; it has lost one or more
electrons.
•
An atom with a net negative charge is
a negative ion; it has gained one or
more electrons.
•
The principle that electrons are neither
created nor destroyed but are simply
transferred from one material to
another is known as conservation of
charge.
32.3 Coulomb’s Law
•
•
q = charge of particle; +q or -q
Coulomb’s law states that for charged particles or objects that are small
compared with the distance between them, the force between the charges
varies directly as the product of the charges and inversely as the square of
the distance between them.
Coulomb applet
Electric filed lines applet
32.3 Coulomb’s Law
•
kq1 q2
F
2
d
•
•
•
•
•
F = kq1q2/d2, where d is the
distance between the charged
particles
q1 represents the quantity of
charge of one particle and q2 the
quantity of charge of the other
particle. The SI unit of charge is
the coulomb, abbreviated C.
The proportionality constant k in
Coulomb’s law is 9.0 x 109
Nm2/C2.
1 electron has a charge of 1.60 x
10-19 C {either (+) or (-)}.
Like all other forces, the
electrostatic force between two
charged objects is measured in
Newtons (N).
-F = attraction and +F = repulsion
32.3 Coulomb’s Law
1.
Consider a pair of charged particles separated by a distance d. If the distance between the particles is multiplied
by 4, how will the electrostatic force between the particles change?
2.
If the charge of each particle tripled and the distance also tripled, how would the electrostatic force between the
particles change?
3.
If the charge of one particle doubled and the charge of the other particle tripled, how would the electrostatic force
between the particles change?
4.
If the charge of one particle were reduced to one-half the original charge and the distance between the charges
were multiplied by 2, how would the electrostatic force between the particles change?
32.3 Coulomb’s Law
1.
Sue rubs two latex balloons against her hair, causing the balloons to become charged negatively with 2.0 x 10 -6 C.
She holds them a distance of 0.70 m apart. a) What is the electric force between the two balloons? b) Is it one of
attraction or repulsion?
2.
Two pieces of puffed rice become equally charged as they are poured out of the box and into Kirk’s cereal bowl. If
the force between the puffed rice pieces is 4 x 10-23 N when the pieces are 0.03 m apart, what is the charge on
each of the pieces?
Atomic Structure
• Every atom has a positively charged nucleus
surrounded by negatively charged electrons.
• Electrons all have same charge and same mass
– same for protons.
• Protons have an amount of positive charge
equal to the negative charge on electrons, but
about 1800 times as much mass.
• Neutrons have almost the same mass a protons,
but no net charge.
• Atoms have as many electrons as protons, so
have no net charge (normally).
How does the electrical force between the proton and the electron in the hydrogen atom
compare to the gravitational force between these two particles. Given: Bohr radius, r =
5.29 x 10-11 m, use the mass of the proton and electron to two decimal places. ?
Coulomb’s Law Review
kq1 q 2
F
d2
• Inverse-squared law
• F – Force; q1 & q2 – charges; k – constant
• d – distance between charges
 Gm1 m2
• Recall gravity:
F
2
d
• charges play the role of masses, k replaces G
• http://www.colorado.edu/physics/2000/applets/nforcefield.html
Conservation of Charge
• Charge is conserved – neither created nor
destroyed.
• This is as fundamental as momentum and
energy conservation.
• When an object becomes charged, it is
charge transferred from another object.
• Normally, electrons can be transferred
from one object to another, not protons.
Conductors, etc.
• Metals have electrons that move very
freely, while nuclei are fixed in place in the
crystal lattice – they are good conductors.
• Substances like rubber and water have
electrons that do not jump between atoms
– they are good insulators.
• Semiconductors can behave either way.
• Superconductors allow electrons to move
with virtually no resistance.
Electrical Charging
• Charging by friction or contact: electrons
transferred from one body to another.
• Charging by induction:
• Induction works because charges in a
conductor are separated by the forces
from another nearby charge.
Charge Polarization
• When an atom is under the influence of a nearby
charge, the force attracts the nucleus and repels
the electron “cloud” or vice, versa.
• In any case their centers no longer coincide, and
we have a polarized molecule known as a dipole
(two poles).
• Some molecules (water, for example) are always
polarized.
• http://www.colorado.edu/physics/2000/applets/h2o.html
Electric Field**
• A gravitational field is a force per unit
mass. We think of the earth as the
producer of a gravitational field, and
smaller masses as feeling a force due to
this field.
• The force the small (test) mass feels
depends only on its own mass, given that
the earth is producing the field.
• Likewise for an electric field.
Electric Field
• Think of a fixed set of charges producing a field that effects a force
on some other charge.
• The electric field of these fixed charges gives a picture of the
magnitude and direction of the force on a unit charge anywhere in
space relative to the fixed charge distribution.
• http://www.colorado.edu/physics/2000/applets/forcefield.html
• E-Field Applet
Electric Field
• We always count a test charge as positive,
so field lines point toward negative
charges and away from positive charges.
• Regions where the field lines are closer
together are where the magnitude of the
force is greater on any given charge, and if
the lines are far apart, the force is weak.
Electric Field
• The electric field inside a conductor is
always zero everywhere inside.
• This allows electrical shielding.
Electric Field Example 1
• Deepika pulls her wool sweater over her head, which charges her
body as the sweater rubs against her cotton shirt. a) What is the
electric field at a location where a 1.60 x 1019 C-piece of lint
experiences a force of 3.2 x 109 N as it floats near Deepika? b)
What will happen if Deepika now touches a conductor such as a
door knob?
Electric Field Example 2
• A fly accumulates 3.0 x 1010 C of positive charge as it flies through
the air. What is the magnitude and direction of the electric field at a
location 2.0 cm away from the fly?
Electric Potential
• Recall gravitational potential energy of an
object – due to its height above the
ground. The potential energy is there
because the Earth puts a force on the
object, enabling it to do work.
• Same for electrical forces.
• Any object with a force on it has potential
energy.
Electric Potential
• Potential Difference: The work done to move a positive test charge
from one location to another.
• Potential Difference = Work/test charge = W/qo
• The SI unit for potential difference is the volt (V), which equals a
joule per coulomb (J/C).
• Analogy, Turning on water hose
• Remember, the term “work” can be replaced with the
term “energy,” because to store energy in, or give energy
to, an object, work must be done.
• Therefore, potential difference can also be defined as
the electrical potential energy per unit test charge.
• Voltage is often used to mean potential difference.
Electric Potential
• Electric potential takes the abstraction a
step further:
– Electric potential is potential energy per unit
charge.
•
http://webphysics.davidson.edu/physlet_resources/bu_semester2/c05_potential.html
• The unit for electric potential is the Volt.
1 volt = 1 joule / coulomb
(Coulomb is the unit for charge)
Electric Potential
• What does it mean to say that your car
has a 12-volt battery?
• It means that 1 coulomb of charge that
moves from one terminal to the other
either does 12 Joules of work on the way,
or picks up 12 Joules of kinetic energy.
• ½ coulomb will pick up 6 joules of kinetic
energy. (volts x coulombs = joules)
Storing Electrical Energy
• Storing electrical energy depends on
keeping positive and negative charges
separated.
• This is very difficult to do, since the
electrical force is so strong.
• But we can use a capacitor, which is two
conducting plates separated by an
insulator, to store energy in the field
between the plates. (Elmo first)
•
http://webphysics.davidson.edu/physlet_resources/bu_semester2/c07_capacitor_energy.html
Voltage
• The field that exists between two charged parallel plates is uniform
except near the plate edges, and depends upon the potential
difference between the plates and the plate separation.
• E = Voltage/distance between plates = V/Dx
• Here, the unit for electric field is the volt/meter. It was noted earlier
that the unit for electric field is the Newton/coulomb. This means that
a volt/meter must equal a Newton/coulomb?
• Volt/meter =
Electric Potential Example 1
• An electron in Tammie’s old black and white TV is accelerated
toward the screen across a potential difference of 22,000 V. How
much kinetic energy does the electron lose when it strikes the TV
screen?
Voltage Example 2
• Amir shuffles his feet across the living room rug, building up a
charge on his body. A spark will jump when there is a potential
difference of 9000 V between the door and the palm of Amir’s hand.
This happens when his hand is 0.3 cm from the door. At this point,
what is the electric field between Amir’s hand and the door?