Transcript Electric Charge

Electric Charge
AP Physics C
Montwood High School
R. Casao
• Two kinds of
electric charge:
positive and
negative.
• Two positive
charges or two
negative charges
repel each other.
• Two unlike
charges attract
each other.
• Charge cannot be created, but can be transferred
from one object to another – charge is
conserved.
• When one object gains a charge, another object
loses this charge; total electric charge on both
bodies does not change.
• Electrons have been removed from the objects
shown below, leaving them positively charged.
Like charges exert equal and opposite repulsive
forces on each other.
• Electrons have been
added to these
objects, making them
positively charged.
Like charges exert
equal and opposite
repulsive forces on
each other.
• Oppositely charged
objects exert equal
and opposite
attractive forces on
each other.
• All matter has charge; most often the positive
charges equal the negative charges and the object
has no net charge.
• More positive charges than negative charges
provides a positive charge on the object.
• More negative charges than positive charges
provides a negative charge on the object.
• Conductors allow the movement of charge
through them; insulators do not allow the
movement of charge through them.
• Most metals are good conductors because one or
more outer electrons in each atom become
detached and can move through the material.
•
The other electrons remain bound to the positive
nuclei, which are bound in fixed positions in the
material.
• Insulators have few, if any, free electrons and
electrons cannot move freely through the material.
• Semi-conductors fall between conductors and
insulators in the ability of electrons to move freely
through the material.
• An object can become charged by direct contact
(friction)
1. Rub a balloon on your hair; electrons from the hair
are transferred to the balloon. Balloon becomes
negatively charged; hair positively charged. Hair is
attracted to balloon when balloon pulled away from
hair.
2. When walking on carpet, movement of shoes on
carpet rubs electrons onto shoes or feet. Charge
distributes itself over body and when reach out to
touch a metal object, charge moves from you to
the metal object (static discharge).
•
An object can be charged by induction.
–
Bring the positively charged rod close to the
spheres, but don’t touch the spheres.
– Negative charges are attracted to the positively
charged rod; positive charges are repelled by the
positively charged rod.
– Separating the spheres ensures that the charges remain
on the respective sphere.
– Removing the rod with the spheres separated causes
the charges on the sphere to repel and seek an
equilibrium position.
• Bring the positively charged rod close to the
sphere, but don’t touch.
• Positively charged rod attracts negative charges
on sphere and repels the positive charges on the
sphere.
• The sphere becomes polarized – one side
positive and the other side negative. Not all
charges move, just enough so that the forces of
attraction equals the forces of repulsion.
• If the positively charged rod is removed, the sphere
goes back to being neutral.
• To keep a charge on the sphere, you can attach a
ground to the sphere. A ground is a conducting path
between an object and the earth to prevent an electric
shock due to excess charge.
• Earth is a conductor and can act as a source for extra
electrons or as a sink for unwanted electrons.
• Electrons from the Earth
pass through the ground into
the sphere leaving a negative
charge on the sphere.
• Take the positively charged
rod away and the sphere
stays negative.
• For a positively charged sphere, use a negatively charged
rod. When the ground is connected, electrons pass from
the sphere to the Earth.
• In either case, the sphere has been charged by induction.
• We can’t say what charge is, we an only describe its
properties and behavior.
• Proton and electron carry the same charge q;
q = 1.602 x 10-19 C.
• Unit of charge: Coulomb, C.
• 1 C = total charge of 6.24 x 1018 electrons.
• All charge is a whole number multiple of q because there
are no fractional portions of protons or electrons.
Conductors and Insulators
• When charge is placed on an insulator, the
charge stays where it is placed and does not
move at all.
• When charge is placed on a conductor, it will
move because of the force of repulsion between
like charges.
– If an object is hollow, the charge will spread
uniformly over the surface.
– If the object is solid, the charge will spread
uniformly over the surface of the object.
CHARGING METAL SPHERE BY INDUCTION
Charges are free to move in a conductor but
are tightly bound in an insulator. The earth
(ground) is a large conductor having many free
charges.
CHARGED COMB ATTRACTS
PAPER
In an insulator the charges
can move slightly (called
polarization of the insulator).
A piece of paper is attracted
to a charged comb because
the positive charges are
closer to the negatively
charged comb (in the upper
figure).
Charge Neutralization
• When two charged conductors touch,
charge neutralization occurs.
• Sphere A contains a charge of +16 C;
sphere B contains a charge of –4 C.
– Allow A to touch B and 4 C of
negative charge combines with 4 C of
positive charge (neutralization). Net
charge = 16 C + -4 C = 12 C.
– 12 C of positive charge remains.
– Positive charges repel, so one half of
the positive charge moves onto A and
the other half of the positive charge
moves onto B, so both A and B will
have 6 C of charge when separated.
Coulomb’s Law
• Coulomb’s law describes the force between any
two charges q1 and q2.
k  q1  q 2
F
2
r
– r is the distance between the charges.
– k is a constant that considers the effect of the medium
on the charges.
• Air or vacuum:
Nm
k  8.9875 x 10
C2
– Unit of force: Newton.
9
2
– This expression for k will be important later in
some of the problems; eo is a constant used in
1
capacitance.
k
4  π  εo
2
1
C
εo 
 8.854 x 10 12
2
4πk
Nm
• The smallest unit of charge known in nature is
the charge on an electron or a proton.
Particle
Electron
Proton
Neutron
Charge (C)
-1.602 x 10-19
1.602 x 10-19
0
Mass (kg)
9.11 x 10-31
1.67 x 10-27
1.67 x 10-27
• Coulomb’s law deals with forces
between point charges or
charged particles.
– These forces are equal and
opposite.
– The sign of the force indicates the
type of force (positive – repulsion;
negative – attractive); but let the
direction of the force vector
determine if the force is
considered positive or negative in
sign.
Small-Angle Approximation
• A small-angle approximation is a useful in situations
involving small angles.
• For such angles, when the angle x is measured in
radians, the trigonometric functions can be
approximated by:
sin x  x
cos x  1
tan x  x
• Small angle approximations are useful in the calculation
of the period of a pendulum, the calculation of the
intensity minima in single slit diffraction, and in
geometric optics.
• Small angle approximation. The value of the small angle X
in radians is approximately equal to its tangent.
• When one angle of a right triangle is small, its hypotenuse is
approximately equal in length to the leg adjacent to the
small angle, so the cosine is approximately 1.
• The short leg is approximately equal to the arc from the
long leg to the hypotenuse, so the sine and tangent are both
approximated by the value of the angle in radians.