Transcript 8.1 Electric Charge and Electric Field

Electric Charges and Fields
The Amber Effect
Ancient Greeks discovered that when amber (fossilized tree
sap – like a plastic) is rubbed, it will attract various
substances like cloth fibers, fine wood shavings, paper,
debris or lint. Amber’s attracting of these materials (when
rubbed) was called the “amber effect”.
Elecktron
The Greek word for amber is elecktron, the root of the
English words, electron and electricity. William Gilbert in
the 1600s used the term electrics to refer to substances
(like amber and glass) that when rubbed, would attract bits
of paper and such. Substances that when rubbed (like
metals) did not attract paper bits were called nonelectrics.
Static Electricity: Insulators and Conductors
Today we call the amber effect static electricity. We call
substances insulators (Gilbert’s electrics) if they will attract
paper bits when rubbed. Substances that do not attract
paper bits when rubbed are called conductors (Gilbert’s
nonelectrics).
Insulators
Conductors
Static Charge
When insulators are rubbed, picking up paper bits, they are
said to possess a static charge (A charge that is stationary
on the insulator, not readily moving out of the insulator).
Electroscopes
An electroscope is a device used to detect static electric
charges on an object. There are two main kinds of
electroscope – the pith ball electroscope and the leaf
electroscope.
Detecting Charge With A Pith Ball Electroscope
When a charged rod is
brought near a neutral
(uncharged) pith ball
on a string (A), the pith
ball moves towards the
rod (B). When the pith
ball touches the rod
(B), it acquires the
same charge as the rod
and then moves away
from the rod (C). This
shows that like
charges repel each
other.
Two Kinds of Static Charge
Charged Glass Rod
Pith Ball Touches
Charged Plastic Rod
Touching Ball Gets Same
Charge as Rod
Similar Charges Repel Each
Other
Balls charged previously used with rods charged previously
Each rod charges its own pith ball. Since each pith ball behaves
differently with a given rod, there must be two kinds of charge.
Positive and Negative Charges
The words positive and negative refer to the two kinds of
electric charge. A glass rod when rubbed with a silk cloth
becomes positively charged while a plastic rod rubbed with
a wool cloth becomes negatively charged.
Glass Rod
Plastic Rod
Wool
Silk
The Laws of Electric Charge
When objects are
charged, it is
observed that likecharged objects
repel each other
while oppositelycharged objects
attract each other.
Neutral objects
attract to either
positively-charged
objects or to
negatively-charged
objects.
Neutral Objects Attract to Charged Objects
Neutral Pith Balls
Atomic Explanation of Static Charges
Neutral atoms are made up of equal numbers of protons
(positively-charged, heavy particles in the nucleus) and
electrons (negatively-charged, light particles moving
briskly around the nucleus).
Atomic Explanation of Static Charges
In solids, protons (positive charges) are fixed and do not
move while electrons (negative charges) can move (to one
side of the atom or from one atom to another atom,
depending on the substance).
Atom holding its electrons around itself.
Atom allowing its electrons to wander to neighboring
atoms.
How Insulators and Conductors Differ Atomically
Atoms in insulators hold their electrons around their nuclei
with no free electron movement from atom to atom while
atoms in conductors electrons are shared and move freely
from atom to atom. Charged objects brought close to
insulators cause their electrons to move towards one side
of their atoms but charged objects brought close to
conductors cause their electrons to move in mass to one
side of the object, giving rise to a large charge separation
which makes one side oppositely charged to the other
side.
Different Atoms Exert Different Attractions For Electrons
Atoms that have electrons closer to their nuclei or that have
more protons in their nuclei tend to attract electrons more
strongly than those atoms having electrons in higher
energy levels or having fewer protons in their nuclei.
The nitrogen atom (left) has less electron
pull than the oxygen atom (right) since
the oxygen atom has the same
number of energy levels but has
one more proton and electron
which provide more attraction.
The phosphorus atom (right)
has less electron pull since
its outer electrons are farther
from the nucleus (one energy
level farther out).
Close Contact of Different Substances (Rubbing)
When different solid objects come into close contact as in
rubbing them against each other, electrons from one
substance commonly move into the other substance. This
happens because the different atoms of each substance
attract electrons either more strongly or weakly. In the
example below, the atoms in the silk cloth attract electrons
more strongly than the atoms in the glass rod. This uneven
attraction for electrons leaves the rod overall positive and
the silk cloth overall negative.
Negative charge is from a gain of electrons while
positive charge is from a loss of electrons.
Different charges come from a deficit (positive charge) or
excess (negative charge) of electrons.
Law of Conservation of Electric Charge
When neutral objects are charged by rubbing, the net charge
produced on both objects together is zero. In other words,
the amount of positive charge produced on one object is
equal to the amount of negative charge produced on the
other object. Their sum is zero due to their opposite signs.
Review of the Explanation for Electric Charges
When a duster cloth is rubbed on polythene plastic, the
plastic has more attraction for electrons which leaves the
duster positive and the polythene equally negative. When
the duster cloth is rubbed on cellulose acetate, the cloth
has more attraction for electrons than the acetate leaving
the cloth neagative and the acetate equally positive.
The
Triboelectric
Series
The Triboelectric
Series is a chart
that shows the
charge that
objects will get
when rubbed
together. When
wool and plastic
(PVC) are
rubbed, the wool
becomes positive
and the plastic
becomes
negative.
Grounding an Object
Grounding is usually used to remove the charge build-up on
an object but it can also be used to charge an object (This
will be discussed later.). When an object is grounded, it is
connected by means of a conductor (metal) to some other
much larger object (often the earth or ground). Electrons are
free to move into or out of the ground into the object until its
electric forces balance with the connection and its
environment.
Grounding an Object
Grounding removes a charge as long as the grounding object
is larger than the discharging object. For example, a tiny pith
ball is neutralized when a person touches it (the person’s
body
is huge compared to
the tiny pith ball.)
Inducing (Causing) a Charge Separation
When a charged object is brought close to an insulated
metallic object, it induces (causes) electron movement
which produces an equal and opposite charge on different
sides. This process is called electrostatic induction.
Opposite charge to the glass rod causes an attraction
between the pith ball and the positively-charged glass
rod.
The positive rod induces (causes) the neutral pith ball to gain a negative charge on
its side facing the rod because electrons can move and are attracted to the positive
rod.
How a Charged Comb Picks Up Paper Bits
The negatively-charged comb induces neutral paper bits to
get positive ends facing the comb (negative electrons
move away from or are repelled by the negative comb).
The positive paper ends are then attracted to the (–) comb.
Methods of Charging an Object
1.
Charging by conduction or contact happens when a neutral
object is touched by a charged object. The neutral object gets
the same charge as the charged object.
2.
Charging by induction happens when a neutral object is
approached by a charged object (not touched) and then
grounded while the charged object is near. In this method the
neutral objects gets a charge opposite to the charged object
that was brought close to it.
Bringing a Charged Object to a Leaf Electroscope
A rod is brought close to the end knob of a leaf electroscope.
As it gets close to the electroscope, the rod repels
electrons down (if it is negative) or attracts electrons up (if
it is positive). Since the bottom leaves are both negative (if
the rod is negative) or both positive (if the rod is positive),
they repel each other and separate.
Removing a Charge by Grounding
A leaf electroscope is charged
negatively. A person touches
the electroscope, gounding it.
Electrons leave through the
hand until the electroscope is
neutral and the leaves drop.
Charging a Leaf Electroscope by Induction
The negative balloon is brought
close to the knob of the
electroscope. This repels
electrons from the knob.
When the electroscope is
grounded, the electrons are
repelled by the balloon out of
the electroscope (leaving it
overall positive). When the
ground is broken and then
the balloon removed, the
electroscope remains
positively-charged (now with
the leaves spread), opposite
to the charge of the balloon.
Measuring Electrical Charge
The unit measuring electrical charge is called the coulomb
(C), named in honor of Charles Coulomb who investigated
the laws of electrical charge. The symbol used in formulas
for charge is Q or q. One coulomb is the amount of charge
on 6.2415 x 10 18 electrons (for a negative coulomb) or on
6.2415 x 10 18 protons (for a positive coulomb)
etc …
… etc
etc …
… etc
The Elementary Charge
A charge on a single proton or a single electron is referred to
as the elementary charge. The value of an electron’s
charge is – 1.6022 x 10-19 C and the value of a proton’s
charge is + 1.6022 x 10-19 C.
The magnitude or size of
the charge on an electron
and proton is the same even
though their sizes and
masses differ greatly.
electron
Coulomb’s Law
Coulomb found that the electric
force between two charged
objects varies directly as the
charge on each object and
inversely as the square of the
distance between their
centres. (F21 means the force
of q2 on q1)
Similar Form: Coulomb’s Law and Gravitation Law
Coulomb’s Law for charges has the same form as Newton’s
Law of Gravitation.
The k constant of Coulomb’s Law is 8.988 x 109 Nm2/C2
The G constant of Newton’s Law is 6.674 x 10-11 Nm2/Kg2
For everyday objects and charges that we handle, gravity is
typically a much weaker force than charge forces.
Getting a Sense of Charge Size and Force Size
A charge of +1 C and – 1C placed 1 m apart will produce an
attractive force of 8.998 x 109 N. This is a force of about a
million tons! We normally do not encounter charges as
large as a coulomb.
Rubbing a comb typically produces a charge of about 1
microcoulomb (10-6 C).
Problem 1 Determining Electric Force
Determine the electric force on an electron in a hydrogen
atom (has one proton) if the average orbit radius is
0.53 x 10-10 m.
F = (9.0 x 109 Nm2/C2)(1.6 x 10-19 C)(1.6 x 10-19 C)
(0.53 x 10-10 M)2
= 8.2 x 10-8 N (in a direction toward the centre)
Problem 2 Determining Electric Forces
Q1 , a charge of 50 µC is 1 m from Q2 , a charge of 1
µC. Which is larger in magnitude, the force that Q1
exerts on Q2, or the force that Q2 exerts on Q1?
Q1
------------1 m-------------
F21 = k(50 µC)(1 µC)
(1 m)2
Q2
F12 = k(1 µC)(50 µC)
(1 m)2
The forces are equal as would be expected from
Newton’s 3rd Law
3: Determining Force with three linear charges
Given three colinear charges, Q1 (-8.0 µC), Q2 (+3.0 µC), Q3 (-4.0
µC) with the distances as shown, determine the net
electrostatic force on Q3.
Q1 (-8.0 µC) <--0.30 m-- Q2 (+3.0 µC) <-0.20 m Q3 (-4.0 µC)
The net force on Q3, FNet is F31 + F32
F31 = (9.0 x 109 Nm2/C2)(8.0 µC)(4.0 µC) = 1.2 N to the right (repulsion)
F32
(0.50 m)2
= (9.0 x 109 Nm2/C2)(3.0 µC)(4.0 µC) = 2.7 N to the left (attraction)
(0.20 m)2
2.7 N
1.2 N
Q3
F = 1.2 N – 2.7 N = -1.5 N (Where – is left and + is right)
= 1.5 N left
Determining Electric Force Using Vectors
Given charges Q1 , Q2 and Q3 as shown, determine
the magnitude and direction of the force on Q3 .
F32
Forces on Q3
60o angle
Q3 = +65 µC
F31
30 cm
60 cm
Resolve F31 into horizontal
and vertical components.
30 o
Q1 = -86 µC
Q2 = +50 µC
52 cm
F31 = (9.0 x 109 Nm2/C2)(6.5 x 10-5 C)(8.6 x 10-5 C) = 140 N [S 60 E]
(0.60 m)2
F32 = (9.0 x 109 Nm2/C2)(6.5 x 10-5 C)(5.0 x 10-5 C) = 330 N [up]
(0.60 m)2
(Continued on next slide)
Determining Electric Force on Q3 (Cont.)
Determine the magnitude and direction of the force on Q3 .
Q3
Angle β
F32
F31x component = F31 cos 30o
260 N [N]
F31y component = F31 cos 60o
Net Force
F31
120 N [E]
60o angle
F31x = F31 cos 30o = 120 N [E]
F31y = F31 cos 60o = -70 N or 70 N [S]
So, Fy = 330 N [N] – 70 N [S] = 260 N [N] and Fx = 120 N [E]
Fnet magnitude = √ ((260 N)2 + (120 N)2 ) = 290 N
Fnet direction = β = tan-1 (120 N/260 N) = 25o
Fnet = 290 N [N 25o E]
Experiments With Charges Reveal Invisible Force Fields
When powder from an insulator is spread over the surface of
a light oil and point charges are inserted into the oil, a
force pattern around the charged point source is revealed.
This pattern makes visible an invisible force field that
exists around a charged object(s).
Electric Fields
An electric field is a sphere of influence around a charged
object. Electric field exert a force on another charged
object. An electric field is a vector quantity and its
direction is determined by the direction a positive point
charge would move in the field. Between positive and
negative charges, the field runs from positive to negative.
Electric Field Strength
The strength of an electric field is related to the number of
field lines passing through a given space around the
charge. Thus a field is stronger closer to the charge
surface than it is farther out from the charge (the electric
force decreases by the distance squared).
Field Line Density Indicates Field Strength
Field line density is the number of field lines per unit volume
(unit of space). The more lines, the stronger a field and
the greater the charge (provided the lines are measured the
same distance from the charge).
Field Line Patterns for 2 Like and 2 Unlike Charges
A field between opposite attracting charges (left diagram) has
connecting field lines between the charges.
A field between like repeling charges (right diagrams) has no
connecting field lines between charges.
The Vector Nature of an Electric Field
Adding the vectors of two point charges at various points in
space produces the field. Vector addition explains the
shape of the field made by point charges.
Faraday’s Ice Pail Experiment
Michael Faraday investigated many aspects of static and
current electricity. In his “ice pail experiment” he
discovered that the static charge on an object is
distributed over the outside of an object, not on the inside.
Faraday’s Butterfly Bag
Faraday found that if an insulated, cone-shaped conductor
cloth is charged, the inside of the cone is neutral while the
outside of the bag is charged. When strings are used to
turn the bag inside out, the former inside (now the outside)
becomes charged while the former outside (now inside) is
neutral. This confirms that static electric charge resides
on the outside of an object.
Electrostatic Shielding: Faraday’s Cage
Faraday’s experiments suggested that an object could be
shielded from electrostatic charge (electric fields) if a wire
mesh cage or a metal container were to surround an
object. Electronic components that needed to be shielded
from electric fields are protected with such cages or metal
containers.
Static Charge Distribution and Object Shape
More static charge can accumulate in pointed parts of an
object than more rounded parts because pointed shapes
allow for greater density of field lines before the repulsive
forces equal those in more rounded regions.
Measuring Electric Field Strength
->
Electric field strength (|E| or E) is defined as the force per unit
charge at a given point in the field (Ex: A or B). Fe is the
force in N on the charge, q. From this relation it can be
seen that Fe = |E|q . This first formula for electric field
strength is defined in terms of a test object in the field.
A Second Formula for Electric Field Strength
Given object Q exerting a force on charge q (qt). The force
between Q and q is given by F = kQq .
r2
Combining the formula from the previous slide with the
formula above we obtain |E| = F or |E| = kQq = kQ
q
( r )2
r2
q
This new formula gives field strength in terms of the fieldproducing object. |E| = kQ
r2
Permittivity
Permittivity (ε) is a measure of the resistance of a medium
(called the dielectric) to an electric field being set up in the
medium. It measures how readily a medium “permits” an
electric field being set up in it. The relative permittivity (εr)
of a substance is a comparison of its permittivity to the
permittivity of a vacuum.
Permittivity of Free Space
The permittivity of free space is the permittivity of a vacuum
which is 8.85 x 10-12 C2/Nm2 . Its symbol is ε0.
Coulomb’s Constant and ε0
Coulomb’s Law can be written with a constant that replaces k
with ε0. Knowing the value of k allows the calculation of ε0.
Thus, ε0 = 1
4πk
=
8.85 x 10-12 C2/Nm2 .
Electric Field Problem
Electric Field Problem
Electric Field
Problem
A
Electric Field
Problem
Part a
Electric
Field
Problem
Part b
A
A
A
A
A
A
Electrical Current
A