Download Physics Chapter 12

9. A pith-ball electroscope may be in a charged or a neutral state.
Describe the steps you would take to determine whether it is
charged or neutral. If the electroscope is charged, how would you
determine what charge it possesses?
Making Connections
electric field: the space around a charged
object where forces of attraction or repulsion
act on other objects
10. While metal car bodies are being spray-painted at the factory,
they are grounded. Explain the advantages of this. (Hint: As the
spray leaves the nozzle at high speeds, it becomes charged.)
11. When clothes made of different materials tumble in a warm
clothes dryer they have a tendency to cling to one another.
Coated strips or spray may be purchased to prevent or remove
the “static cling.” Research how “anti-static cling” formulations
work. Follow the links for Nelson Physics 11, 12.1.
GO TO
www.science.nelson.com
12. Electrostatic printing, commonly known as xerography or photocopying, uses the principles of static electricity to print on paper
or other materials. Research and explain the steps in the process
where static electricity plays a role. Follow the links for Nelson
Physics 11, 12.1.
+
GO TO
www.science.nelson.com
Reflecting
13. Would you feel comfortable working in a high-tech clean room
knowing that you would have to be extremely careful about static
charge? List some advantages and disadvantages of such a job.
Figure 1
Electric field around a single positive charge
12.2
(a)
+
+
Electric Fields and
Electric Charge
What causes electric force? How is electric charge measured? The study of
charges will be far more productive if we address these questions.
Electric Fields
(b)
–
+
Figure 2
Some typical electric fields. Notice that
these field lines are directed away from the
positive spheres and toward the negative
spheres.
(a) Like charges
(b) Opposite charges
432 Chapter 12
Electric charges exert forces that can attract and repel each other even when they
are not in direct contact. What causes the force? We don’t see anything between
the charges that could be responsible for it. Yet this kind of force is already
familiar to you. The force of gravity was explained in terms of a gravitational
field of force—when a mass is placed in the gravitational field of another mass,
the first mass experiences a force of attraction toward the second mass.
It is reasonable to assume that the forces between charged objects may
also be due to a field of force. If this is true, then every charged object creates
an electric field of force in the space around it (Figure 1) and any other charged
object in that field will experience a force of electrical attraction or repulsion.
The electric field is represented by drawing a series of field lines around the
charged object. Field lines show the direction of the electric force on a small positive test charge placed at each and every point in the field. It is customary to use
a positive charge as a test charge. The relative distance between adjacent field
lines at a given point is an indication of the strength of the electric field at that
point. Some typical electric fields are shown in Figure 2.
12.2
Measuring Electric Charge
A quantitative analysis of the factors affecting electric force was first performed
by the French physicist Charles Augustin de Coulomb (1736–1806). By performing experiments similar to that shown in Figure 3, Coulomb found that the
magnitude of the force between two charged objects is directly proportional to
the product of the charges and inversely proportional to the square of the distance between them. This famous relationship, called Coulomb’s law, was of
immense importance to our understanding of electric forces. In his honour, the
unit of electric charge is called the coulomb (C).
To give you an idea of the magnitude of a coulomb: 1 C of electric charge is
approximately the amount that would pass through a 100 W light bulb in 1 s,
operating at 100 V. The relationship discovered by Coulomb can be written as:
fine support wire
A
––
repulsion
––
light
horizontal bar
B
Coulomb’s Law
kQ Q2
F = 1
d2
where k is a constant
Early in the 20th century Robert A. Millikan (1868–1953), an American
physicist, performed a series of experiments proving the existence of a smallest
unit of electric charge; all other electric charges are simple multiples of this
smallest charge. He reasoned that this elementary charge (e) is the charge on a
single electron.
Oil drops were sprayed into the space between two parallel metal plates
(Figure 4). A light was shone on the oil drops, and they were observed through a
telescope. A power supply was connected to the plates so that an electric force
would act on the oil drops between the plates. An upward electric force was
exerted on those drops whose charge was the same sign as the lower plate’s. By
adjusting the amount of charge on the plates, it was possible to isolate a single oil
drop and balance it so that the downward gravitational force and the upward
electrical force were equal.
Using measurements related to the “balancing field,” and the speed with
which the oil drops fell when the field was removed, Millikan was able to calculate the amount of electric charge on the oil drop, in coulombs.
Figure 3
Coulomb devised an experiment to measure the
force of repulsion between two charged objects,
with one object suspended from a bar by a vertical
wire. When charged object B was brought close to
charged object A, it repelled A and caused the
wire to twist a measurable amount.
Coulomb’s law: the magnitude of the
force between two charged objects is directly
proportional to the product of the charges
and inversely proportional to the square of
the distance between them
coulomb: (C) the SI unit of electric charge
atomizer
electrical force
metal
plate
light source
–
+
–
charged
oil drop
metal
plate
battery
calibrated telescope
gravitational force
Figure 4
Millikan assumed that when tiny oil drops
are sprayed from an atomizer, they become
charged by friction—some acquiring an
excess of a few electrons, while others have
a deficit. Although there was no way of
knowing how many extra electrons there
were on an oil drop, or how many were
missing, Millikan was able to devise a technique for measuring the total amount of
charge on each individual drop.
Electricity 433
By repeating this procedure many times, using the same oil drop with different amounts of charge on it, and using different oil drops, Millikan was able
to compile a long list of values for the amount of charge on an oil drop. But how
was he able to determine the value of the charge on an electron from this list of
values for the total charge on a drop?
Lab Exercise 12.2.1
Investigating Data from Millikan’s Oil Drop
Experiment
By 1909, Robert Millikan (Figure 5) was able to determine the charge on an electron by studying the behaviour of charged oil drops. Using an apparatus where
charged drops of oil fell in the presence of a strong electric field, he was able to
determine that the charge on an electron was a fundamental constant of electricity. In this lab exercise, you will analyze experimental evidence obtained from
Millikan’s oil drop experiment and search for patterns that yield the fundamental
charge on an electron.
Observations
Note: The values listed below represent the charges calculated on 12 oil drops, a
very small portion of the data collected by Millikan.
Figure 5
Robert A. Millikan (1868–1953) was awarded
the Nobel Prize for Physics in 1923.
3.2 10–19 C = 1.6 10–19 C _____________
16.0 10–19 C = 1.6 10–19 C _____________
17.6 10–19 C = 1.6 10–19 C _____________
6.4 10–19 C = 1.6 10–19 C _____________
8.0 10–19 C = 1.6 10–19 C _____________
12.8 10–19 C = 1.6 10–19 C _____________
11.2 10–19 C = 1.6 10–19 C _____________
4.8 10–19 C = 1.6 10–19 C _____________
1.6 10–19 C = 1.6 10–19 C _____________
9.6 10–19 C = 1.6 10–19 C _____________
19.2 10–19 C = 1.6 10–19 C _____________
14.4 10–19 C = 1.6 10–19 C _____________
Analysis
DID YOU KNOW ?
Nobel Prizes for physics, chemistry, and other
fields have been awarded almost annually
since 1901, according to the terms of the will
of Alfred Bernard Nobel (1833–96), the
Swedish industrialist who invented dynamite.
The awards are made by the Swedish Royal
Academy of Sciences. Each prize has a cash
value, which increases from year to year.
(a) Copy the observations into your notebook. See if you can spot the patterns
that Millikan did. (Use a calculator if necessary.)
(b) List all the patterns you can find. In your own words, try to describe what
these patterns might mean.
Two observations were evident to Millikan when he analyzed his oil drop data:
1. The smallest value for the charge on an oil drop is 1.6 × 10–19 C.
2. All the other values are whole-numbered multiples of 1.6 × 10–19 C.
Millikan called the smallest unit of charge, which is the absolute value of the
charge on an electron, the elementary charge (e).
The elementary charge (e) has magnitude
e = 1.60 × 10–19 C
434 Chapter 12
12.2
Since an electron is a negative elementary charge and a proton is a positive
elementary charge, we can conclude that the charge on one electron is
–e = –1.6 × 10–19 C, and the charge on one proton is e = 1.6 × 10–19 C.
1
Also, if the elementary charge is 1.60 × 10–19 C, then it must take 1.60 × 10–19
18
or 6.24 × 10 electrons to make up 1 C of charge. For the present, we will use
this as the value of a coulomb: 1 C = 6.24 × 1018 e.
Using this value for the elementary charge, we can devise an equation to
make an important calculation. If a charged object has an excess or deficit of N
electrons, each with a charge e (the elementary charge), then the total charge, Q,
on the object, measured in coulombs, is given by
Q = Ne
Sample Problem
How many electrons have been removed from a positively charged pith-ball electroscope if it has a charge of 7.5 × 10–11 C?
Solution
Q = 7.5 × 10–11 C
e = 1.6 × 10–19 C
N=?
Q
N = e
7.5 × 10–11 C
= 1.6 × 10–9 C
N = 4.7 × 108 electrons
The number of electrons removed was 4.7 × 108 electrons.
Practice
Understanding Concepts
1. What is the charge in coulombs on an object that has
(a) an excess of 6.25 × 1019 electrons?
(b) a deficiency of 1.0 × 108 electrons?
2. A polyethylene strip has a charge of –5.2 × 10–7 C. What is the excess
number of electrons on the strip?
SUMMARY
Answers
1. (a) –1.0 × 101 C
(b) +1.6 × 10–11 C
2. 3.3 × 1012
Electric Fields and Electric Charge
• Every charged object creates an electric field of force in the space around it;
any other charged object in that field will experience a force of electrical
attraction or repulsion.
• Electric charge is measured in units called coulombs (C).
• Millikan’s oil drop experiment proved the existence of a smallest unit of
electric charge, which he called the elementary charge (e).
• The total charge, Q, on an object, measured in coulombs, is given by the
equation Q = Ne.
Electricity 435
Section 12.2 Questions
Understanding Concepts
1. Assuming the object marked with a P in Figure 6 is positively
charged and the lines represent the electric field, determine the
signs of the charges on the other objects and place arrows on the
lines in the correct directions.
P
2. In a lightning bolt, it is estimated that a charge of 22.0 C is transferred from a cloud to Earth. How many electrons make up the
lightning bolt?
3. A metal-leaf electroscope is given a negative charge of 1.2 µC by
induction and grounding. How many electrons move through
your finger when you touch the knob of the electroscope?
Figure 6
4. An ebonite rod with an excess of 6.4 108 electrons shares its
charge equally with a pith ball when they touch. What is the
charge on the pith ball, in coulombs?
5. In Millikan’s experiment, oil drops that have similar charges to
that on the bottom plate can become balanced so that they will
float. Draw a free-body diagram of the oil drop and explain why
this must be so.
6. Draw a straight horizontal line about 5 cm long in your notebook
to represent a positively charged wire. Draw the electric field
lines above and below the wire. (Hint: The direction of the electric
field line is determined by the direction of the force experienced
by a small positive test charge near the wire.)
7. Draw two straight horizontal lines about 5 cm long and parallel to
each other, separated by about 2 cm. If the top line represents a
positively charged plate and the bottom one a negatively charged
plate, draw the electric field between the plates.
Applying Inquiry Skills
8. After completing an experiment similar to Millikan’s, a student
claims that the charge on the oil drop is 3.8 10–19 C. Is the
measurement reasonable or is it suspect? Explain your reasoning.
DID YOU KNOW ?
Electric Fields in the Ocean
Sharks are sensitive to the small electric field
surrounding possible prey, such as fish.
Experiments have shown that a shark will
attack an artificial electric field and ignore a
piece of food. Artificial electric fields were
used at the 2000 Olympics in Australia to
keep sharks away from triathalon competitors
swimming in Sydney harbour.
9. Discuss how the mass of an individual marble could be calculated given several bags containing different numbers of identical
marbles. You would not be allowed to see into the bag or handle
it in any way. Assume the bags have very small masses and that
an electronic balance is available. If the materials are available,
try your method to see if it works.
10. Many people believe that electric fields can be used to treat
human diseases. There are claims that exposure to low frequency
electric fields is effective in treating conditions such as osteoporosis, arthritis, muscle pain, cancer, and AIDS. Research these
controversial claims and determine whether they are credible.
Follow the links for Nelson Physics 11, 12.2.
GO TO
www.science.nelson.com
Reflecting
11. When Millikan was performing his famous oil drop experiment
he was unaware that there existed a smallest electric charge.
Initially he might have been discouraged since the measurements
of the charge on the oil drop seemed to vary with no discernible
pattern. What kinds of characteristics must a scientist (like
Millikan) have to make such a discovery? Do you think you possess these characteristics?
436 Chapter 12