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Electrostatics
All matter is electrical in nature
Atoms -
Neutral Atom
Ion
Positive ion
Negative ion
Objects are charged when they have an excess or deficiency of electrons
Conductor
Insulator
The smallest charge found in nature is the charge found on
The elementary charge:
1e=
Does it make sense for an atom or group of atoms to have half an electron?
Charge is quantized. Charge on any object is an integer multiple of the elementary charge ‘e’
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q = net charge =
Example:
q = -8 x 10-19 C
Example:
q = -1.92 x 10-19 C
Conservation of Charge
In a closed system
Charges cannot be created or destroyed; only transferred.
Example: 2 identical conducting spheres
Example: 2 identical conducting spheres
Problems:
1. Which of the following net charges could be found on an object?
a)
7 elementary charges
b)
1.6 x 10-19 elementary charges
c)
-1.8 x 10-19 C
d)
+3.2 x 10-19 C
2. A conducting sphere with net charge q = -16 elementary charges is touched by an identical
conducting sphere with 0 charge.
a)
What is the net charge on the conducting sphere in elementary charges?
b)
What is the net charge on the conducting sphere in Coulombs?
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3. What is the net charge of an object with 5,000 excess electrons?
Transferring Charge – 3 methods for charging an object
Only electrons move when transferring charge. Positively charged objects lose electrons, they do not
gain protons
1 – Charging by Friction
Both objects begin neutral.
When one object is rubbed against the other (friction) electrons are transferred.
This occurs because one object has a higher affinity for electrons than the other.
Examples:
Rubber & Fur
Glass & Silk
2 – Charging by contact
A charged object touches another object. The objects then share the charge.
A conducting sphere with charge +8 is brought in contact with an identical sphere which is neutral.
What is the net charge on each sphere after contact?
Electroscope – The electroscope was an early invention for detecting the presence of charge. There is a
conductor at the top which connects to leaf(s) which will move depending on the charge of the
electroscope.
Neutral electroscope
Negatively charged
Positively Charged
Grounding – A ground is any large object that can accept or donate electrons. Best ground is the Earth.
Grounding an object makes the object neutral
Negatively charged object
Positively charged object
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“Be the electron”
3 – Charging by Induction
1. What would happen if a charged object
was brought near an electroscope?
2. And then the electroscope
is grounded?
3. The ground is disconnected
4. And the charged object is removed
What happens to the electroscope? Is it charged?
Did it ever touch the original charged object? Where did the charge come from?
Charge Polarization
Opposite charges ___________
Similar charges ___________
What happens when a charged object is brought near a neutral object?
The neutral object is still neutral,
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4. What is the force due to gravity between an electron and a proton, separated by 0.6 x 10-10 m?
Electrostatic Force - Coulomb’s Law
Four Fundamental Forces
1. Strong (nuclear) force – keeps protons in atomic nuclei together
2. Electromagnetism
3. Weak (nuclear) force – responsible for radioactive decay
4. Gravity
Electrostatic force – responsible for:
Electrostatic force studied by Charles Coulomb (France, 1785)
Fe
Fg
Both gravity and electrostatic force follow an inverse square law
Unlike gravity,
5. What is the electrostatic force between two 1 Coulomb charges separated by 1 m?
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6. What is the electrostatic force between an electron and a proton, separated by 0.6 x 10-10 m?
In what direction is the force? How does the magnitude of this force compare to Fg (from the Do Now)?
7. What is the electrostatic force exerted between two charged spheres at a distance of 5 nanometers if
the first sphere has a charge of -5 micro-coulombs and the second has a charge of -2 micro-coulombs?
8. When two spheres, each with charge Q, are positioned a distance R apart, they are attracted to one another
by a force of magnitude F. By what factor of F would this force change if…
a) …one of the charges was tripled, while the other was doubled?
b) …one of the charges was doubled, while the separation distance was tripled?
c) …both of the charges were halved, while the separation distance was doubled?
d) …one of the charged was doubled, while the separation distance was halved?
9. Sphere A has an excess of 5 x 1016 electrons. Sphere B has an excess of 6 x 1017 electrons.
a) Determine the charge on each sphere in coulombs.
b) Calculate the electrostatic force that sphere A exerts on sphere B when they are separated by a
distance of 2 x 103 meter.
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10. What is the electrostatic force between a 3 nC (nanoCoulomb) object and a 6 nC object separated by
0.5 m?
Electric Fields
Review: Gravitational field
Electric fields:
The region in which electrical forces act on a charge
The direction of the field is the direction a force acts on a positive test charge (test charge = infinitely
small positive charge)
Electric field lines
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Electric Field
E=
E=
Example: What is the electric field strength for a 0.1 C charge experiencing a 100 N electrostatic force?
Electric field lines never cross
2 Parallel Plates
Practice
11. Sketch the electric field lines that surround each of the following arrangements of charged objects.
12. An electron is placed within a uniform electric field with strength of 5.0 x10-8 newtons per coulomb.
a. Calculate the electrostatic force that is experienced by the electron.
b. Calculate the acceleration of the electron. [electron mass = 9.11 x 10-31 kg]
13. An object with a charge of -4 x 10-3 coulombs is placed between a set of oppositely charged, parallel
plates. The object experiences a force of 5 x 10-6 newtons while between the plates.
a. Sketch a set of vectors showing the direction in which the electric field lines point between the plates.
b. Sketch a vector showing the direction in which the object will travel when placed between the plates.
c. Calculate the strength of the electric field between the plates.
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Review Checklist
Convert between elementary charge and charge in coulombs. Determine if a charge is possible.
Determine how charge will be distributed in conservation of charge problems.
1. What is the charge on an object with four excess electrons in Coulombs?
2. What is the charge on an object that contains 35 electrons and 85 protons?
3. Which set of particles would produce a charge of +3.2 x 10-18 coulombs?
(1) 400 electrons and 200 protons
(2) 40 electrons and 20 protons
(3) 200 electrons and 400 protons
(4) 20 electrons and 40 protons
4. Which charges could NOT exist on a real-world object?
(a) 3.2 x 10-19 C
(e) 0.5 x 10-19 C
(b) 6.5 C
(f) 3.2 x 10-21 C
(c) 3.5 e
(g) -20 e
(d) 1.2 x 102 e
(h) 1.6 x 10-19 e
5. Object A begins with a charge of -3.0 coulombs; object B begins with a charge of -7.0 coulombs; and
object C begins with no charge. Object A is touched to object B then removed. Object B is then touched
to object C and removed. What is the final charge on each of the three objects?
Determine the direction in which electrons flow. Explain the process of conduction, induction, and
charging by induction. Explain the rules for testing an object to determine its charge. Explain how an
uncharged object will react to the presence of a charge one. Explain how electroscopes become charged
and how to test them.
6. Using the pictures to the right, which best describes
the charges of neutral metal spheres x, y, and z when
a. A negative object is held to the left
b. A negative object is held to the right
c. A positive object is held to the left
d. A positive object is held to the right
7. When a neutral metal sphere is charged by contact
with a positively charged glass rod, the sphere
loses electrons
3. loses protons
1.
2. gains electrons
4. gains protons
8. A negatively charged plastic comb is brought close
to, but does not touch, a small piece of paper. If the
comb and the paper are attracted to each other, the
charge on the paper
1. may be negative or neutral
2. may be positive or neutral
3. must be negative
4. must be positive
9. Describe the process of charging an electroscope by induction, and what happens to the leaves.
Use equation to determine electrostatic force; charge; and/or distance. Determine the effects of
changing parameters on strength of electrostatic force.
10. Determine the electrostatic force that a +4.0 coulomb charge exerts on a -6.0 coulomb charge when
2.0 meters apart.
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11. If two charged objects are attracted to one another by an electrostatic force of 5.0 newtons, what
force would they be attracted by if the charge on both of them were doubled?
12. An electrostatic force F acts between two objects with charges +q and +q when they are a distance
R apart. If the distance between the objects is halved, the electrostatic force would become.
13. An object with 12,000 excess electrons is brought 0.5 meters away from an object with 20,000
excess electrons. Determine the electrostatic force between them.
Use equation to determine electric field strength; force; and/or charge. Map or recognize proper
electric field maps for point charges or systems of charges. Explain the effect of charged parallel plates
on electric field strength, electrostatic force, and acceleration of charges between such plates.
14. A +2.0 coulomb charge experiences a force of 10 newtons while in an electric field. What is the
strength of the electric field?
15. What force will a 3.0 coulomb charge experience if place in an electric field with a strength of 15
newtons per coulomb?
16. What is the charge on an object that experiences a force of 20 newtons when it is placed in an
electric field with a strength of 4.0 newtons per coulomb?
17. Determine the direction of the
electric field at the points selected in
each picture.
18. An proton is fired into the space between two parallel, oppositely charged plates that produce an
electric field of strength 2.0 x 10-11 newtons per coulomb.
a. Sketch the path of the electron as it passes between the plates.
b. Determine the amount of force exerted on the proton.
c. Determine the acceleration of the proton.
Answers
1. -6.4 x 10-19 C
2. +8 x 10-19 C
3. (4)
4. c,e,f,h
5. A:-5C
B:-2.5C
C:-2.5C
6. a (3)
b (4)
c (4)
d (3)
7. (1)
8. (2)
9. –
10. 5.4 x 1010 N
11. 20 N
12. F/4
13. 2.2 x 10-19 N
14. 5 N/C
15. 45 N
16. 5 C
17. A left, B right, C right, D left, E, right
18.
a. up
b. 3.2 x 10-30 N
c. 1.9 x 10-3 m/s2
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Review Topic: Circular Motion & Universal Gravitation
1. The diagram shows a 2.0-kilogram model
airplane attached to a wire. The airplane is flying
clockwise in a horizontal circle of radius 20. meters
at 30. meters per second.
3. A 3.0-kilogram mass is traveling in a circle of
0.20-meter radius with a speed of 2.0 meters per
second. What is the centripetal acceleration?
4. The diagram shows an object with a mass of 1.0
kg attached to a string 0.50 meter long. The object is
moving at a constant speed of 5.0 meters per second
in a horizontal
circular path with
center at point O.
a. What is the
magnitude of the
centripetal force
acting on the object?
a. The centripetal force acting on the airplane at the
position shown is directed toward point:
b. What is the magnitude of the centripetal
acceleration of the airplane?
c. If the wire breaks when the airplane is at the
position shown, the airplane will move toward point:
2. The diagram below shows a ball undergoing
uniform circular motion as it travels clockwise on a
string.
b. While the object is undergoing uniform circular
motion, its acceleration
1. has a magnitude of zero
2. increases in magnitude
3. is directed toward the center of the circle
4. is directed away from the center of the circle
c. If the string is cut when the object is at the
position shown, the path the object will travel from
this position will be
1. toward the center of the circle
2. a curve away from the circle
3. a straight line tangent to the circle
5. An object with a mass of 0.5 kilogram is swung
by a string in a horizontal circle of radius 1 meter at
a speed of 2 meters per second.
a. The magnitude of the force on the mass is:
At the moment shown in the diagram, what are the
correct directions of both the velocity and centripetal
acceleration of the ball?
b. As the speed of the object increases, the force
needed to keep it in a circular path will
1. decrease
2. increase
3. remain the same
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6. Calculate the force of gravity between two 70kg
students separated by 3 meters.
13. A person weighing 785 newtons on the surface
of Earth would weigh 298 newtons on the surface of
Mars. What is the magnitude of the gravitational
field strength on the surface of Mars?
7. Calculate the force of gravity between the Earth
and a 950g satellite orbiting at a distance of
7.8x106 m from the center of the Earth.
14. What is the weight of a 2.00-kilogram object on
the surface of Earth?
15. Which graph represents the relationship between
8. A space probe is launched into space from
Earth’s surface. Which graph represents the
relationship between the magnitude of the
gravitational force exerted on Earth by the space
probe and the distance between the space probe
and the center of Earth?
the magnitude of the gravitational force exerted by
Earth on a spacecraft and the distance between the
center of the spacecraft and center of Earth?
[Assume constant mass for the spacecraft.]
9. A 60-kg physics student would weigh 1560 N on
the surface of planet X. What is the magnitude of the
acceleration due to gravity on the surface of planet
X?
10. What happens to the force of gravity between
two objects when the distance between them
doubles?
1. ½ as much
2. 1/4th as much
3. 2X as much
4. 4X as much
11. An object weighs 100 newtons on Earth’s
surface. When it is moved to a point one Earth
radius above Earth’s surface, it will weigh:
12. A container of rocks with a mass of 65
kilograms is brought back from the Moon’s surface
where the acceleration due to gravity is 1.62 meters
per second2 .What is the weight of the container of
rocks on Earth’s surface?
16. A 2.00-kilogram object weighs 19.6 newtons on
Earth. If the acceleration due to gravity on Mars is
3.71 meters per second2 , what is the object’s mass
on Mars?
17. As an astronaut travels from the surface of Earth
to a position that is four times as far away from the
center of Earth, the astronaut’s
1. mass decreases
2. mass remains the same
3. weight increases
4. weight remains the same
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