Date:
History of Electricity & Magnetism
Chapter 23- part1
Electric Charge and Electric Force
• After discovery of lodestone (Fe3O4) itself alignment, 1263 Pierre de
Maricourt mapped lodestone to a compass and discovered North and South
poles.
• In the 1600's William Gilbert, concluded that Earth itself is a giant magnet.
• In the 1785, Charles Coulomb confirmed inverse square law form for electric forces.
• In 1820 Hans Christian discovered an electric current flowing through a wire
can cause a compass needle to deflect, relation between magnetism and
electricity.
• In 1830 Michael Faraday and Joseph Henry independently discovered that a
changing magnetic field produced a current in a coil of wire.
• In the 19th century James Clerk Maxwell mathematically unified the electric
and magnetic forces.
Unified electricity and magnetism
• In the late 19th century Pierre Curie discovered that magnets loose their
magnetism above a certain temperature.
• In the 1900's scientists discover superconductivity.
1/23/19
Electric Charges
Content of Chapter
• Static Electricity; Electric Charge
•
Coulomb’s Law
• Electric Charge in the Atom
•
Charge is quantized
• Insulators and Conductors
•
Charge is conserved
(a) The two glass rods were each rubbed with
a silk cloth and one was suspended by
thread. When they are close to each other,
they repel each other.
• Induced Charge; the Electroscope
(b) The plastic rod was rubbed with fur. When
brought close to the glass rod, the rods
attract each other.
The word electromagnetism is the combination of electric and magnetic phenomena.
This physics is the root of modern technology. Eg: Lights, computers, TV, telephones,
motors and other electronics. And also this field of physics produces several natural
behaviors. Eg: lightning and rainbows!
Objects can be charged by rubbing!!
In physics 1, we learnt about many forces that we can see and feel in day today life.
Eg: Friction, gravity, normal, tension and centripetal forces. Now we are going to deal
with electric forces acting at atomic level.
How does this happened,
no contact!
Magic???
In this chapter we begin with electrical phenomena and discuss electric charge and
electric forces! The concept of force links the study of electromagnetism to previous
study.
Origin of electroticity?
Matter is made up of atoms.
+
–
atom
neutron (neutral)
+
+
–
Proton (positive charge)
+
–
– electron (negative charge)
nucleus
If electrons = protons ⇒neutral
If electrons > protons ⇒ gaining electrons, negative charge
If electrons < protons ⇒ losing electrons, positive charge
Electro-negativity
Relative electro-negativity ranking for some common materials
from electron donating materials (+, glass) to electron accepting
materials (-, teflon)
+++++
++++
+++
++
+
Glass
Human Hair
Rubbing materials does NOT create electric
charges. It just transfers electrons from one
material to the other.
Nylon
Silk
Fur
Aluminum
Paper
-----------
Cotton
Copper
Rubber
PVC
Teflon
1
Date:
Electric Charging process
Electric Charges
• When we rub the glass rod with silk cloth àa small amount of
-ve charge moves to the silk by leaving the rod with a small
amount of excess +ve charge!
• When we hang the rod with a thread à electrically isolate
(a) Two charged rods of the same sign repel each
other.
(b) Two charged rods of opposite signs attract each
other.
Plus signs indicate a positive net charge, and minus
signs indicate a negative net charge.
A charge comes in two types, positive and negative; like
same charges repel and opposite charges attract! Extra
charge is said to be an excess charge!
ConcepTest
Electric Charge
Two charged balls are
repelling each other as
they hang from the
ceiling. What can you
say about their charges?
Electric charge is always conserved in an isolated system.
• For example, charge is not created in the process of rubbing two
objects together.
• The electrification is due to a transfer of charge from one object to
another.
• A glass rod is rubbed with silk.
• Electrons are transferred from
the glass to the silk.
• Each electron adds a negative
charge to the silk.
• An equal positive charge is left
on the rod.
ConcepTest
a) one is positive, the
other is negative
b) both are positive
c) both are negative
d) both are positive or
both are negative
Electric Charge
Two charged balls are
repelling each other as
they hang from the
ceiling. What can you
say about their charges?
a) one is positive, the
other is negative
b) both are positive
c) both are negative
d) both are positive or
both are negative
The fact that the balls repel each
other only can tell you that they
have the same charge, but you do
not know the sign. So they can be
either both positive or both
negative.
ConcepTest Electric Charge
From the picture,
what can you
conclude about
the charges?
ConcepTest Electric Charge
a)
have opposite charges
b)
have the same charge
c)
all have the same charge
d) one ball must be neutral (no charge)
From the picture,
what can you
conclude about
the charges?
a)
have opposite charges
b)
have the same charge
c)
all have the same charge
d) one ball must be neutral (no charge)
The GREEN and RED balls must
have the same charge, since
they repel each other. The
YELLOW ball also repels the
GREEN, so it must also have
the same charge as the GREEN
(and the RED).
2
Date:
Materials
Atomic structure
Materials are classified based on their ability to move charges!
Atom:
•
Conductors are materials in which a significant number of electrons are
free to move. Examples: metals.
Nucleus (small, massive, positive charge)
•
The charged particles in nonconductors (insulators) are not free to
move. Examples: rubber, plastic, glass.
Electron cloud (large, very low density, negative
charge)
Charged Particles. The properties of conductors and insulators are due
to the structure and electrical nature of atoms. Atoms consist of positively
charged protons, negatively charged electrons, and electrically neutral
neutrons. The protons and neutrons are packed tightly together in a
central nucleus and do not move.
•
Semiconductors are materials that are intermediate between conductors
and insulators; Examples: silicon and germanium in computer chips.
•
Superconductors are materials that are perfect conductors, allowing
charge to move without any hindrance. Examples: Mercury, diamond
Atom is electrically neutral. Rubbing charges objects by moving electrons from one
to the other.
Charging by Induction
Charging Methods
Induced Charge. A neutral copper rod is electrically isolated from its surroundings
by being suspended on a non-conducting thread. Either end of the copper rod will be
attracted by a charged rod. Here, conduction electrons in the copper rod are repelled
to the far end of that rod by the negative charge on the plastic rod. Then that
negative charge attracts the remaining positive charge on the near end of the copper
rod!
Although the Copper rod is still neutral, it is said to have an
Induced charge, which means that some of its +ve and –ve
charges have been separated due to the presence of a
nearby charge!!
• Metal objects can be charged by conduction:
• They can also be charged by induction
conduction electrons: When atoms of a conductor like copper come together to form
the solid, some of their outermost—and so most loosely held—electrons become free
to move within the solid, leaving behind positively charged atoms ( positive ions). We
call the mobile electrons as conduction electrons.
• Charging by induction requires no contact with the
object inducing the charge. Assume we start with
a neutral metallic sphere. The sphere has the
same number of positive and negative charges
• A charged rubber rod is placed near the sphere.
It does not touch the sphere. The electrons in
the neutral sphere are redistributed.
Electrons (-ve) are moving
• Nonconductors won’t become charged by conduction or
induction, but will experience charge separation:
Charging by Induction
• The ground wire is removed. There will now be
more positive charges. The charges are not
uniformly distributed. The positive charge has
been induced in the sphere.
• The rod is removed. The electrons remaining
on the sphere redistribute themselves. There
is still a net positive charge on the sphere.
The charge is now uniformly distributed. Note
the rod lost none of its negative charge
during this process.
• The sphere is grounded. Some electrons can
leave the sphere through the ground wire.
Point Charge
• The term point charge refers to a particle of zero size that carries
an electric charge. The electrical behavior of electrons and
protons is well described by modeling them as point charges.
• The smallest unit of “free” charge known in nature is the charge
of an electron or proton, which has a magnitude of
e= 1.602 x 10-19 C.
• Charge of any ordinary matter is quantized in \multiples of e. An
electron carries one unit of negative charge, −e , while a proton
carries one unit of positive charge, +e . In a closed system, the
total amount of charge is conserved since charge can neither
be created nor destroyed. A charge can, however, be
transferred from one body to another.
3
Date:
ConcepTest
Conductors
ConcepTest
a) positive
A metal ball hangs from the ceiling by
A metal ball hangs from the ceiling by
b) negative
an insulating thread. The ball is
an insulating thread. The ball is
c) neutral
attracted to a positive-charged rod
Conductors
attracted to a positive-charged rod
a) positive
b) negative
c) neutral
held near the ball. The charge of the
d) positive or neutral
held near the ball. The charge of the
d) positive or neutral
ball must be:
e) negative or neutral
ball must be:
e) negative or neutral
Clearly, the ball will be attracted if its
charge is negative. However, even if
the ball is neutral, the charges in the
ball can be separated by induction
(polarization), leading to a net
remember
the ball is a
conductor!
attraction.
ConcepTest
Conductors
ConcepTest
a)
0
0
b)
+
–
c)
–
+
removed. What are the charges on the
d)
+
+
conductors?
e)
–
–
Two neutral conductors are connected
by a wire and a charged rod is brought
near, but does not touch. The wire is
taken away, and then the charged rod is
0
0
Conductors
a)
0
0
b)
+
–
c)
–
+
removed. What are the charges on the
d)
+
+
conductors?
e)
–
–
Two neutral conductors are connected
by a wire and a charged rod is brought
near, but does not touch. The wire is
taken away, and then the charged rod is
While the conductors are connected,
0
0
?
?
negative charge will flow from the green to
the blue ball. Once disconnected, the
charges will remain on the separate
conductors even when the rod is removed.
?
?
Lightning
kills more than
60 people and
one mile every five
seconds
injures more
than 400
people a year
in the US
about 20,000 C
Voltage of up to
1.2x108 volts
4
Date:
Coulomb’s Law
Coulomb’s Law
Coulomb’s law describes the electrostatic force (or electric force)
between two charged particles. If the particles have charges q1 and
q2, are separated by distance r, and are at rest (or moving only
slowly) relative to each other, then the magnitude of the force
acting on each due to the other is given by
Valid for r>>size of the particles
The electrostatic force on particle 1 can be
described in terms of a unit vector r along an
axis through the two particles, radially away
from particle 2.
where ε0 = 8.85 ×10-12 C2/N.m2 is the permittivity constant. The ratio 1/4πε0 is
often replaced with the electrostatic constant (or Coulomb constant) k=8.99×109
N.m2/C2. Thus k = 1/4πε0 . Unit of charge: coulomb, C and Charge on the
electron: e = 1.602 × 10−19 C
Example 1
Two charges are separated by a distance r and have a force
F on each other.
F
q1
qq
F = k 1 22
r
• The electrostatic force vector acting on a
charged particle due to a second
charged particle is either directly toward
the second particle (opposite signs of
charge) or directly away from it (same
sign of charge).
• Multiple Forces: If multiple electrostatic
forces act on a particle, the net force is
the vector sum (not scalar sum) of the
individual forces. “Principle of
superposition”
F12=F21, Newton 3rd laws
Two charged particles repel each other if they have the
same sign of charge, either (a) both positive or (b) both
negative. (c) They attract each other if they have opposite
signs of charge.
ConcepTest
Coulomb’s Law
a) 1.0 N
What is the
b) 1.5 N
magnitude of the
q2
F
force F2?
F1 = 3N
r
Q
Q
c) 2.0 N
F2 = ?
d) 3.0 N
e) 6.0 N
If r is doubled then F is : ¼ F
If q1 is doubled then F is : 2F
If q1 and q2 are doubled and r is halved then F is : 16F
Answer: (a) left towards the electron
(b) left away from the other proton
(c) left
ConcepTest
Coulomb’s Law
a) 1.0 N
What is the
F1 = 3N
Q
Q
F1 = 3N
b) 1.5 N
magnitude of the
force F2?
ConcepTest
F2 = ?
Q
Coulomb’s Law
Q
F2 = ?
a) 3/4 N
b) 3.0 N
c) 2.0 N
If we increase one charge to 4Q,
c) 12 N
d) 3.0 N
what is the magnitude of F1?
d) 16 N
e) 6.0 N
F1 = ?
4Q
Q
F2 = ?
e) 48 N
The force F2 must have the same magnitude as F1. This is
due to the fact that the form of Coulomb’s Law is totally
symmetric with respect to the two charges involved. The
force of one on the other of a pair is the same as the reverse.
Note that this sounds suspiciously like Newton’s 3rd Law!!
5
Date:
ConcepTest
F1 = 3N
Coulomb’s Law
Q
Q
F2 = ?
ConcepTest
The force between two charges
b) 3.0 N
separated by a distance d is F. If
If we increase one charge to 4Q,
c) 12 N
what is the magnitude of F1?
d) 16 N
F1 = ?
4Q
Q
F2 = ?
Coulomb’s Law
a) 3/4 N
b) 3 F
the charges are pulled apart to a
c) F
distance 3d, what is the force on
d) 1/3 F
each charge?
e) 48 N
e) 1/9 F
Originally we had:
F
Q
F1 = k(Q)(Q)/r2 = 3 N
Now we have:
F
Q
d
?
F1 = k(4Q)(Q)/r2
?
Q
Q
which is 4 times bigger than before.
ConcepTest
a) 9 F
3d
Coulomb’s Law
The force between two charges
ConcepTest
separated by a distance d is F. If
b) 3 F
the charges are pulled apart to a
c) F
distance 3d, what is the force on
Electric Force
Two balls with charges +Q and +4Q are separated by 3R. Where
should you place another charged ball Q0 on the line between the two
charges such that the net force on Q0 will be zero?
a) 9 F
d) 1/3 F
each charge?
e) 1/9 F
F
Originally we had:
Q
Fbefore = k(Q)(Q)/d2 = F
Now we have:
Q
+4Q
+Q
a)
d
?
b)
c)
d)
e)
2R
R
?
Q
Fafter = k(Q)(Q)/(3d)2 = 1/9 F
F
Q
3R
3d
ConcepTest
Electric Force
Two balls with charges +Q and +4Q are separated by 3R. Where
should you place another charged ball Q0 on the line between the two
charges such that the net force on Q0 will be zero?
+4Q
+Q
a)
b)
c)
d)
ConcepTest
Electric Force
Two balls with charges +Q and –4Q are
fixed at a separation distance of 3R. Is
it possible to place another charged ball
Q0 anywhere on the line such that the
net force on Q0 will be zero?
e)
a) yes, but only if Q0 is positive
b) yes, but only if Q0 is negative
c) yes, independent of the sign
(or value) of Q0
d) no, the net force can never
be zero
2R
R
3R
The force on Q0 due to +Q is:
F = k(Q0)(Q)/R2
The force on Q0 due to +4Q is:
F = k(Q0)(4Q)/(2R)2
– 4Q
+Q
3R
Since +4Q is 4 times bigger than +Q, then Q0 needs to be
farther from +4Q. In fact, Q0 must be twice as far from +4Q,
since the distance is squared in Coulomb’s Law.
6
Date:
ConcepTest
Electric Force
Two balls with charges +Q and –4Q are
fixed at a separation distance of 3R. Is
it possible to place another charged ball
Q0 anywhere on the line such that the
net force on Q0 will be zero?
ConcepTest
a) yes, but only if Q0 is positive
b) yes, but only if Q0 is negative
c) yes, independent of the sign
(or value) of Q0
d) no, the net force can never
be zero
a)
Forces in 2D
b)
c)
Which of the arrows best
d)
represents the direction of
the net force on charge +Q
+2Q
d
due to the other two
charges?
+Q
e)
d
+4Q
A charge (positive or negative) can be
placed to the left of the +Q charge,
– 4Q
+Q
such that the repulsive force from the
3R
+Q charge cancels the attractive
force from –4Q.
ConcepTest
A)
Forces in 2D
B)
Charge is Quantized
C)
Which of the arrows best
D)
represents the direction of
+2Q
the net force on charge +Q
d
due to the other two
+Q
E)
d
charges?
• Electric charge is quantized (restricted to certain values).
• The charge of a particle can be written as ne, where n is a positive or
negative integer and e is the elementary charge. Any positive or negative
charge q that can be detected can be written as
in which e, the elementary charge, has the approximate value
+4Q
The charge +2Q repels +Q towards
the right. The charge +4Q repels +Q
upwards, but with a stronger force.
Therefore, the net force is up and to
+2Q
the right, but mostly up.
+4Q
Charge is Quantized
When a physical quantity such as charge can have only discrete
values rather than any value, we say that the quantity is quantized.
It is possible, for example, to find a particle that has no charge at all
or a charge of +10e or -6e, but not a particle with a charge of, say,
3.57e.
• The electron and proton are identical in the magnitude of their charge, but
very different in mass.
• The proton and the neutron are similar in mass, but very different in charge.
• Number of protons of the nucleus equals to number of electrons!
Charge is Conserved
The net electric charge of any isolated system is always conserved.
If two charged particles undergo an annihilation process, they have equal
and opposite signs of charge.
If two charged particles appear as a result of a pair production process,
they have equal and opposite signs of charge.
Answer: -15e
7
Date:
Example: Finding the net force due to two other particles
Examples
Following figure shows two +ve charged particles fixed in place on x-axis. The charges
are q1=1.60x10-19C and q2=3.20x10-19C and the particle separation is R=0.0200m.
What are the magnitude and direction of the electrostatic force F12 on particle 1 from
particle 2?
1. Where is the resultant force equal to zero?
• The magnitudes of the individual forces
will be equal.
• Directions will be opposite.
Take k=8.99×109 N.m2/C2. Thus k = 1/4πε0 .
F12=-1.15x10-24N
2. Find electrical Force with Other Forces?
• Since they are separated, they exert a repulsive
force on each other.
• Model each sphere as a particle in equilibrium.
• Draw free body diagram
1/23/19
Example: Finding the net force due to two other particles
Example: Finding the net force due to two other particles
Following figure shows two +ve charged particles fixed in place on x-axis. Now there
is a particle 3 lies in between 1 and 2 with charge q3= -3.20x10-19C and is at (3/4)R from
particle 1. What is the net electrostatic force F1,net on particle 1 due to particle 2 and 3?
Following figure shows two +ve charged particles fixed in place on x-axis. Now the
Particle 4 is included with charge are q4=-3.20x10-19C and is at (3/4)R from
particle 1 and lies on a line that makes an angle 600 with x-axis. What is the net
electrostatic force F1,net on particle 1 due to particle 2 and 4?
Take k=8.99×109 N.m2/C2. Thus k = 1/4πε0 .
Take k=8.99×109 N.m2/C2. Thus k = 1/4πε0 .
F12=-1.15x10-24N from first part
F12=-1.15x10-24N from first part
F13= 2.05x10-24N
F14= 2.05x10-24N
=9.00x10-25N
F1,net= F12+F13
And direction is X positive
1/23/19
1/23/19
F1,net,x=F12,x +F14,x
F1,net,x=-1.25x10-25N
F1,net,y=F12,y+F14,y
F1,net,y=1.78x10-24N
F1,net=Sqrt(F21,net,x+F21,net,y)
F1,net= 1.78 x10-24N
Θ= tan-1(F1,net,y/F1,net,x)= -86.00
Θ= 94.00
Summary
Electric Charge
Coulomb’s Law
• The strength of a particle’s electrical
interaction with objects around it
depends on its electric charge,
which can be either positive or
negative.
• The magnitude of the electrical
force between two charged
particles is proportional to the
product of their charges and
inversely proportional to the
square of their separation
distance.
Conductors and Insulators
• Conductors are materials in which a
significant number of electrons are
free to move. The charged particles
in nonconductors (insulators) are
not free to move.
Conservation of Charge
• .
The Elementary Charge
• Electric charge is quantized
(restricted to certain values).
• e is the elementary charge
1. Complete the following statement: When a glass rod is rubbed with
silk cloth, the rod becomes positively charged as
a) negative charges are transferred from the rod to the silk.
b) negative charges are transferred from the silk to the rod.
c) positive charges are created on the surface of the rod.
d) positive charges are transferred from the silk to the rod.
e) positive charges are transferred from the rod to the silk.
• The net electric charge of any isolated
system is always conserved.
1/23/19
8
Date:
2. Which one of the following statements concerning electrical
conductors is false?
2. Which one of the following statements concerning electrical
conductors is false?
a) Rubber is an excellent electrical conductor.
a) Rubber is an excellent electrical conductor.
b) A material that is a good electrical conductor has many free
electrons that can easily move around inside the material.
b) A material that is a good electrical conductor has many free
electrons that can easily move around inside the material.
c) When a positively-charged object is moved into contact with an
electrical conductor, electrons move toward the object.
c) When a positively-charged object is moved into contact with an
electrical conductor, electrons move toward the object.
d) Materials that are good thermal conductors are often good
electrical conductors.
d) Materials that are good thermal conductors are often good
electrical conductors.
e) 1/23/19
Most metals are very good electrical conductors.
e) 1/23/19
Most metals are very good electrical conductors.
3. Which of the following terms is used to describe a material that
does not allow electrons to easily move through it?
3. Which of the following terms is used to describe a material that
does not allow electrons to easily move through it?
a) conductor
a) conductor
b) resistor
b) resistor
c) insulator
c) insulator
d) transformer
d) transformer
e) inductor
e) inductor
1/23/19
1/23/19
4. A conductor that is initially electrically neutral is touched by a rod
that has a net positive charge. Which of the following statements
describing the conductor after the rod is removed is true?
a) The conductor will have a net positive charge.
b) The conductor will electrically neutral.
c) The conductor will have a net negative charge.
1/23/19
4. A conductor that is initially electrically neutral is touched by a rod
that has a net positive charge. Which of the following statements
describing the conductor after the rod is removed is true?
a) The conductor will have a net positive charge.
b) The conductor will electrically neutral.
c) The conductor will have a net negative charge.
1/23/19
9
Date:
5. Silicon is an example of what type of material?
5. Silicon is an example of what type of material?
a) metal
a) metal
b) insulator
b) insulator
c) semiconductor
c) semiconductor
d) superconductor
d) superconductor
e) perfect conductor
e) perfect conductor
1/23/19
1/23/19
6. An initially electrically neutral conducting sphere is placed on an
insulating stand. A negatively-charged glass rod is brought near,
but does not touch the sphere. Without moving the rod, a wire is
then attached to the sphere that connects it to earth ground. The
rod and wire are then removed simultaneously. What is the final
charge on the sphere?
6. An initially electrically neutral conducting sphere is placed on an
insulating stand. A negatively-charged glass rod is brought near,
but does not touch the sphere. Without moving the rod, a wire is
then attached to the sphere that connects it to earth ground. The
rod and wire are then removed simultaneously. What is the final
charge on the sphere?
a) negative
a) negative
b) positive
b) positive
c) neutral
c) neutral
d) It has a fifty percent chance of having a positive charge and a fifty
percent chance of having a negative charge.
1/23/19
d) It has a fifty percent chance of having a positive charge and a fifty
percent chance of having a negative charge.
1/23/19
7. Three identical conducting spheres on individual insulating stands are initially
electrically neutral. The three spheres are arranged so that they are in a line and
touching as shown. A negatively-charged conducting rod is brought into contact
with sphere A. Subsequently, someone takes sphere C away. Then, someone
takes sphere B away. Finally, the rod is taken away. What is the sign of the
final charge, if any, of the three spheres?
7. Three identical conducting spheres on individual insulating stands are initially
electrically neutral. The three spheres are arranged so that they are in a line and
touching as shown. A negatively-charged conducting rod is brought into contact
with sphere A. Subsequently, someone takes sphere C away. Then, someone
takes sphere B away. Finally, the rod is taken away. What is the sign of the
final charge, if any, of the three spheres?
B
+
C
-
a)
b) +
-
+
c)
+
0
-
d) -
+
e)
-
a)
A
+
-
1/23/19
A
+
B
+
C
-
b) +
-
+
c)
+
0
-
0
d) -
+
0
-
e)
-
-
-
1/23/19
10
Date:
8. Three insulating balls are hung from a wooden rod using thread. The three balls
are then individually charged via induction. Subsequently, balls A and B are
observed to attract each other, while ball C is repelled by ball B. Which one of
the following statements concerning this situation is correct?
8. Three insulating balls are hung from a wooden rod using thread. The three balls
are then individually charged via induction. Subsequently, balls A and B are
observed to attract each other, while ball C is repelled by ball B. Which one of
the following statements concerning this situation is correct?
a) A and B are charged with charges of opposite
signs; and C is charged with charge that has the
same sign as B.
a) A and B are charged with charges of opposite
signs; and C is charged with charge that has the
same sign as B.
b) A and B are charged with charges of the same
sign; and C is electrically neutral.
b) A and B are charged with charges of the same
sign; and C is electrically neutral.
c) A is electrically neutral; and C is charged with
charge that has the same sign as B.
c) A is electrically neutral; and C is charged with
charge that has the same sign as B.
d) B is electrically neutral; and C is charged with charge that has the same sign as A.
d) B is electrically neutral; and C is charged with charge that has the same sign as A.
e) 1/23/19
Choices a and c are both possible configurations.
e) 1/23/19
Choices a and c are both possible configurations.
9. Consider the conducting spheres labeled A, B, and C shown in the drawing. The
spheres are initially charged as shown on the left, then wires are connected and
disconnected in a sequence shown moving toward the right. What is the final
charge on sphere A at the end of the sequence?
9. Consider the conducting spheres labeled A, B, and C shown in the drawing. The
spheres are initially charged as shown on the left, then wires are connected and
disconnected in a sequence shown moving toward the right. What is the final
charge on sphere A at the end of the sequence?
a) +Q
a) +Q
b) + Q/2
b) + Q/2
c) + Q/3
c) + Q/3
d) + Q/4
d) + Q/4
e) + Q/8
e) + Q/8
1/23/19
1/23/19
10. Consider the conducting spheres labeled A, B, and C shown in the
drawing. The spheres are initially charged as shown on the left,
then wires are connected and disconnected in a sequence shown
moving toward the right. What is the final charge on sphere C at
the end of the sequence?
10. Consider the conducting spheres labeled A, B, and C shown in the
drawing. The spheres are initially charged as shown on the left,
then wires are connected and disconnected in a sequence shown
moving toward the right. What is the final charge on sphere C at
the end of the sequence?
a) +Q
a) +Q
b) + Q/2
b) + Q/2
c) + Q/3
c) + Q/3
d) +2Q
d) +2Q
e) 1/23/19
+3Q
e) 1/23/19
+3Q
11
Date:
11. Two objects separated by a distance r are each carrying a charge q. The magnitude of the force exerted on the second object by the
first is F. If the first object is removed and replaced with an
identical object that carries a charge +4q, what is the magnitude of
the electric force on the second object?
11. Two objects separated by a distance r are each carrying a charge q. The magnitude of the force exerted on the second object by the
first is F. If the first object is removed and replaced with an
identical object that carries a charge +4q, what is the magnitude of
the electric force on the second object?
a) 4F
a) 4F
b) 2F
b) 2F
c) F
c) F
d) F/2
d) F/2
e) 1/23/19
F/4
e) 1/23/19
F/4
12. Two objects, A with charge +Q and B with charge +4Q, are
separated by a distance r. The magnitude of the force exerted on
the second object by the first is F. If the first object is moved to a
distance 2r from the second object, what is the magnitude of the
electric force on the second object?
12. Two objects, A with charge +Q and B with charge +4Q, are
separated by a distance r. The magnitude of the force exerted on
the second object by the first is F. If the first object is moved to a
distance 2r from the second object, what is the magnitude of the
electric force on the second object?
a) zero newtons
a) zero newtons
b) 2F
b) 2F
c) F
c) F
d) F/2
d) F/2
e) 1/23/19
F/4
e) 1/23/19
F/4
13. Two point charges are stationary and separated by a distance R.
Which one of the following pairs of charges would result in the
largest repulsive force?
13. Two point charges are stationary and separated by a distance R.
Which one of the following pairs of charges would result in the
largest repulsive force?
a) –2q and +4q
a) –2q and +4q
b) –3q and -2q
b) –3q and -2q
c) +3q and -2q
c) +3q and -2q
d) +2q and +4q
d) +2q and +4q
e) –3q and -q
e) –3q and -q
1/23/19
1/23/19
12
Date:
14. What is the magnitude of the electrostatic force that two electrons
separated by 1.0 nm exert on each other?
14. What is the magnitude of the electrostatic force that two electrons
separated by 1.0 nm exert on each other?
a) 2.3 × 10-10 N
a) 2.3 × 10-10 N
b) 3.2 × 10-19 N
b) 3.2 × 10-19 N
c) 4.6 × 10-14 N
c) 4.6 × 10-14 N
d) 5.2 × 10-6 N
d) 5.2 × 10-6 N
e) 7.8 × 10-4 N
e) 7.8 × 10-4 N
1/23/19
1/23/19
15. A charged particle, labeled A, is located at the midpoint between two other
charged particles, labeled B and C, as shown. The sign of the charges on all
three particles is the same. When particle A is released, it starts drifting toward
B. What can be determined from this behavior?
15. A charged particle, labeled A, is located at the midpoint between two other
charged particles, labeled B and C, as shown. The sign of the charges on all
three particles is the same. When particle A is released, it starts drifting toward
B. What can be determined from this behavior?
a) The charge on A is larger than the charge on B.
a) The charge on A is larger than the charge on B.
b) The charge on A is larger than the charge on C.
b) The charge on A is larger than the charge on C.
c) The charge on C is larger than the charge on B.
c) The charge on C is larger than the charge on B.
d) The charge on B is larger than the charge on A.
d) The charge on B is larger than the charge on A.
e) 1/23/19
The charge on B is larger than the charge on C.
e) 1/23/19
The charge on B is larger than the charge on C.
13