Chapter 7 - Static Electricity
Basics of Static Electricity:
There are two basic types of charges. For lack of better terms, they are called positive and negative charges. The rule is that like charges repel while unlike charges attract. This means that two negative charges will repel each other. Two positives will also repel each other. But a positive and negative charge will attract each other. In the form of a diagram it looks like this;
The term neutral is often used. Neutral means there is a balance of positive and negative charge. It does not mean there is no charge. So an object charged like you see to the right would be called neutral even though it has charges. It just has
no net charge because there are 4 negative and 4 positive charges. When a neutral object is placed near a charged object, the charges are induced to move to create a “more positive” side and a “more negative” side. Because the attractive force acts over a slightly smaller distance than the repulsive force, the neutral object is attracted to the charged object.
Problems
1. Two charged objects attract each other. What does this indicate about their charges?
2. Two charged objects repel each other. What does this indicate about their charges?
3. What kind of force (attractive or repulsive) is there between a charged object, such as the plastic, and an uncharged object, such as the bits of paper?
4. Three charged pieces of tape are tested with each other. Tape "A" attracts tape "B". Tape "B" attracts tape "C". What reaction will occur between tape "A" and tape "C"?
5. Four charged pieces of tape are tested with each other. Tape "A" repels tape "B". Tape "B" attracts tape "C". Tape "C" attracts tape "D". What reaction will occur between tapes "A" and tape "D"?
6. Three pieces of tape are tested with each other. Tape "A" repels tape "B". Tape "A" attracts tape "C". Tape "B" attracts tape "C". Which tape could be uncharged?
This electroscope
is neutral. There
are equal
numbers of
positive and
negative charges.
This electroscope is
charged. There is an
excess of positive
charges. (Only the
excess
positive charges
are shown.)
Negative charges leave the electroscope and go into the rod if the rod touches the electroscope
Chapter 7 - Static Electricity
Using an Electroscope:
A device called an electroscope is often used to determine the presence of electrical charges. An electroscope has a very lightweight conductor (often a thin leaf of pure gold or aluminum or a needle) that moves in the presence of a charge. So when there is a net charge on the leaf it will repel and stand out. With no net charge the leaf stays flat.
By just looking at the electroscope pictured above right, it would be impossible to tell if it were positively or negatively charged. (Of course, with the charges drawn it is easy to tell.)
Suppose that a positively charged rod is brought near a neutral electroscope. When the rod is brought near the neutral electroscope the charges will rearrange themselves; Because the negative charges in the electroscope are attracted to the positive charges of the rod, they move to the top. This leaves more positive charges in the lower part of the electroscope, the leaf is repelled and it moves out.
If the rod is now touched to the electroscope, the positive charges on the rod will attract negative charges which will move to the
rod
leaving an excess of positive charge on the electroscope. This leaves the electroscope with a net positive charge;
Chapter 7 - Static Electricity
The other method of charging an object is by induction. When objects are charged in this way the charged object does not touch the object being charged. Here is how this works. The rod is brought near the neutral electroscope, but not allowed to touch it.
Again, the charges rearrange as expected. But this time instead of touching the rod to the electroscope, we touch the electroscope with our finger.
Because the negative charges are attracted to the positive rod they move to the ball on the electroscope. Also, there are additional negative charges in your finger that are attracted to the positively charged rod and can move toward the positive charges in the lower part of the electroscope, so the arrangement now looks like this:
This means there is now a net negative charge on the electroscope. When the finger is taken from the electroscope and then the rod is removed, the excess negative charge will still remain on the electroscope. It has been charged by induction. (The charges were induced to rearrange themselves.)
Problems
1. A conducting ball is hanging from a nylon thread that is not a conductor. (A conductor allows charges to move around, a non-conductor will not allow the charges to move. A non-non-conductor is often called an insulator.) The ball is touched to allow any charge it might have had to be removed. a) How does touching the ball remove the charge?
b) Now a negatively charged rod is brought near but not touching the ball. Diagram the charge on the ball now.
c) While the rod is held there you bring in your finger and touch the ball. Keep your finger there and diagram the charge on the ball now.
d) Now the finger is removed from the ball. Diagram the charge on the ball now.
e) Now the rod is removed and is no longer near the ball. What charge is on the ball?
f) Was the ball charged by induction or conduction?
2. Two conducting spheres are hanging near each other. They are attracting each other. You know that one of the spheres is neutral. Diagram the charges on the spheres and explain why they attract each other.
3. A neutral electroscope is charged negative by conduction. Diagram the process.
4. A positively charged rod is brought near a negatively charged electroscope. Diagram the electroscope and the position of the leaf while the rod is near.
Before charging During charging After charging
Before charging During charging After charging
Chapter 7 - Static Electricity
Conduction, Induction, Static Electricity
1. The sphere below is neutral. Diagram the charges inside the sphere.
2. A positively charged rod is held near, but not touching, this neutral sphere. Diagram the charges on the sphere now.
3. Diagram the charges on this neutral electroscope.
4. Draw what the electroscope looks like before, during and after an electroscope is charged negatively by conduction. Be sure to draw what the “leaf” of the electroscope looks like. Show what happens during the charging process, including the charged rod. Diagram the charges on the electroscope.
5. Draw what the electroscope looks like before, during and after an electroscope is charged negatively by induction. Be sure to draw what the “leaf” of the electroscope looks like. Show what happens during the charging process, including the charged rod. Diagram the charges on the electroscope.
+ + + + + + + +
Chapter 7 - Static Electricity
Forces between Two Charged Objects
Whenever two charged objects are near each other, there will be a force between them. The force will either be attractive (if the charges are different) or repulsive (if the charges are the same). The strength of the force depends on the amount of charge
and the distance between the charges.
The amount of charge is measured in Coulombs in the metric system. Think of a Coulomb as being a "gallon of charge". The abbreviation for Coulombs is C. Because we are really measuring the quantity of charge, in an equation the symbol is Q (or
q). So, if a sphere has 5 Coulombs of charge on it, our given information would be Q= 5 C.
In early days it took a lot of charge to see any real effects, so the Coulomb is a very large amount of charge (equal to 6.25 X 1018 electrons!). Often millicoulombs, mC, (10-3C), microcoulombs, C, (10-6C), or nanocoulombs, nC, (10-9), are used. To put
this in perspective, lightning strikes contain about 20 C of charge while the sparks created by rubbing your feet on a carpet are
much less than a microcoulomb.
The distance between two charged objects is measured from the center of one mass to the center of the second mass. Because the masses are often moving around each other, the distance between is just the radius of the rotation, so the radius R
measures the distance. As in all other cases, R is just measured in the standard MKS distance units of meters.
The entire equation to use for electrical force becomes;
F = k Q1 Q2
R2 In this equation,
F = the force in Newtons
Q1= the charge in coulombs on the first object
Q2= the charge in coulombs on the second object
R = the distance between the two objects
k = Coulomb's Constant, a number used to make the units Newtons. The value of k never changes, and equals
8.99 x 109 Nm2/C2
Example: A 1.2 C positively charged sphere and a 1.6 C negatively charged sphere are 20 cm apart. What is the force between the two spheres?
Given: Q1 = 1.2 C
Q2 = 1.6 C
R = 20 cm = 0.20 m Equation:
F = k Q1 Q2
R2
Substitution: F= (8.99 x 109 Nm /C2 2 ) (1.2 C)(-1.6 C) = 1.72608 x 1010 N
(0.20 m)2 0.04
A
B
C
4.0 cm
A
3.5 cm
B C
Chapter 7 - Static Electricity
Problems
1. Two positive charges, each of 5 C are 0.50 m apart. Find the force that exists between the charges.
2. A negative charge of -3.0 x 10-5 C is placed 0.35 m from a positive charge of 9.6 x 10-5 C. What is the force between the
two charges?
3. A negative charge is placed 0.75 m from a positive charge of 5 mC. An attractive force of 2 N exists between the two charges. Find the unknown charge.
4. An unknown charge is placed 58 cm from a known negative charge of –9.1 X 10-4 C. A repulsive force of 0.93 N is
measured between the two charges. Find the unknown charge.
5. Two equal charges are placed 0.45 m from each other. The repulsive force between them is 0.25 N. Find each unknown charge.
6. How far apart must two equal charges of –6.2 C be placed so that a force of 0.015 N exists between them?
7. The three spheres A, B, and C, are fixed in the positions shown. Draw a vector diagram that represents the direction of each force acting on C as well as the direction of the resultant (net electrical force) acting on C which is positively charged if
a. A and B have equal positive charges.
b. A and B have charges of equal magnitude, but the charge on B is negative and the charge on A is positive.
8. Find the force between two electrons in an atom which are 10-10 m apart. (Charge on an electron = q
e = -1.6 x10-19 C.)
9. What is the net force on B (-4.5 nC) shown below? A and C have charges of +3.0 nC.
10. Find the net force on charge A (Q = +5.4 C) from both charge B (Q = +2.5 C) which is 2.5 cm south of charge A, and charge C (Q =-4.2 C) which is 3.8 cm east of charge A.
11. Find the force between the negatively charged lower part of a cloud and the positively charged ground 2.5 km below it. Each has a charge of approximately 15 C.
*12. In a simple model of the hydrogen atom, an electron (-1.6 x 10-19 C) goes in a circular orbit around a proton (+1.6 x 10-19
C) with a speed of 1.1 x 106 m/s. Determine the radius of the electron’s orbit. The mass of an electron is 9.11 x 10-31 kg.
Lightning Rods
(from How Stuff Works)
©Fyzics Softext, Inc. Page 126
Answers:
1) 0.9 N 2) –210 N 3) –3 X 10-8 C 4) –3.8 X 10-8 C
5) 2.4 C 6) 4.8 m 8) 2 X 10-8 N 9) 1.2 X 10-4 N, @ 322
Chapter 7 - Static Electricity
Lightning rods were originally developed by Benjamin Franklin. A lightning rod is very simple -- it's a pointed metal rod attached to the roof of a building. The rod might be an inch (2 cm) in diameter. It connects to a huge piece of copper or aluminum wire that's also an inch or so in diameter. The wire is connected to a conductive grid buried in the ground nearby.
The purpose of lightning rods is often misunderstood. Many people believe that lightning rods "attract" lightning. It is better stated to say that lightning rods provide a low-resistance path to ground that can be used to conduct the enormous electrical currents when lightning strikes occur. If lightning strikes, the system attempts to carry the harmful electrical current away from the structure and safely to ground. The system has the ability to handle the enormous electrical current associated with the strike. If the strike contacts a material that is not a good conductor, the material will suffer massive heat damage. The lightning-rod system is an excellent conductor and thus allows the current to flow to ground without causing any heat damage.
Lightning can "jump around" when it strikes. This "jumping" is associated with the electrical potential of the strike target with respect to the earth's potential. The lightning can strike and then "seek" a path of least resistance by jumping around to nearby objects that provide a better path to ground. If the strike occurs near the lightning-rod system, the system will have a very low-resistance path and can then receive a "jump," diverting the strike current to ground before it can do any more damage.
As you can see, the purpose of the lightning rod is not to attract lightning -- it merely provides a safe option for the lightning strike to choose. This may sound a little picky, but it's not if you consider that the lightning rods only become relevant when a strike occurs or immediately after a strike occurs. Regardless of whether or not a lightning-rod system is present, the strike will still occur.
If the structure that you are attempting to protect is out in an open, flat area, you often create a lightning protection system that uses a very tall lightning rod. This rod should be taller than the structure. If the area finds itself in a strong electric field, the tall rod can begin sending up positive streamers in an attempt to dissipate the electric field. While it is not a given that the rod will always conduct the lightning discharged in the immediate area, it does have a better possibility than the structure. Again, the goal is to provide a low-resistance path to ground in an area that has the possibility to receive a strike. This possibility arises from the strength of the electric field generated by the storm clouds.
Safety in a Storm
Over 1,000 people get struck by lightning every year in the United States, and over 100 of them die as a result of the strike. Lightning is not something to toy with.
If you are caught outside in a storm, always look for appropriate shelter. Do not take any chances -- lightning can use you as a path to the earth just as easily as it can use any other object. Appropriate shelter would be a building or a car. If you do not have anywhere to go, then you should avoid taking shelter under trees. Trees attract lightning. Put your feet as close together as possible and crouch down with your head as low as possible without touching the ground.
Never lay down on the ground. After lightning strikes the ground, there is an electric potential that radiates outward from the point of contact. If your body is in this area, current can flow through you. You never want the current to have the ability to pass through your body. This could cause cardiac arrest, not to mention other organ damage and burns. By making your body as low to the ground as possible and minimizing the amount of your body in contact with the ground, you can lower the possibility of a lightning-related injury. If a strike were to occur near you, the current would have a much more difficult time flowing through your body in this position.
A
B
C
2.0 cm 1.0 cm
Chapter 7 - Static Electricity
Review Problems
1.
How far apart would two point charges, each of 2
C, have to be placed in a vacuum so that they would
exert a force of 0.1 N on each other?
2.
Two positive point charges, each 5 nC, are separated in a vacuum by 0.01 m. What force do they exert
on each other?
3.
The attractive force that point charge A exerts on point charge B at a distance of 1.0 cm in a vacuum is
-3.0 x 10
-2N. If A has a charge of +2.4 x 10
-8C, what is the charge on B?
4.
Two point charges are separated by a distance of 0.10 cm in a vacuum. They exert a force of 9 x 10
-5N
on each other. If the separation between them is increased to 0.30 cm, what does the force become?
5.
Three equally charged objects are located a shown below. The electric force exerted by A on B is 3.0 x
10
-6N.
a) What electric force does C exert upon B? b) What is the net electric force on B?
6.
A small charged metal sphere, A, is touched to another small uncharged metal sphere, B, of the same
radius. The two spheres are then placed 15 mm apart in a vacuum. It is found that they exert a force of
0.79 N on each other. Find the charge on each sphere.
7.
What is the force on a positive point charge A (Q = 4.0 nC) at a distance of 0.20 m from another positive
point charge B (Q = 2.0 x 10
-5C)?
8.
You find that object A repels object B, A attracts C, and C repels D. If you know that D is positively
charged, what kind of charge does A have? Explain your answer.
9.
Three point charges (each has a charge of +3.6
C) are arranged as follows: A is 16 cm west of B; C is
13 cm south of B. Find the net force on B.
10.
Must all negative charges be removed in order for a rod to become positively charged? Explain.
11.
Why do gasoline truck drivers attach a metal cable from their truck to a metal hook in the ground before
filling the station tanks with gas?
12.
You have two metal spheres of the same size mounted on insulated stands, a strip of vinyl, and a piece of
wool. Describe what you would do to give the two spheres equal electrical charges of:a) the same sign;
b) opposite signs.
13.
Explain how a lightning rod works.
*14.
Three positive particles of equal charge (+11µC) are located at the corners of an equilateral triangle
with sides 15 cm long. Calculate the magnitude and direction of the net force on the top charge.
©Fyzics Softext, Inc. Page 128
Answers:
1) 0.6 m 2) 0.002 N 3) 1.4 X 10-8 C 4) 1 X 10-5 N
5a) 1.2 X 10-5 N 5b) 9.0 X 10 –6 N, to the left 6) 1.4 X 10 -7 C 7) 0.018 N
Chapter 7 - Static Electricity
Make a table like you see below an describe the reaction that will occur
Charge of #1 Charge of #2 Reaction
(attract, repel, or no Reaction)
+ +
-
-Neutral Neutral
+ Neutral
Neutral
-+
-- +
1) How many types of charges are there? List them.
2) What particle in the atom causes positive charges?
3) What particle in the atom causes Negative charges?
4) Is neutral a type of charge?
5) Can Protons move when referring to static charges?
6) If you have 17 positive charges and 18 Negative charges what is the net charge?
7) What is it called when you connect an object to the ground so excess charges can leak off?
8) What is an object called when an object allows charges to flow easily?
9) What is an object called when an object does not allow charges to flow easily?
10) You find that object A repels object B, A attracts C, and C repels D. If you know that D is positively charged, what kind of charge does A have?
11) You find that object A attracts object B, A Repels C, and C repels D. Which object could be neutral?
12) Must all negative charges be removed in order for a rod to become positively charged? Explain.
13) Why do gasoline truck drivers attach a metal cable from their truck to a metal hook in the ground before filling the station tanks with gas?
For the next several questions do the conversions and put the answer in proper scientific notation
14) Convert 5.2 nC to C
37) Rod 38) Rod 36) Rod
Chapter 7 - Static Electricity
16) Convert 520.0 µC to C
For the next several questions your answer will be one of the two methods of charging an object, conduction or induction.
17)Which method requires the object (Rod) you are using to charge the object to touch the object (electroscope) you are charging?
18)Which method results in the object (electroscope) you are charging having the same charge as the object (Rod) you are using to charge?
19)Which method results in the object (electroscope) you are charging having the opposite charge as the object (Rod) you are using to charge?
20)Which method requires the object (electroscope) you are charging to be grounded?
21)What method can use a positive rod held close but not touching a neutrally charged sphere, a person then touches the sphere with a finger; finally both the finger and rod are removed.
22)What charge will the sphere have in #22?
23)What method can use a positive rod being rubbed directly onto a neutrally charged sphere and then the rod is removed?
24)What charge will the sphere have in #24?
For the next several questions write down the variables name and the what the correct unit is
Answer Type of Term Choices for answers
25)Kinetic energy a) Coulomb
26)Weight b) Watt
27)Power c) N
28)Actual Mechanical Advantage d) kg
29)Work e) No units
30)Charge f) J
31)Force
32)Two spheres are hanging near each other. They are attracted to each other. Can one of the spheres be neutral? Explain your reasoning.
33) Two spheres are hanging near each other. They are repelled by each other. One of the spheres is positive. What is the charge on the other sphere? Explain your reasoning.
34)Two spheres are hanging near each other. They are attracted to each other. One of the spheres is negative. What are the possibilities for the charge on the other sphere? Explain your reasoning.
What is the charge on the rod based on the charge on the electroscope
Chapter 7 - Static Electricity
39) Based on the Coulombs law formula, what happens to the net force between 2 charged objects when the distance between two charges is cut in half, but the charges stay the same?
40) Based on the Coulombs law formula, what happens to the net force between 2 charged objects when the distance between two charges is doubled , but the charges stay the same?
41) Based on the Coulombs law formula, what happens to the net force between 2 charged objects when the distance between two charges remains the same, but the charge of one is doubled?
42) Based on the Coulombs law formula, what happens to the net force between 2 charged objects when the distance between two charges remains the same, but the charge of both objects is doubled?
43) What are two different ways a lightning rod works and which is the best method?
44) A cloud develops a charge of -54 C while the ground has an equal but opposite charge. If the cloud is 300 meters above the ground what is the force on the cloud as it is attracted to the?
45) Two charged balloons are brought close to each other. One balloon has a charge of positive 6.6 X 10-7 C and the other a charge of negative 8.8 x 10-7 C. If the force between the two balloons is -1.08x10-1 N, how far apart are the balloons?
46) Two charged balloons are brought to where they are 11 cm apart. If one balloon has a charge of positive 6.6 X 10-7 C and the force between the two balloons is 2.2 x 10-2 N, what is the charge on the other balloon?
47) How far apart would two point charges, each of 2 C, have to be placed in a vacuum so that they would exert a force of 0.1 N on each other?
48) Two positive point charges, each 5 nC, are separated in a vacuum by 0.01 m. What force do they exert on each other?
49) The attractive force that point charge A exerts on point charge B at a distance of 1.0 cm in a vacuum is -3.0 x 10-2 N. If A has a charge of +2.4 x 10 -8 C, what is the charge on B?
2.0 cm
1.0 cm
-6.6 x 10-7C +2.6 x 10-7C
A B C
+6.6 x 10-7C
2.0 cm
1.0 cm
-6.6 x 10-7C +2.6 x 10-7C
A B C
+6.6 x 10-7C
Chapter 7 - Static Electricity
51) Three equally charged objects are located as shown below. Find the net force on A
52) Three equally charged objects are located as shown below. Find the net force on B
53) Three point charges (each has a charge of +3.6 C) are arranged as follows: A is 16 cm west of B; C is 13 cm south of B. Find the net force on B.
54) Three point charges, each has a charge of 2.2 nC, if A & B are positively charged and C is negatively charged and they are arranged as follows: A is 11 cm west of B; C is 15 cm south of B. What is the net force on B?
©Fyzics Softext, Inc. Page 132
Answers:
1) Repel, Repel, No Reaction, Attract, Attract, Attract, Attract,
2) 2 positive and negative 3) proton 4) electron 5) no 6) no 7) negative
8) grounding 9) conductor 10) insulator 11) A must be negative 12) B could be neutral 13) no because a positive charge only means there are more positives then negatives
14) to make the charge between the truck and the gas station equal
15) 5.2 x10-9 C 16) 52 x10-12 C = 5.2 x10-11 C 17) 520.0 x10-6 C = 5.200 x10-4 C
18) conduction 19) conduction 20) induction 21) induction 22) induction 23) negative 24) conduction 25) positive
26) f 27) c 28) b 29) e 30) f 31) a 32) c
33) yes 34) Positive 35) Positive or Neutral 36) Neutral 37) Negative 38) Positive 39) the force will be 4 times larger 40) the force will be 1/4 what it was