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**Foundations of Physics**

CPO Science Foundations of Physics Unit 7, Chapter 21

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**Unit 7: Electricity and Magnetism**

Chapter 21 Electric Charges and Forces 21.1 Electric Charge 21.2 Coulomb’s Law 21.3 Capacitors

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Chapter 21 Objectives Describe and calculate the forces between like and unlike electric charges. Identify the parts of the atom that carry electric charge. Apply the concept of an electric field to describe how charges exert force on other charges. Sketch the electric field around a positive or negative point charge. Describe how a conductor shields electric fields from its interior. Describe the voltage and current in a circuit with a battery, switch, resistor, and capacitor. Calculate the charge stored in a capacitor.

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**Chapter 21 Vocabulary Terms**

charge electrically neutral static electricity positive charge negative charge electric forces charge by friction electroscope protons neutrons electrons gravitational field charged induction Coulomb’s law capacitor parallel plate capacitor microfarad coulomb electric field capacitance charge polarization shielding test farad field inverse square law discharged field lines

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**21.1 Electric Charge Key Question: How do electric charges interact?**

*Students read Section AFTER Investigation 21.1

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21.1 Electric Charge All ordinary matter contains both positive and negative charge. You do not usually notice the charge because most matter contains the exact same number of positive and negative charges. An object is electrically neutral when it has equal amounts of both types of charge.

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**21.1 Electric Charge Objects can lose or gain electric charges.**

The net charge is also sometimes called excess charge because a charged object has an excess of either positive or negative charges. A tiny imbalance in either positive or negative charge on an object is the cause of static electricity.

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21.1 Electric Charge Electric charge is a property of tiny particles in atoms. The unit of electric charge is the coulomb (C). A quantity of charge should always be identified with a positive or a negative sign.

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21.1 Electric forces Electric forces are created between all electric charges. Because there are two kinds of charge (positive and negative) the electrical force between charges can attract or repel.

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21.1 Electric forces The forces between the two kinds of charge can be observed with an electroscope. An electroscope contains two very thin leaves of metal that can swing from a central rod connected to a metal ball. Charges can flow freely between the ball and the leaves. Suppose a positively charged rod touches the metal ball of an electroscope. Some negative electrons are attracted to the rod. The metal ball and leaves of the electroscope are left with a net positive charge. Since both leaves have the same positive charge, the leaves repel each other and spread apart. Once an electroscope is charged, it can be used to test other charged objects. The leaves spread farther apart if another positively charged rod is brought near the metal ball. This happens because the positive rod attracts some negative electrons from the leaves toward the ball, increasing the positive charge on the leaves.

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**21.1 Electric forces Charge can be transferred by conduction.**

If a negatively charged rod touches the ball, the opposite effect occurs. A negatively charged rod repels negative electrons from the ball into the leaves where they neutralize some of the positive charge. The positive charge on the leaves is reduced and the leaves reduce their repulsion.

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21.1 Electric current The direction of current was historically defined as the direction that positive charges move. Both positive and negative charges can carry current. In conductive liquids (salt water) both positive and negative charges carry current. In solid metal conductors, only the electrons can move, so current is carried by the flow of negative electrons.

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21.1 Electric current Current is the movement of electric charge through a substance. Charge that flows (coulombs) Current (amps) i = q t Time (sec)

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21.1 Calculate current Two coulombs of charge pass through a wire in five seconds. Calculate the current in the wire. 1) You are asked to find the current. 2) You are given the charge and the time. 3) Use the equation I = q/t. 4) Solve: I = (2 C) ÷ (5 sec) = 0.4 C/sec or 0.4 A

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**21.1 Conductors and insulators**

All materials contain electrons. The electrons are what carry the current in a conductor. The electrons in insulators are not free to move, they are tightly bound inside atoms.

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**21.1 Conductors and insulators**

A semiconductor has a few free electrons and atoms with bound electrons that act as insulators.

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**21.1 Conductors and insulators**

When two neutral objects are rubbed together, charge is transferred from one to the other and the objects become oppositely charged. This is called charging by friction. Objects charged by this method will attract each other. A charged balloon will stick to a (neutral) wall or other insulating surface. When a negatively charged balloon is near a wall, electrons inside atoms in the wall are repelled. Since the wall is made of insulating material, the repelled electrons are not free to travel between atoms. The electrons can move within each atom, so they spend more time on the side of the atom that is farthest from the balloon.

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**The atoms become polarized; one end is positive and the other is negative.**

Atoms in a material only become polarized if the material is an insulator. In a conductor, electrons are free to move from atom to atom so the entire object becomes polarized. This is why a balloon sticks to a wood door but not a metal doorknob.

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21.2 Coulomb's Law Coulomb’s law relates the force between two single charges separated by a distance. Constant 9 x109 N.m2/C2 Force (N) F = K q1 q2 r2 Charges (C) Distance (m)

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21.2 Coulomb's Law The force between two charges gets stronger as the charges move closer together. The force also gets stronger if the amount of charge becomes larger.

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21.2 Coulomb's Law The force between two charges is directed along the line connecting their centers. Electric forces always occur in pairs according to Newton’s third law, like all forces.

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21.1 Coulomb's Law The force between charges is directly proportional to the magnitude, or amount, of each charge. Doubling one charge doubles the force. Doubling both charges quadruples the force.

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21.1 Coulomb's Law The force between charges is inversely proportional to the square of the distance between them. Doubling the distance reduces the force by a factor of 22 = (4), decreasing the force to one-fourth its original value (1/4). This relationship is called an inverse square law because force and distance follow an inverse square relationship.

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21.2 Calculating force Two balls are each given a static electric charge of one ten-thousandth (0.0001) of a coulomb. Calculate the force between the charges when they are separated by one-tenth (0.1) of a meter. Compare the force with the weight of an average 70 kg person. 1) You are asked to calculate the force and compare it to a person’s weight. 2) You are given the charges and separation, and the mass of the person. 3) Use Coulomb’s law, F= -Kq1q2/R2, for the electric force and F=mg for the weight. 4) Solve: F = (9×109 N•m2/C2)(0.0001C)(.0001C) ÷ (0.1 m)2 = 9,000 N The weight of a 70 kg person: F = mg = (70 kg)(9.8 N/kg) = 686 N The force between the charges is 13.1 times the weight of an average person (9,000 ÷ 686).

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21.2 Fields and forces The concept of a field is used to describe any quantity that has a value for all points in space. You can think of the field as the way forces are transmitted between objects. Charge creates an electric field that creates forces on other charges.

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21.2 Fields and forces Mass creates a gravitational field that exerts forces on other masses.

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21.2 Fields and forces Gravitational forces are far weaker than electric forces.

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**21.2 Drawing the electric field**

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**21.2 Electric fields and electric force**

On the Earth’s surface, the gravitational field creates 9.8 N of force on each kilogram of mass. With gravity, the strength of the field is in newtons per kilogram (N/kg) because the field describes the amount of force per kilogram of mass.

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**21.2 Electric fields and electric force**

With the electric field, the strength is in newtons per coulomb (N/C). The electric field describes the amount of force per coulomb of charge.

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21.2 Accelerators An electric field can be produced by maintaining a voltage difference across any insulating space, such as air or a vacuum. Electric fields are used to create beams of high-speed electrons by accelerating them. Electron beams are used in x-ray machines, televisions, computer displays, and many other technologies. Suppose a flat plate is given a negative voltage and a metal screen is given a positive voltage. Electrons are repelled from the plate and attracted to the screen. Because the screen has holes, many of the electrons pass right through. Because the electrons feel a force between the plates, this device is an accelerator for electrons. It is easily possible to make a beam of electrons move at a speed of 1 million m/sec.

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21.2 Electric shielding Electric fields are created all around us by electric appliances, lightning, and even static electricity. These stray electric fields can interfere with the operation of computers and other sensitive electronics. Many electrical devices and wires that connect them are enclosed in conducting metal shells to take advantage of the shielding effect.

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**21.2 Coulomb’s Law Key Question: How strong are electrical forces?**

*Students read Section BEFORE Investigation 21.2

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**21.3 Capacitors A capacitor is a storage device for electric charge.**

Capacitors can be connected in series or parallel in circuits, just like resistors.

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21.3 Capacitors A capacitor can be charged by connecting it to a battery or any other source of current. A capacitor can be discharged by connecting it to any closed circuit that allows current to flow.

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21.3 Capacitors The current flowing into or out of a particular capacitor depends on four things: The amount of charge already in the capacitor. The voltage applied to the capacitor by the circuit. Any circuit resistance that limits the current flowing in the circuit. The capacitance of the capacitor.

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**21.3 How a capacitor works inside**

The simplest type of capacitor is called a parallel plate capacitor. It is made of two conductive metal plates that are close together, with an insulating plate in between to keep the charges from coming together. Wires conduct charges coming in and out of the capacitor.

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**21.3 How a capacitor works inside**

The amount of charge a capacitor can store depends on several factors: The voltage applied to the capacitor. The insulating ability of the material between the positive and negative plates. The area of the two plates (larger areas can hold more charge). The separation distance between the plates.

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21.3 Capacitance The ability of a capacitor to store charge is called capacitance (C). Capacitance (coulombs/volt) Charge (C) q = C V Voltage (volts) Cameras use capacitors to supply quick bursts of energy to flash bulbs.

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**21.3 Capacitance Capacitance is measured in farads (F).**

A one-farad capacitor can store one coulomb of charge when the voltage across its plates is one volt. One farad is a large amount of capacitance, so the microfarad (μF) is frequently used in place of the farad.

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**21.3 Calculate capacitance**

A capacitor holds coulombs of charge when fully charged by a 12-volt battery. Calculate its capacitance and the voltage that would be required for it to hold one coulomb of charge. 1) You are asked to find the capacitance and the voltage needed to hold 1 C of charge. 2) You are given the voltage and corresponding charge. 3) Use C = q/V to calculate the capacitance. 4) Solve: C=(0.02 C) ÷ (12 V) = F or 1667 μF Rearrange C = q/V to get V = q/C and calculate the voltage required to store a charge of 1 C on the capacitor. V = (1 C) ÷ ( F) = 600 V The capacitor would hold one coulomb of charge at a voltage of 600 volts. Most capacitors would be destroyed by a voltage this high.

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**21.3 Capacitors Key Question: How does a capacitor work?**

*Students read Section BEFORE Investigation 21.3

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**Application: How a Television Works**

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