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Chapter 21 Electric Charge

Main Points of Chapter 21 Charge Electric forces Two types of charge Induction Conservation and quantization of charge Coulomb’s law Forces involving multiple charges

21-1 Charge - a property of matter Electric charge, whether we know it or not, is responsible for many familiar phenomena: The binding of electrons to a nucleus, forming an atom Atoms binding together into molecules Atoms or molecules binding together into liquids and solids Biological processes Chemical reactions

21-1 Charge - a property of matter Electric charge is a new quantity – it is not any combination of mass, length, or time All electrons in any atom have the same charge:

21-1 Charge - a property of matter Materials in which the outermost electron(s) that are very loosely bound to the atoms, and can move freely through the material are called conductors. Most other materials are insulators; some are semiconductors, which will be discussed later

21-1 Charge - a property of matter Can transfer charge from one material to another suitable material simply by rubbing: A Teflon rod rubbed with fur acquires a negative charge, while the fur becomes positively charged. This is called charging by friction.

21-1 Charge - a property of matter Electric charges are of two types, called positive (+) and negative (-) Like charges repel; opposite charges attract

21-1 Charge - a property of matter The fact that both attractive and repulsive forces exist shows that there must be two different types of charges. In the presence of a charged object, a neutral object can polarize – the charges opposite to those on the charged object move closer to it, and the other charges move away.

21-1 Charge – a property of matter Conductors can be charged by induction:

Charge is measured in Coulombs (C); the smallest unit of charge is the magnitude of the charge on the electron: 21-1 Charge - a property of matter (21-1)

21-1 Charge – a property of matter The electroscope is a device that detects the presence of excess free charge on an object. This can be done in two ways: First, when a charged rod transfers charge directly to the electroscope, that charge spreads uniformly over its metal surfaces. The leaf and stem then have same-sign charges, and repel.

21-1 Charge – a property of matter Second, when a charged rod is brought near, but not touching, the electroscope, it attracts opposite charges. The like charges tend to move away from the rod; once again the stem and leaf have same- sign charges, and repel.

In observed reactions involving the so-called elementary particles, no one has ever seen a single case of net charge appearing or disappearing Charge is conserved and quantized

Examples of charge-conserving subatomic reactions: In summary: Charge is conserved absolutely Free charge is quantized in positive or negative integral multiples of e.

21-3 Coulomb’s Law As early as Benjamin Franklin's experiments, it was known that the force between electric charges obeys an inverse square law; Coulomb showed that it is also central: and proportional to the magnitudes of the charges: (21-2) (21-3)

21-3 Coulomb’s Law Combining gives Coulomb’s law: The constant k is found to be: Including full vector information, we have the final form of Coulomb’s law: (21-4) (21-5,7) (21-8)

21-3 Coulomb’s Law The Coulomb force acts along the line connecting the two charges, whether they are opposite or like:

When there are multiple charges, the net force on any one of them is the vector sum of the forces due to each of the others Forces Involving Multiple Charges (21-10)

21-4 Forces Involving Multiple Charges For a continuous distribution of charge, first think of it as a collection of very small charges: The total force is found by summing the force from each piece: (21-11)

21-4 Forces Involving Multiple Charges If we know the charge density as a function of position, we can go to the limit where the charges are infinitesimally small, and integrate. For a linear distribution of charge, the linear charge density is and the charge element is (21-12) This can be integrated to find the force: (21-13)

21-4 Forces Involving Multiple Charges Similarly, for a surface distribution of charge, the surface charge density is σ and the charge element is (21-14) This can be integrated to find the force: (21-15)

21-4 Forces Involving Multiple Charges Finally, for a volume distribution of charge, the volume charge density is and the charge element is This can be integrated to find the force: (21-16) (21-17)

If a charge distribution is spherically symmetric, the charge can be treated as though it were concentrated at the center of the sphere: 21-4 Forces Involving Multiple Charges

Summary of Chapter 21 Electric charge comes in two types, positive and negative. Opposite charges attract; like charges repel. Metals are good conductors – electrons are able to move freely through them; most other materials are insulators Basic charge is that on the electron: (21-1) All other charges are multiples of e.

Summary of Chapter 21, cont. Charge is conserved: net charge before an interaction is the same as net charge afterwards Coulomb’s law for the force between two point charges: (21-8) For multiple, or continuous, charges, the superposition principle applies.

Summary of Chapter 21, cont. Forces due to linear, surface, and volume charge densities, respectively: (21-13) (21-15) (21-17)