Physics Chapter 16 Test: Comprehensive Study Guide

Distribution of Charge in a Metal Conductor

1. Any net charge on a conductor distributes itself on the surface (for a negatively charged conductor, these negative charges repel one another, and race to the surface to get as far away from one another as possible); 2. A charge inside a neutral spherical metal shell induces charge on its surfaces; the electric field exists even around the shell, but not within the conductor itself

Test Charge

Can investigate the electric field surrounding a charge or group of charges by measuring the force on a small positive test charge (a charge so small that the force it exerts doesn't significantly alter the distribution of the other charges that create the electric field)

Point Charges

Coulomb's law equation applies to objects whose size is much smaller than the distance between them; ideally, it's mathematically precise for point charges (spatial size negligible compared to other distances); for finite sizes, it's not clear what value to use for "r," but is the two objects are spheres, and the charge is distributed uniformly on each, then "r" is the distance between their centers

Quantized Electric Charge

Since an object can't gain or lose a fraction of an electron, the net charge on any object must be an integral multiple of this charge; electric charge is thus described as quantized, as it exists in only discrete amounts (i.e. 1ℓ, 2ℓ, 3ℓ, etc.)

Conventions For Direction of Electric Field

The electric field "E" due to a positive charge points away from the charge, whereas "E" due to a negative charge points toward that charge

Positive and Negative Electric Charge

The two types of electric charge are referred to as positive and negative; whenever a certain amount of charge is produced on one object, an equal amount of the opposite type of charge is produced on another object (note: the positive and negative are treated algebraically, so during any process, the net change in the amount of charge produced in zero)

How "E" Does Not Depend on Magnitude of Test Charge "q"

"E" is defined as F/q so that "E" does not depend on the magnitude of test charge "q"; this means that "E" described only the effect of the charges creating the electric field at that point

Detecting Charge of an Object With an Electroscope

1. An electroscope can be used to determine the sign of the charge if it is first charged by conduction (ex: negatively), and subsequently, if a negatively-charged object if brought close, more e- are induced to move down into the leaves, and they separate further (on other hand, you know object has positive charge if the separation of the previously-charged leaves is reduced, because the e- are induced to flow upward) 2. *Thus, a previously-charged electroscope can be used to determine the sign of a charged object

Electroscopy/Electroscope

1. An electroscope is a device that can be used for detecting charge: two metal leaves are connected by a conductor to a metal knob on the outside of the case, insulated from the case itself; if a positively-charged object is brought close to the knob, a separation of charge is induced; e- are attracted to the knob, leaving the leaves positively charged (and the two leaves repel each other because they're positively charged) 2. Thus, the greater the amount of charge, the greater separation of the leaves

How the Electric Field is Depicted

1. As the electric field is a vector, it is sometimes referred to as a "vector field"; thus, we indicate the electric field with arrows at various points when specifying one point, q; 2. So that the electric field can be easily discerned/specified at many points, we use field lines to portray it

Inducing a Net Charge by Connection to Ground

1. As the ground is a huge source of electric charge, another way to induce a net charge on a metal object is to first connect it with a conducting wire to the ground (object is then said to be "grounded"); the earth easily accepts or gives up e-, and thus acts like a reservoir for charge; 2. Thus, if a charged object (ex: negative) is brought close to the metal object, free e- in the metal are repelled, and many of them move down the wire into the earth, thus leaving the metal positively charged (if the wire were cut, the metal object would have a positive induced charge on it, and if the wire were cut after the negative object is moved away, the e- would all have moved back into the metal object and it would be neutral)

Development of Coulomb's Law

1. Coulomb investigated what factors affect the magnitude of the force of attraction or repulsion between charges, arguing that the force one tiny charged object exerted on a second tiny, charged object is directly proportional to the charge on each of the objects 2. (Ex: if the charge on either one of the objects is doubled, the force is doubled, and if the charge on both of them is doubled, the charge increases fourfold, in the case that the distance between the two charges remains the same)

Electrostatics

1. Coulomb's law describes the force between two charges when they're at rest; we discuss only charges at rest in the study of electrostatics; 2. NOTE: when calculating with Coulomb's law, the signs of the charges are usually ignored, but we determine the direction of a force separately based on whether the force is attractive or repulsive

Step-by-Step Method of Solving Electrostatics Problems

1. Draw a free-body diagram: for each object, either showing all the forces acting on that object, or showing the direction of the electric field at a point due to all significant charges present surrounding the point; make sure to determine the direction of each force or electric field physically (like charges repel each other, unlike charges attract; fields point away from a positive charge "Q," and toward a negative charge "Q") 2. Apply Coulomb's law: to calculate the magnitude of the force that each contributing charge exerts on a charged object, or the magnitude of the electric field at a certain/specified point (leaving out minus signs), and obtain the magnitude of each force or each electric field 3. Add vectorially: all the forces on an object, or the contributing fields at a point, to get the resultant (if necessary, break vectors up into their components); use symmetry whenever possible to streamline process

General Summary of the Properties of Electric Field Lines

1. Electric field lines indicate the direction of the EF; the field points in the direction tangent to the field line at any point 2. The lines are drawn so that the magnitude of the electric field, "E," is proportional to the # lines crossing unit area perpendicular to the lines (the closer together the lines, the stronger the field) 3. Electric field lines start on positive charges and end on negative charges; the number starting or ending is proportional to the magnitude of the charge 4. *NOTE: electric field lines never cross, because it would not make sense for the EF to have two directions at the same point

Conceptual Example Involving Electric Field Inside a Hollow Metal Box

1. Ex: a neutral hollow metal box is placed between two parallel charged plates; what is the field like inside the box? 2. Answer: note: if the metal box were solid, not hollow. Free e- in the box would have redistributed themselves along the surface until all their individual fields would have cancelled each other inside the box, making the net field inside the box zero: for a hollow box, the external field is not changed, since the e- in the metal can move just as freely as before to the surface; thus, the field inside the hollow metal box is zero (i.e. inside of metal box is shielded from charge)

Conceptual Example Involving Direction of Electric Field

1. Ex: given the same two charges Q1 and Q2 as in the previously example, determine the direction of each of the component electric fields, E1 and E2, as well as of the total electric field for two positions: (a) a point just slightly to the left of Q1 and (b) a point slightly to the right of Q2 2. Sol: (a) E1 would point to the right, E2 to the left, and net/total E would point to the right, since Q1 is closer in proximity to point "P" (b) E2 would point to right, E1 to left, and net/total E would point to right, since Q2 is closer in proximity to point "P"

Effect of Distance Between Particles on Force Exerted Between Them

1. If the distance between the particles was allowed to increase, Coulomb found that the force decreased with the square of the distance between them 2. (i.e. if the distance was doubled, the force fell to ¼ the original value; thus, he concluded that the force one small charged object exerts on a second one is proportional to the product of the magnitude of the charge on one times that of the other, and inversely proportional to the square of the distance "r" between them)

Composition of Solid Materials

1. In solid materials, the nuclei tend to remain close to fixed positions, while some of the e- may move freely-when an object is neutral, it contains equal amount of protons and e-/positive and negative charge 2. (Ex: the charging of solid object through rubbing can be explained by the transfer of e- from one object to the other; when ruler become negatively charged by rubbing, the transfer of e- from the towel to the ruler leaves the towel with a positive charge equal in magnitude to the negative charge acquired by the plastic)

Coulomb Based Upon Charge of an Electron

1. Objects that carry a positive charge have a deficit of e-, while negatively charged objects have an excess of e-; the charge on one e- has been determined to have a magnitude of about 1.602*10-19 C, negative (smallest, most fundamental charge found in nature-referred to as the elementary charge), where ℓ = -1.602*10-19 C; 2. NOTE: charge on a proton is +ℓ, or +1.602*10-19 C

Two Crucial Properties of Test Charges

1. They're tiny - have no volume, have in infinitesimally small charge, and as such, do not significantly affect magnitude of electric field, where E = F/q 2. They're always positive; the field always points in the direction that the force exerts on the charge (thus, in drawing field lines, arrows emanating from positive point charge point away from that charge, and lines emanating from negative point charge point towards that point charge)

Electric Field Lines

1. To visualize the direction of the electric field near positive and negative point charges, we draw a series of lines to indicate the direction of the electric field at various points in space (drawn so that they indicate direction of the force due to the given field on a positive test charge) without actually drawing the test charge itself 2. Note: sometimes called "lines of force," field lines indicate the direction of the electric field

Water Molecules and Polarity

1. When the rubbed solid objects return to neutral state eventually, this is because the charge "leaks off" into water molecules in the air (because water molecules are polar)-i.e. Even though they are neutral, their charge is not distributed uniformly; 2. Thus, the extra e- on a charged plastic ruler can "leak off" into the air because they're attracted to the positive end of water molecules (conversely. A positively-charged object can be neutralized by a transfer of loosely held e- from water molecules in the air)

Use of Hollow Metal Conductors for Protection

A conducting box is an effective device for shielding delicate instruments and electronic circuits from unwanted external electric fields; because of this, a safe place to be during a lightning storm is inside of a car, surrounded by metal (functions as a hollow metal box shielded from charge)

Semiconductors

A few materials (Ex: silicon and germanium) fall into the intermediate category known as a semiconductor

Presence of Electric Field Between Two Parallel Conducting Plates

Always, the EF between two parallel plates carrying equal but opposite charges is constant; the EF lines between two plates start out perpendicular to the surface of the metal plates, and go directly from one plate to the other, because: we would expect a positive test charge placed between the plates to feel a strong repulsion from the positive plate, and a strong attraction to the negative plate

Simplified Model of an Atom

An atom has a tiny, but heavy, positively-charged nucleus, surrounding by one or more negatively charged electrons (note: minimum constituent of positive charge is protons, and that for negative charge is electrons)

SI Units of Electric Field

As E is defined as the limit of F/q, as "q" is taken smaller and smaller, approaching zero, "q" is so tiny that it almost exerts no force on the other charges which created the field; thus, the electric field at any point in space is a vector whose direction is the direction of the force on a tiny positive test charge at that point, and whose magnitude is the "force per unit charge"; thus, "E" has SI units of Newtons per Coulomb (N/C)

Two Types of Electric Charge

As demonstrated when two plastic rulers are rubbed by cloth and thought brought close together, they repel each other (and if a glass rod is rubbed and brought near the ruler, it is attracted to it), all charged objects fall into two categories (i.e. there are only two types of electric charge); Each type of electric charge repels the same type, but attracts the opposite type (i.e. unlike charges attract, like charges repel)

Static Electricity

Electric charge produced/electric force between still objects (Ex: rubbing ruler or comb with towel will induce electric charge; in each case, an object becomes "charged" as a result of rubbing, and possesses a net electric charge)

Example of Induced Charge on Macroscopic Level

Ex: A comb that temporarily adheres to scraps of paper has acquired a static electric charge (either from passing through hair, or being rubbed by cloth or paper towel); the electric charge on the comb thereafter induces a polarization (i.e. separation of charge) in scraps of paper, and thus attracts them

Conceptual Question Involving Placement of 3rd Charge

Ex: If there are two point charges of same magnitude, but opposite sign (+Q and -Q), which are fixed a distance "d" apart, can you find a location where a third positive charge Q could be placed so that the net electric force on this third charge is zero? (b) What if the first two charges were both +Q? Answer: (a) No (b) yes; midway between them

Exercise Involving Calculating Electric Field

Ex: What is the magnitude and the direction of the electric field due to a +2.5 μC charge at a point 50 cm below it? Sol: E = kQ/r2 = (9*109 Nm2/C2)(2.5*10-6)/(0.52) = 9.0*104 N/C

Example of Law of Conservation of Electric Charge

Ex: if you rub a balloon on your head, you would be able to then stick it on the wall, because you've donated charge to the balloon (Note: protons cannot be transferred between substances/atoms, only the electrons travel)

Effect of Doubling Distance and Magnitude of Charge on Force Exerted Between Charges

Ex: two identical spheres have the same electric charge; if the electric charge on each of them is doubled, and their separation is also doubled. The force each exerts on the other will be unchanged, because F = (2/2)*(k2Q/r2) = same force

Charge Separation in Nonconductors

If a positively charged object is brought close to a neutral nonconductor, the e- can move slightly within their own atoms and molecules: in this situation, the negatively-charged e-, attracted to the external positive charge, tend to move in its direction within their molecules: In this situation, the negatively-charged e-, attracted to the external positive charge, tend to move in its direction within their molecules

Charging by Induction

If a positively-charged object is brought close to a neutral metal rod, but does not touch it, while the free e- of the metal rod don't leave it, they still move within the rod itself toward the external positive charge, thus leaving a positive charge at the opposite end of the rod; in this situation, a charge is induced at the two ends of the metal rod (when an induced charge occurs, no net charge has been created in the rod: the charges have merely been separated; net charge on metal rod is still zero)

Charging by Conduction

If positively charged metal is brought close to an uncharged metal object, when they touch, the free e- in the neutral one are attracted to the positively-charged object, and some will pass over it (and now the originally neutral object is missing some of its e- and thus will have a net positive charge)-this process is "charging by conduction"/ "by contact," and the two objects end up with the same sign of charge

Conductors

If there are two metal spheres, one highly charged and the other electrically neutral, and a metal object (Ex: a nail) is placed so that it touches both spheres, the previously uncharged sphere quickly becomes charged; thus, materials like iron nail (anything metal) are conductors; they allow electricity to flow easily (metals are generally good conductors, whereas most other materials are insulators)

Non Conductors/Insulators

If we'd connected the two spheres by a wooden rod or piece of rubber, the uncharged ball would not become noticeably charged; materials like rubber and wood are insulators, in which almost no charge is conducted through the object of interest

Example of Superposition of Charges

If you have a system of four charges, the net force on charge 1, say, if the sum of the forces exerted on charge 1 by charges 2, 3, and 4; the magnitudes of those three forces are determined from Coulomb's Law, and then are added vectorially

Applying Coulomb's Law in Vectoral Situations

In applying Coulomb's law, just input charge magnitudes (leave out signs), and then determine separately the direction of the force physically along line joining the particles, and finally add all the forces on one object together as vectors to obtain the net force on that object

Relationship Between Number of Field Lines and Magnitude of Charge

NOTE: in drawing of field lines, the number of lines starting on a positive charge, or ending on a negative charge, is proportional to the magnitude of the charge

Conventions Involved in Adding Electric Forces

Principle of Superposition: Upon dealing with several charges, use double subscripts on each of the forces involved; **first subscript refers to particle ON which the force acts, and second refers to the particle that exerts the force (e: F31 means force exerted on particle 3 by particle 1); must draw free-body diagram for each of charges (show all forces acting on the object of interest)

Developing Rule About Electric Field Between Two Parallel Conducting Plates

Since the field lines between two close plates are parallel, and equally spaced in the center region (they fringe outward a little near the edges), thus, in the central region, the EF has the same magnitude around all points (remember: this is because the proximity of lines to each other indicates the strength of the EF, and thus, equally spaced EF lines indicate that the EF is constant)

Rule for the Electric Field Inside of a Conductor

The electric field inside a conductor is zero in the static situation (when the charges are at rest); if there were an electric field within a conductor, there would be a force in the free electrons, and the e- would move until they reached positions where the electric field (and therefore the force on them) did become zero

Election Composition of Conductors and Insulators

The electrons in an insulating material are bound very tightly to the nuclei, while in a good conductor, some of the e- are bound very loosely, can can move freely within the material (although they can't leave easily), often referred to as "free electrons" or "conducting electrons"

Gravitational Field

The field concept can be applied to the gravitational force; thus, a gravitational field exists for every object that has mass; the gravitational field always attracts (i.e. one object attracts another by means of gravitational field, which is responsible for the gravitational force on objects; the gravitational field is defined as the force per unit mass, where the magnitude of the earth's gravitational field at any point above earth's surface is GmE/r2 (where mE = mass of earth); at earth's surface, gravitational field is equal to "g"

Law of Conservation of Electric Charge

The net amount of electric charge produced in any process is zero (i.e. no electric charge can be created or destroyed; if one object or region of space acquires a positive charge, then an equal amount of negative charge will be found in neighboring areas or objects)

Composition of Electric Charge in Nucleus

The nucleus of the atom contains protons (positively charged) and neutrons (no net electric charge); all protons and electrons have exactly same magnitude of charge, while they are opposite in sign (thus, neutral atoms-having no electric charge-contain equal numbers of protons and electrons)

Induced Charge

When a positively-charged object is brought close to or touches a conductor, the free electrons in the conductor are attracted by the positively-charged object and move quickly toward it; conversely, the free e- move away from a negatively charged object that is brought close (in a semiconductor, there are many fewer free e-, and in an insulator, almost none)