Physics Electric Force and Field

Superimposition of Electrical Forces Follow this procedure:

1. Assume all charges, other than the one that the initial net force is being calculated for, are immobile - this will allow the determination of the direction of the individual initial forces. 2. Draw a free body diagram for each charge, using the fact that opposite charges attract and like charges repel. 3. Use Coulomb's Law to find the magnitude of each force. 4. Sum the forces, taking into account that they are vectors with direction and magnitudes. Use the free body diagrams to assign signs to the forces - if they point to the right, they are positive; if they point to the left, they are negative.

Electric Field Visualization There are four rules to help us draw these fields:

1. Electric Field Lines begin on a positive charge and end on a negative charge. 2. The density of the Electric Field lines distribution is proportional to the size of the charges. 3. The lines never cross (or else there would be multiple values of Electric Force at the intersection point). 4. The lines are continuous.

The Net Electric Field Objective: Find the net electric charge at the origin for this charge configuration. Strategy:

1. Mark the point on the sketch where the Electric Field is to be calculated (the point is at x = 0 in this example). 2. Draw the Electric fields acting at that point. 3. Calculate E1, E2 and E3, assigning negative values to fields pointing to the left, and positive values to fields pointing to the right. 4. Sum the electric fields:

Millikan and Fletcher's work and subsequent experiments have established the value of "e" as _____________- It has also been demonstrated that this is the ________ value of charge (with the exception of quarks which will be covered shortly) and all larger charges are an integral _________ of this number. Because small amounts of charge can generate large amounts of _______, charge is often measured in: milli-Coulombs (mC) = ______ C micro-Coulombs (μC) = _____C nano-Coulombs (nC) = ______C

1.602 x 10-19 Coulombs. smallest, multiple force milli-Coulombs (mC) = 10-3 C micro-Coulombs (μC) = 10-6 C nano-Coulombs (nC) = 10-9 C

Electric Force relationship to Gravitational Force Both forces are expressed using a similar mathematical formula, where the magnitude of the force decreases as ______ Electric force can be _______ or _________ (like charges repel, opposite charges attract). Gravitational force is always ___________. The electric force is on the order of _________ times stronger than the gravitational force!

1/r2. attractive or repulsive attractive 10^36

If an atom was magnified so that the nucleus was the size of a baseball, the atom would have a radius of ___ km. And the electrons would be approximately the size of the ______ at the end of this sentence. Atoms are almost all ________ Since everything (including us) is made of ______, that means everything (including us) is mostly ____________

4 km, period empty space atoms, empty space

Properties of the Electron Further research showed that the electron has a mass of ____________ While finding the charge on an electron, it was discovered that the charge on any object was an _____________ of the electron charge. Thus, you can have a charge of 3.2 x 10-19 C on an object, but you can't have a charge of 3.0 x 10-19 C! The charge on any object is always an ______ (1, 2, ..., 1,000,056, ...) _______ of 1.6 x 10 -19 C.

9.1 x 10-31 kg. integral multiple

Electroscope charging by Induction

A neutral electroscope is connected to ground and a negatively charged bar is brought near. Electrons in the scope will be repelled out of the scope to the ground. The scope will then have a positive net charge. As with charging a sphere by induction, note that the charge on the rod does NOT change. now positively charged - leaves repel each other positively charged A similar effect occurs for a bar with a net positive charge; except the scope will end up with a net negative charge since electrons will come up from the ground to the scope. Again, the charge on the rod does NOT change. now negatively charged - leaves repel each other

Charging by conduction with an electroscope

A neutral electroscope will become negatively charged when touched by a negatively charged object. Negative electrical charge will distribute across the electroscope and the gold leaves will repel, since they have the same charge, and like charges repel. The bar is moved away and there is a negative net charge on the scope. Negative charge moved from the rod to the electroscope; the rod has less negative charge (Conservation of Charge). The gold leaves repel. The leaves would also repel if the experiment had been done with a positively charged bar

In the 18th century, ______________ named the two types of charge when he observed the attraction between a rubber rod and animal fur when they were rubbed together. Benjamin named the charge on the rod, ________, and the charge on the fur, __________.

Benjamin Franklin negative, positive

What does charging by conduction involve? Why is the insulator necessary?

Charging by conduction involves conductors that are insulated from the ground, touching and transferring the charge between them. The insulator is necessary to prevent electrons from leaving or entering the spheres from the Earth.

What does charging by induction involve?

Charging by induction involves transferring charge between two objects without them touching.

Divide the above equation by q, and define the result, the ________ The charge _____ creates the electric field - it is a property of the space surrounding Q. The _______________________ determine the strength of the electric field (E) at that point. E is measured in _______

Electric Field. (E = kQ/r^2 r) Q size of charge Q and the distance to a point N/C (Newtons per Coulomb).

The free rod accelerated towards the stationary rod so there must be a force present. We call this the _________-, and as with all forces, it is measured in ________

Electric Force Newtons

for induction what happens when a negatively charged rod is brought near but does not touch a sphere? what happens when the ground is removed? What happens when the rod is removed?

Electrons within the sphere are repelled by the rod, and pass through the wire to the ground, leaving a net positive charge on the sphere. The electrons are being pushed down this wire into the ground. While the negatively charged rod remains near the sphere, the ground is removed. Note that there can be no more movement of electrons since the sphere is isolated from the ground. Electrons cannot jump the gap between the rod and the sphere or between the ground and the sphere. The wire is removed, disconnecting the sphere from the ground. The rod is then removed. It is important to note that the charge on the rod remains constant (negative). The charge on the sphere is now positive as it lost electrons to Earth.

The absolute value signs will be ______, as we will now consider the vector quality of the Force (note the arrow on the top of the F - that means that F is a vector - it has magnitude and direction). r (with something over it) is a _________ - it has a magnitude of ____, and is in the direction of the _________

F = kQq/r^2 r removed unit vector one force vector

The Electric Field starts with Coulomb's Law: This gives the force between two charges, q1 and q2. Similar to the gravitational force, no _______ is needed between the two charges for them to feel a force from the other charge. This "_____________" is best understood by assuming that each charge has a field surrounding it that affects other charges - this is called the _________

F = kq1q2/r^2 contact action at a distance Electric Field

Coulomb's Law states that the magnitude of the electrical force is:

Fe = k q1 q2/ r12^2 k = the Coulomb constant that equals 9.0x10 9 N-m2/C2 |q1| = the absolute value of the net charge on one object |q2| = the absolute value of the net charge on the other object r12 = the distance between object 1 and object 2 if they are point charges, or between the centers of the objects if they are spherical.

Electroscope charging by Induction Charging by Induction describe the effects of the bar being removed first or vice versa

If the charging bar is removed while the ground is still attached, the electrons will return either to the ground or to the leaves until they have a neutral charge and will fall back together. In order to leave the charge on the electroscope (and keep the leaves separated), the ground must be removed before the charging bar. The electrons will now have no place to go and a net positive or negative charge will be left on the electroscope.

Charging by Conduction what happens when the two spheres touch? What do the electrons do and what happens to the total charge?

If the spheres are brought together to touch, their electrons push as far apart as they can, and the total charge is distributed equally between the two spheres. Note that the total charge stays the same.

The electron was discovered by __________ in 1897, and in a series of experiments between 1909 and 1913, Robert Millikan and his graduate student, Harvey Fletcher, established the value of the charge, "____," on an electron.

J.J. Thomson e

________ found a particle that had a very low mass for its charge. In fact, its mass per charge was 1800 times less than the previous lowest amount measured for a particle. Before this work, physicists were speculating that the ________ was the smallest fundamental particle. This led Thomson to propose that this negatively charged particle was new - and he called them "__________." The name "______" was taken from George Johnstone Stoney's work in 1874, and proposed again by George F. Fitzgerald - and the name stuck. Furthermore, since the electron was so much lighter than the hydrogen atom, it was concluded that it must be part of the ________.

J.J. Thomson hydrogen atom corpuscles, electron atom

___________ created the concept of the Electric Field. Faraday was born in London in 1791. He came from a poor family. At 13, he apprenticed as a book seller and binder while also attending local lectures on philosophical and scientific topics. A member of the Royal Institute took notice of Faraday and bought him tickets to several Royal Institute lectures. In 1813, he was invited to work at the Royal Institute where he made numerous contributions to physics and chemistry.

Michael Faraday

Gravity involves Electric involves

Newton's Law of Universal Gravitation, mass, distance, r, between centers of mass, gravitational field coulomb's law, charge (coulombs), distance, r, between centers of charge, electric field

The study of Quarks is called ........... But one final interesting point - the quark is subject to all four fundamental forces - electricity and magnetism, gravity, strong nuclear, and the weak nuclear.

Quantum Chromodynamics

The weight of an object on a planet, or the measure of the force between the obect and the planet is expressed by: The _____ of the object remains the same wherever it is, but its ______ is dependent on the gravitational attraction, g, of its surroundings.

W = Fg = mg mass, weight

What will happen to the charges on Rod A (neutral rod conductor) if it is moved towards Rod B (stationary negatively charged)?

When A is brought towards B the electrons in A will be repelled. Electrons in A will move to the left side of the rod. This causes the left and right sides of the rod to have a different charge (overall, the rod remains neutral) - the rod is "polarized." The positive net charge on the right side of A will cause A to move towards B (opposites attract).

Since the Electric Field of a single charge is a vector, the Electric Field of multiple charges may be calculated by _______, point by point, the Electric Fields due to each charge. The addition is not carried out by just adding the magnitudes of the individual fields. It must be done by adding their _______ - vector addition.

adding vectors

Electric Force relationship to Contact Forces Large (macro) objects are made up of _______. Atoms are composed of a positive nucleus, surrounded by a "cloud" of negative electrons. The predominant force acting between atoms is thee _________(later we will see how this is really a part of the electromagnetic force). At the _______ level, the predominant force is still the electric force. Since there are so many atoms involved at this level, it is easier to describe these interactions in terms of _________, such as the Normal force, Tension force and Friction.

atoms electric force macro level non fundamental forces

Further experimentation showed that dissimilar materials would _____ each other after rubbing, while similar materials would _____ each other. These effects would not happen without the _______, and later, given enough time, the forces of attraction and repulsion would _______. This led to the thought that something was being exchanged between the materials - and this something was later named "__________." Because objects would be repelled or attracted, it was postulated that this charge came in _____ types.

attract, repel contact, stop charge, two

It has been known since ancient times that when certain materials are rubbed together, they develop an _________ for each other (This can be seen today when you take clothes out of a dryer) In ancient Greece - people noticed that when thread was spun over a spindle of amber, the thread was attracted to the spindle. The Greek word for amber was "elektron," hence this FORCE was called _______.

attraction electric

Positive Charge If there is an isolated positive charge, it will create an Electric Field that points radially ________ it in all directions, since a positive test charge in the field will be _______ by this charge. The charge creates a spherically symmetric field since it is proportional to _____. At any distance, r, from the charge, the value of the field is the ______. Since r can point in any direction, we get the field lines centered on the charge, generating a ________ (remember, a charge exists in three dimensional space, which is represented in two dimensions here).

away from repelled 1/r^2 same sphere

In the chapter on Electric Charge and Force, the similarity between the electric force and the gravitational force was noted. There is a similar relationship between the Electric Field and the Gravitational Field because they are both generate _______ Central forces: · are directed in a _________ to or from an object from a point in space. · The magnitude of the force depends only on the _________

central forces straight line distance between the point and the object.

Determining the type of charge When the leaves of the electroscope repel, there is a _____ present. It could be ............. The electroscope can also be used to find out the charge on the ______. Take an object known to be positive or negative, place it near the top of the scope, and watch the reaction.

charge positive or negative leaves

Electric Field lines are mathematical abstractions that enable us to visualize the strength of the ________ that generates the field, and the ______ that it exerts on other charges that enter the field. When you multiply the strength of the Electric Field at any point by the charge which is placed there, it gives you the ____________ The direction of the field gives you the direction of the force on a ________ charge (the force on a ________ charge would be in the opposite direction).

charge, force magnitude of the force on that charge. positive, negative

There are six types, or flavors, of quarks that describe their properties, and they are further classified according to their ______ (not a real color - just a handy inventory management tool). They are: ............. And they have charges that are either ___________! Before this work in the 1960's, it was thought that the smallest charge on a particle was e. A neutron (to the left) is composed of an _____ quark and two _____ quarks.

color up, down, strange, charm, top and bottom. ±2/3 e or ±1/3 e up, down

Electrical circuits and devices are usually grounded to protect them from accumulating a net charge that could shock you. To ground an electrical device, a __________ must run from the device into the ground. Plugs for many electrical devices have a _______ grounding pin that connects to a wire in the outlet box which goes to the ground.

conductor third

In ______, some electrons are mobile and can move freely inside and on the surface of the solid. ___________ are materials that have strongly bound electrons that can move only short distances within the solid. Different __________ have varying levels of insulation capabilities.

conductors insulators

Electric Charge is a ____________ quantity. The total amount of electric charge in a closed system remains ________ - it is neither _______ or __________. Just like energy, linear momentum, and angular momentum are conserved quantities.

conserved constant, created or destroyed

Like energy and momentum, charge is neither created nor destroyed, it is ___________. Opposite charges _______ and like charges ______. As a result negatively charged ___________ are attracted to the positive __________.

conserved attract, repel electrons, nucleus

Electric Force relationship to Contact Forces The Normal, Tension and Friction forces are called ________, as they involve objects ___________ each other. The source of the Contact force is the ____________

contact forces touching electric force

grounding used to be called "________," because of the flow of electrons to and from the ______.

earthing Earth

The electroscope measures ........... The conductor rod is _______ from the glass container. When the scope is neutral, the leaves hang ______ to due to their own ______. Electroscopes can be charged by ___________ or ______________.

electrical charge (both sign and magnitude). insulated down, mass conduction or induction

what are fundamental particles and what are not?

electrons and quark are fundamental particles protons and neutrons are not

The ________ are the particles that will move between atoms - they are not bound together as tightly as the ______ and the _________

electrons, protons and neutrons

No new charge is created - instead, it is just separated - the positive charge acquired by one object is exactly __________________to the charge lost by the other object.

equal in magnitude and opposite in sign

Protons and electrons have _____ and _______ charge. By convention (set by Ben Franklin), electrons have a ________ charge and protons have a ______ charge. This is the origin of charges on material objects. Neutrons have ______ charge (neutral). Atoms are electrically _______ - not because they contain no charge - but because they have equal numbers of _____________ - their total charge adds up to zero.

equal, opposite negative, postive, no charge neutral, protons and electrons

What happens when a wire is attached between the earth and a negatively charged conductor? what will a positively charged object cause?

excess electrons flow to the earth leaving the conductor neutral. This is "grounding." electrons to flow to it from the ground

The Net Electric Field Net Electric fields will now be calculated mathematically, and for more than just a pair of charges. Where n is the total number of ______ present at a location. The direction of each electric field determines the _____ used.

fields sign

Solids are a form of matter whose atoms form a ________ ______, with their protons and neutrons, are "locked" into position. Solids are classified as either ____________ In conductors, some electrons are........... Electrons are bound to their ______ in insulators, and may move ______ distances, but much less than the electrons in a conductor. Semiconductors, depending on their situation, act as either ..................

fixed structure nuclei conductors, insulators, or semiconductors free to move through the solid and are not bound to any specific atom atoms, short conductors or insulators

Coulomb's Law is used to calculate the magnitude of the ______. Each object exerts the ______ force on the other - except in ________ directions (Newton's Third Law applies to all forces, not just mechanical ones). Since electric force, like all forces, is a ______, you need to specify the ________ of the force whose magnitude was determined by Coulomb's Law. This is done by looking at the _____ of both charges (like charges repel & opposite charges attract).

force same, opposite vector, direction signs

In the late 18th Century, Joseph Priestly reasoned and John Robison measured that the force between two objects followed the same principles as the __________. And that the force between two charged objects depends on .......

gravitational force the inverse square of the distance between them (F is indirectly proportional to 1/r^2)

Given that a mass m is located at the surface of the planet with a mass of M and radius R, Newton's Law of Universal Gravitation is used to determine the magnitude of the ____________-between the planet and mass m: Divide this expression by m (where m<<M) - similar to what was done with the small positive test charge, q, and call this "g", the Gravitational Field:

gravitational force, FG, F = GMm/R^2 g = Fg/m = GM/R^2

Despite the great mass difference, the charge on an electron is exactly equal in _________ to the charge on a proton, and its magnitude is denoted by "______." An electron has a charge of ____ and a proton, a charge of _____

magnitude e -e, +e

Determining the size of the Charge Intuitively, it would seem that the further apart the leaves move, the greater the ........ This is true, and the next section will talk about the force due to electric charges, which is responsible for the leaves moving against the forces of gravity and tension.

magnitude (size) of the charge present

Electric Field relationship to Gravitational Field There is a key difference between the two fields and forces. _____, which is the source of the gravitational field is always ______, and the force is always ______. The gravitational field always points ______ the mass generating it. ________, the source of the Electric Field, can be _____ or _____ and the force is either ________ or _________-. The direction of the Electric Field points ____ from a positive charge and ______ a negative charge.

mass, positive, attractive towards charge, negative, positive, attractive or repulsive away, towards

To understand where the phenomenon of electric charge comes from, the basic structure of _______ needs to be discussed. All matter is made up of ______, which are made up of _____________ Each atom contain a central ______ that is composed of ___________________. ____________ move around the nucleus in the empty space of the atom. Electrons are _________________- they have no underlying __________. Protons and neutrons are not fundamental particles. They are made up of ______ - which are fundamental particles.

matter atoms, protons, neutrons, and electrons nucleus, protons and neutrons (nucleons) electrons fundamental particles, structure quarks

Electric Field of Multiple Charges There is no electric field ______ between the two like charges - the individual electric field vectors cancel out

midway

You know that Helium has two electrons - yet they're not shown on this picture. That's because we don't know exactly where those electrons are. We only know a probability of where they are. The darker the shade means that it is ............

more probable that the electrons are found within that shape.

Charging by Induction A neutral electroscope can also be charged by induction. If a bar with a negative net charge is brought near the scope then the electrons in the electroscope will ..............If the bar is removed, the leaves will ................This induction is ____________ - and no _______ is transferred from the rod to the leaves. A similar effect is caused by a bar with a positive net charge. The leaves will again _____ since like charges _____. One more piece is needed to effect a permanent charge on the electroscope. The missing piece is a _______.

move down to the leaves and the leaves will repel. go back to their original positions. temporary charge repel ground

Many times, there is a configuration consisting of multiple charges and you need to calculate the ___________ on each charge. The charge configuration will then change, as the charges react to their initial net forces - but that is way beyond the scope of this course. The simplest configuration to handle is when the charges are all in a _____, for example, on the x axis.

net initial force line

If an atom gains electrons, it has a ________________If it loses electrons, then it has a _________

net negative charge and is called a negative ion. positive charge and is called a positive ion.

Conduction Through physical contact, a charged object will transfer a portion of its charge to a _______ object. Because of the Conservation of Charge, the amount of charge on the initially charged object will __________. For example, a positively charged object will transfer ________ charge to a _______ object, leaving it with a net positive charge. The amount of positive charge on the initial object will _______. Similarly, a negatively charged object will transfer _______ charge to a ______ object.

neutral decrease positive, neutral, decrease negative, neutral

Induction A charged rod will be brought close to a ____________object, but it will not _________ A positively charged rod will ..............A negatively charged rod will ................. The ground is then __________. The neutral object will be left with a charge ________ to the charged rode The rod will not lose any ________ - the extra charge on the originally neutral object comes from the _______. As long as the ground is disconnected before the initial object is removed, the neutral object will ______ charge. If the ground were left in place, once the charged rod is removed, the neutral object will .................

neutral, grounded touch it attract electrons from the ground to the neutral object. repel electrons to the ground. removed opposite charge, ground gain pass its gained charge back to the ground.

When you take two non metallic objects, such as a plastic ruler and animal fur and rub them together, you get an interesting effect. Before they are rubbed, the plastic ruler is held over bits of paper and _____________. After the rubbing, the plastic ruler is held over the bits of paper and they are ___________________- Since the paper bits were accelerated upwards, against the force of gravity, what interaction was occurring between the ruler and the paper?

nothing happens accelerated towards the ruler A Force.

Electrons can flow between ______ - both _______ and ________. Electrons can also flow from ______, which is an excellent ___________, to the objects, and from the objects to Earth. Because of its massive size, the Earth serves as the ultimate source and destination for ___________.

objects, conductors and insulators Earth, conductor electrons

Objects charge is electroscope's reaction charge on the scope is

positive positive negative negative Leaves move apart positive Leaves move closer negative Leaves move apart negative Leaves move closer positive positive negative negative positive

Neutrons and protons are actually made up of elementary particles called ______. Murray Gell-Man, along with George Zweig, proposed the existence of these particles to help explain the many different types of particles that make up matter.

quarks

When you touch an object with a net negative charge, you may get a _______. Why? and how do you do this?

shock This is because the conductor wants to get rid of its excess electrons. To do this, electrons flow through you to the ground. If the conductor had an excess positive charge, the electrons would flow from the earth to you. In either case - there is a spark!

Charles Coulomb published a paper (1785), based on detailed experiments, that definitively proved Priestly and Robison's work, and that the force was also proportional to the ___________ He used a _________ which was based on the same principle as Henry Cavendish's experiment that measured the _________ constant.

size of the charges. torsion balance gravitational

Find the Electric Field due to one charge. The notation in Coulomb's Law will be modified slightly - assuming that one charge is very large - and the other charge is a _______________that will have a negligible Electric Field due to its size. The large charge will be labeled, ___, and the small charge, ___, and the distance between them is r.

small, positive test charge Q, q

Newton's First Law (the law of inertia)

states that objects moving at a certain velocity will maintain that velocity unless acted on by an external force. Objects will only accelerate if acted on by an external force.

Charging by Conduction What cannot happen once the spheres move apart again? What results from this?

the charges cannot get back to where they came from, as air serves as an excellent insulator. This results in an equal distribution of charge.

describes what happens when a glass rod is rubbed by silk

the rod acquires a positive charge and the silk obtains a negative charge. The two rubber rods now repel each other, and a rubber rod is attracted to a glass rod.

Negative Charge If there is an isolated negative charge, it will create an Electric Field that points radially _______ it in all directions, since a positive test charge in the field will be _________ by this charge. The definition of the Electric Field shows that the strength of the field __________ as distance _____________ This can be seen by looking at the ______ of the field lines. Note that the Electric Field lines are closer together (more dense) when they are closer to the ______ that is generating the Field. This indicates the Electric Field is _________ near the charge

towards, attracted decreases, increases (F is indirectly proportional to E which is indirectly proportional to 1/r^2) density charge, greater

Electric Field of Multiple Charges There are no places where the electric field is _______ for two opposite charges .

zero