19.1 Electric Potential Energy: Potential Difference

Explain point charges and express the equation for electric potential of a point charge.

Determine the electric potential of a point charge.

Tell us about the action of grounding an appliance.

Discuss the process of increasing the capacitance.

Determine the charge and voltage.

The effective capacitance can be calculated in series and parallel.

The energy is stored in aCapacitor.

We scratched the surface of electrical phenomena in Electric Charge and Electric Field.

Electricity's energy and voltage are familiar.
We know that a lot of electrical energy can be stored in batteries, that it can be transmitted across the country through power lines, and that it can jump from the clouds to explode trees.
In a similar way, ion cross cell membranes and transfer information.
We are aware of the voltages associated with electricity.
Power lines can be as high as hundreds of thousands of volts, batteries can be a few volts, and the outlets in your home can produce 120 volts.
The two things are not the same.
A motorcycle battery is small and not very successful in replacing a larger car battery, yet each has the same voltage.
We will begin to explore some of the many applications of electricity in this chapter.

The process is similar to an object being accelerated.

It's like the charge is going down an electrical hill where the potential energy is converted to energy.
We can develop a definition of electric potential energy if we explore the work done on a charge by the electric field.

A mass going down a hill is similar to a charge being accelerated by an electric field.

Potential energy can be converted to another form.
Since the force is conservative, we can write.

The work done on is independent of the path taken because of the conservative Coulomb force.

This is similar to the force of gravity in the absence of dissipative forces.
When a force is conservative, it is possible to define a potential energy associated with the force, and it is usually easier to deal with the potential energy than to calculate the work directly.

The letters PE are used to indicate electric potential energy, which has units of joules.

The change in potential energy is important since the work done by a conservative force is the negative of the change in potential energy.

There must be a minus sign in front of the positive sign.

PE can be found by taking one point as a reference and calculating the work needed to move a charge to another point.

There must be a minus sign in front of the positive sign.

PE can be found by taking one point as a reference and calculating the work needed to move a charge to another point.

Electric potential energy is quite similar to girtational potential energy.

Potential energy accounts for work done by a conservative force and gives added insight regarding energy and energy transformation without the necessity of dealing with the force directly.
It is more common to use the concept of voltage than it is to deal with the Coulomb force directly.

Calculating the work directly is difficult, since the direction and magnitude can be complex for multiple charges, for odd-shaped objects, and along arbitrary paths.

The electric potential energy per unit charge is what this is.

The dependence on cancels is proportional to PE.

The units of potential difference are called joules per coulomb.

The potential difference between points A and B is defined as the change in potential energy of a charge divided by the charge.

The units of potential difference are called joules per coulomb.

It is understood that the potential difference between two points is quoted whenever a voltage is quoted.

The potential difference between the two terminals is what makes every battery different.
The point at which you choose to be zero volts is arbitrary.
This is similar to the fact that there is an arbitrary zero on the floor of a lecture hall.

The second equation is the same as the first.

It is not the same as energy.

The energy per unit charge is called the voltage.
A motorcycle battery and a car battery both have the same potential difference between battery terminals, yet one can store more energy than the other.
The car battery can move more charge than the motorcycle battery.

You have a motorcycle battery that can move 5000 C of charge, and a car battery that can move 60,000 C of charge.

The 12.0 V battery's terminals have a 12.0 V potential difference.

The charge is moved by the potential difference to find the energy output.

They are not the same thing.

The batteries have the same voltages, but the energy supplied by them is different.
When headlights dim because of a low car battery, some of its energy is used internally and the terminal voltage drops.
The calculation of the energy supplied by the battery is the same as it was in this example.

The calculation of the energies in the previous example are not absolute values.

Since the battery loses energy, the change in potential energy is negative.
The batteries move negative charge--electrons in particular.
When the battery has moved from A to B, the potential energy has decreased because the charge is negative.

A battery has a negative terminal and a positive terminal.

The negative terminal has an excess of negative charge, which is repelled by it and attracted to the excess positive charge on the other terminal.
The positive terminal has more potential than the negative.
Positive and negative charges move inside the battery.

To find the number of electrons, we need the charge that moved in 1.00 s. A lamp uses a lot of energy.

The electrons are going from the negative terminal to the positive since the battery loses energy.

The total charge is divided by the charge per electron.

This number is large.

We don't usually observe individual electrons with so many being present in ordinary systems.
Electricity had been in use for a long time before it was determined that the moving charges were negative.
Positive charge moving in the opposite direction of negative charge can produce the same effects, making it difficult to determine which is moving or not.

In the previous example, the energy per electron was a tiny fraction of a joule.

The energy per particle is important on a submicroscopic scale.
Even a tiny fraction of a joule can be enough to cause harm to living tissue.
The particle can cause damage by direct collision or it can cause damage by creating x rays.
It is useful to have an energy unit.
An electron can be accelerated between two metal plates if it is in an old-model television tube.
The light in the television tube is converted to another form of light by the electron.
We can think of the joule as a coulomb-volt since energy is related to voltage.

An electron gun uses a potential difference between two metal plates to accelerate electrons.

The voltage between the plates and the energy of the electron are the same.
5000 eV electrons are produced by a 5000 V potential difference.

An electron is given an energy of 1 eV if it is accelerated through a potential difference of 1 V. The electron is given 50 eV.

An electron will have an energy of 100,000 eV (100 keV) if there is a 100,000 V difference.
200 eV of energy will be given to an ion with a double positive charge.
The electron volt is a simple and convenient energy unit because of the simple relationships between the two charged particles.

The eV is the most common energy unit.

In the chapters on modern physics, this will be noticeable.
There is a tendency to define a special energy unit for each major topic, because energy is so important to so many subjects.
There are calories for food energy, kilowatt-hours for electrical energy, and therms for natural gas energy.

5 eV of energy is required to break up certain organic molecules.

If a proton is accelerated from rest through a potential difference of 30 kV, it can break up as many as 6000 of these molecules.
Nuclear decay energies are on the order of 1 MeV (1,000,000 eV) per event and can cause significant biological damage.

If there is no net addition of work or heat transfer, the total energy of the system is conserved.

The mechanical energy is a constant for conservative forces.

An increase in the charged particle's ke is caused by a loss of PE.

The electric potential energy is called PE.

Considering energy can give us insights and help us solve problems.

The system we have is conservative.

If the electron is accelerated in a vacuum, all of the electrical potential energy is converted into energy.

The forces on small particles are very large compared to the forces on larger particles.

The large final speed confirms that the force is negligible here.

The large speed shows how easy it is to accelerate electrons with small voltages because of their small mass.
electron guns are usually used with higher voltages than 100 V. The electron speeds produced by those higher voltages must be taken into account.
In this example, a low voltage is considered.

We looked at the relationship between energy and voltage in the previous section.

The relationship between electric field and voltage will be explored in this section.
A uniform electric field can be produced by placing a potential difference across two metal plates labeled A and B.
The relationship between electric potential and electric field will be revealed when we examine this.
Any charge distribution can be described from a physicist's point of view.

The force in moving a charge from point A to point B is calculated to reveal the relationship between and.

In Electric Potential Energy: Potential Difference, it is noted that this is complex for arbitrary charge distributions.
A uniform electric field is an interesting special case.

There is a relationship between parallel conducting plates.

A minus sign is needed for a charge that is moved from plate A at higher potential to plate B at lower potential.

Since the path is parallel to the field, work is here.

The units for electric field are indicated by the above equation.

The distance from A to B is determined by the distance between the plates.

The air is a conductor because the field creates enough ion in the air to make it a conductor.

The discharge or spark can reduce the field.

The maximum electric field is between the plates and the distance between them.

The maximum voltage can be calculated using the equation.

It limits the voltages that can be found between conductors.

If there are points on the surface, a smaller voltage will cause a spark.
Humid air breaks down at a lower field strength, meaning that a smaller voltage will make a spark jump through it.
On dry days, the largest voltages can be built up.

A spark chamber can be used to trace high-energy particles.

Ionization created by the particles as they pass through the gas allows a spark to jump.
The sparks follow electric field lines between the plates.

The potential difference between adjacent plates is not high enough to cause sparks.

The electric field strength can be calculated from the expression.

The force on a charge is found using the electric field strength.
The electric field is only one direction, so we can write this equation in terms of magnitudes.

The potential difference must be 25.0 kV since the electron is a single charge.

The units are newtons.

The force on the charge is the same regardless of where the charge is.
The electric field between the plates is uniform.

Regardless of whether the electric field is uniform, it points in the direction of decreasing potential because the force on a positive charge is in the direction of lower potential.

The greater the electric field, the faster the decrease.

The minus sign tells us that the potential is decreasing.

The electric potential is said to be determined by the electric field.

The minus sign tells us that the potential is decreasing.

The electric potential is said to be determined by the electric field.

The electric field can be determined with differential calculus and infinitesimals.

electrons are one of the fundamental building blocks of matter.

The external electric fields created by spherical charge distributions are exactly like a point charge.
We need to consider the case of the electric potential due to a point charge.

The potential is zero.

The electric potential has no direction, whereas the electric field has a direction.

The individual voltages are added as numbers to find the voltage due to a combination of point charges.
Taking magnitude and direction into account, you must add individual fields as vectors to find the total electric field.

There are charges in the range of microcoulomb to nanocoulomb.

In Electric Charge and Electric Field, we talked about how a metal sphere can spread out and produce a field similar to a point charge located at its center.

The equation can be used to find the voltage.

Since the potential is lower than at larger distances, a positive charge would be attracted from a larger distance.

A negative charge would be repelled.

A Van de Graaff generator with a metal sphere that is 25.0 cm in diameter produces a voltage of 100 kV near its surface.

The Van de Graaff generator has a charged sphere and ground.

As a reference, Earth's potential is zero.
The charged conducting sphere has the same potential as an equal point charge at its center.