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# Electric Potential And Electric Potential Energy Pdf

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*Recall that earlier we defined electric field to be a quantity independent of the test charge in a given system, which would nonetheless allow us to calculate the force that would result on an arbitrary test charge.*

- 3.2 Electric Potential and Potential Difference
- Electric potential
- The Electric Field and the Electric Potential
- 3.2 Electric Potential and Potential Difference

*Electric potential , the amount of work needed to move a unit charge from a reference point to a specific point against an electric field. Typically, the reference point is Earth , although any point beyond the influence of the electric field charge can be used. The diagram shows the forces acting on a positive charge q located between two plates, A and B, of an electric field E.*

Recall that earlier we defined electric field to be a quantity independent of the test charge in a given system, which would nonetheless allow us to calculate the force that would result on an arbitrary test charge. The default assumption in the absence of other information is that the test charge is positive. We briefly defined a field for gravity, but gravity is always attractive, whereas the electric force can be either attractive or repulsive.

Therefore, although potential energy is perfectly adequate in a gravitational system, it is convenient to define a quantity that allows us to calculate the work on a charge independent of the magnitude of the charge.

To have a physical quantity that is independent of test charge, we define electric potential V or simply potential, since electric is understood to be the potential energy per unit charge:.

Since U is proportional to q , the dependence on q cancels. Thus, V does not depend on q. Units of potential difference are joules per coulomb, given the name volt V after Alessandro Volta. The familiar term voltage is the common name for electric potential difference.

Keep in mind that whenever a voltage is quoted, it is understood to be the potential difference between two points. For example, every battery has two terminals, and its voltage is the potential difference between them. More fundamentally, the point you choose to be zero volts is arbitrary.

This is analogous to the fact that gravitational potential energy has an arbitrary zero, such as sea level or perhaps a lecture hall floor. It is worthwhile to emphasize the distinction between potential difference and electrical potential energy. The relationship between potential difference or voltage and electrical potential energy is given by. Voltage is not the same as energy. Voltage is the energy per unit charge. The car battery can move more charge than the motorcycle battery, although both are V batteries.

Note that the energies calculated in the previous example are absolute values. The change in potential energy for the battery is negative, since it loses energy. These batteries, like many electrical systems, actually move negative charge—electrons in particular.

The batteries repel electrons from their negative terminals A through whatever circuitry is involved and attract them to their positive terminals B , as shown in Figure 7. The number of electrons n e n e is the total charge divided by the charge per electron. That is,. The energy per electron is very small in macroscopic situations like that in the previous example—a tiny fraction of a joule. But on a submicroscopic scale, such energy per particle electron, proton, or ion can be of great importance.

For example, even a tiny fraction of a joule can be great enough for these particles to destroy organic molecules and harm living tissue. The particle may do its damage by direct collision, or it may create harmful X-rays, which can also inflict damage. It is useful to have an energy unit related to submicroscopic effects.

Figure 7. An electron is accelerated between two charged metal plates, as it might be in an old-model television tube or oscilloscope. The electron gains kinetic energy that is later converted into another form—light in the television tube, for example. On the submicroscopic scale, it is more convenient to define an energy unit called the electron-volt eV , which is the energy given to a fundamental charge accelerated through a potential difference of 1 V.

In equation form,. An electron accelerated through a potential difference of 1 V is given an energy of 1 eV.

It follows that an electron accelerated through 50 V gains 50 eV. A potential difference of , V kV gives an electron an energy of , eV keV , and so on. Similarly, an ion with a double positive charge accelerated through V gains eV of energy. These simple relationships between accelerating voltage and particle charges make the electron-volt a simple and convenient energy unit in such circumstances.

The electron-volt is commonly employed in submicroscopic processes—chemical valence energies and molecular and nuclear binding energies are among the quantities often expressed in electron-volts. For example, about 5 eV of energy is required to break up certain organic molecules. Nuclear decay energies are on the order of 1 MeV 1,, eV per event and can thus produce significant biological damage. The total energy of a system is conserved if there is no net addition or subtraction due to work or heat transfer.

For conservative forces, such as the electrostatic force, conservation of energy states that mechanical energy is a constant. A loss of U for a charged particle becomes an increase in its K. Conservation of energy is stated in equation form as.

As we have found many times before, considering energy can give us insights and facilitate problem solving. Entering values for q , V , and m gives. How would this example change with a positron? A positron is identical to an electron except the charge is positive. So far, we have explored the relationship between voltage and energy. Now we want to explore the relationship between voltage and electric field. Recall that our general formula for the potential energy of a test charge q at point P relative to reference point R is.

From our previous discussion of the potential energy of a charge in an electric field, the result is independent of the path chosen, and hence we can pick the integral path that is most convenient. Consider the special case of a positive point charge q at the origin. When we evaluate the integral. This will be explored further in the next section. Examining this situation will tell us what voltage is needed to produce a certain electric field strength. It will also reveal a more fundamental relationship between electric potential and electric field.

Note that the magnitude of the electric field, a scalar quantity, is represented by E. But, as noted earlier, arbitrary charge distributions require calculus. We therefore look at a uniform electric field as an interesting special case. The work done by the electric field in Figure 7. The potential difference between points A and B is. The charge cancels, so we obtain for the voltage between points A and B. Note that this equation implies that the units for electric field are volts per meter.

We already know the units for electric field are newtons per coulomb; thus, the following relation among units is valid:.

Furthermore, we may extend this to the integral form. Substituting Equation 7. As a demonstration, from this we may calculate the potential difference between two points A and B equidistant from a point charge q at the origin, as shown in Figure 7. This result, that there is no difference in potential along a constant radius from a point charge, will come in handy when we map potentials. Entering the given values for E and d gives. The answer is quoted to only two digits, since the maximum field strength is approximate.

Adding the two parts together, we get V. From the examples, how does the energy of a lightning strike vary with the height of the clouds from the ground? Consider the cloud-ground system to be two parallel plates.

Before presenting problems involving electrostatics, we suggest a problem-solving strategy to follow for this topic. As an Amazon Associate we earn from qualifying purchases. Want to cite, share, or modify this book? This book is Creative Commons Attribution License 4. Skip to Content. University Physics Volume 2 7.

My highlights. Table of contents. Chapter Review. Electricity and Magnetism. Answer Key. By the end of this section, you will be able to: Define electric potential, voltage, and potential difference Define the electron-volt Calculate electric potential and potential difference from potential energy and electric field Describe systems in which the electron-volt is a useful unit Apply conservation of energy to electric systems.

Calculating Energy You have a How much energy does each deliver? Assume that the numerical value of each charge is accurate to three significant figures. Strategy To say we have a When such a battery moves charge, it puts the charge through a potential difference of To find the energy output, we multiply the charge moved by the potential difference.

How much energy does a 1. Appropriate combinations of chemicals in the battery separate charges so that 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.

In terms of potential, the positive terminal is at a higher voltage than the negative terminal. Inside the battery, both positive and negative charges move. When a

The electric potential also called the electric field potential , potential drop, the electrostatic potential is the amount of work energy needed to move a unit of electric charge a Coulomb from a reference point to the specific point in an electric field with negligible acceleration of the test charge to avoid producing kinetic energy or radiation by test charge. Typically, the reference point is the Earth or a point at infinity , although any point can be used. More precisely it is the energy per unit charge for a small test charge that does not disturb significantly the field and the charge distribution producing the field under consideration. By dividing out the charge on the particle a quotient is obtained that is a property of the electric field itself. In short, electric potential is the electric potential energy per unit charge.

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Recall that earlier we defined electric field to be a quantity independent of the test charge in a given system, which would nonetheless allow us to calculate the force that would result on an arbitrary test charge. The default assumption in the absence of other information is that the test charge is positive. We briefly defined a field for gravity, but gravity is always attractive, whereas the electric force can be either attractive or repulsive. Therefore, although potential energy is perfectly adequate in a gravitational system, it is convenient to define a quantity that allows us to calculate the work on a charge independent of the magnitude of the charge.

The process is analogous to an object being accelerated by a gravitational field. It is as if the charge is going down an electrical hill where its electric potential energy is converted to kinetic energy. This is exactly analogous to the gravitational force in the absence of dissipative forces such as friction. 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 because it depends only on position than to calculate the work directly.

The electric potential tells you how much potential energy a single point charge at a given location will have. The electric potential at a point is equal to the electric potential energy measured in joules of any charged particle at that location divided by the charge measured in coulombs of the particle. Another way of saying this is that because PE is dependent on q, the q in the above equation will cancel out, so V is not dependent on q.

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