# What is the relationship of electric potential energy charge and voltage

### Electric potential, voltage (article) | Khan Academy

Figure 2: An electric charge q is moved from point A towards point B with an Figure 3, 4: When it is moved through a distance d, its potential energy at the point. Electric potential: It is the amount of electrical potential energy that a unitary point Potential = Potential energy / some quantity relating to that energy in context. .. Voltage is the amount of potential energy change for 1 coulomb of charge. When you move the book, you add or remove potential energy relative to where it started. For moving charges, you add or subtract electric potential energy.

### Electric potential (article) | Khan Academy

The size of this attraction decreases as the distance between them increases. When you point the North ends of two magnets towards each other or if you do the same with two South endsthe magnets will repel each other. The same effect happens when you put two electrons near each other or two protons. But once again, the magnitude of this repulsion gets smaller as the charges get further apart.

Unlike magnets, though, which always have a North and a South end, positive and negative charges can be separated and then brought back together. What is electric field? We know that if you have a single positively charged particle, a positively charged particle will be pushed away from it by the electric force.

## Electric potential

It also shows us how hard a push the electric force would give. Imagine we have a sphere that is negatively charged. The electric field would show that an imaginary positively charged particle is pulled towards the sphere by the electric force.

The electric field would always point towards the sphere, because we always use an imaginary positively charged particle to determine the electric field. As we move away from the sphere, the electric field gets weaker and weaker. Now say we have two flat plates with a space between them. The left one is positively charged and the right-hand one is negatively charged.

The electric field between the plates is going to be strong, because we not only have a negatively charged plate pulling our imaginary positive particle that we use to measure the electric field, remember to the right, we also have a positively charged plate pushing it to the right.

The plates are working together to make the imaginary particle move toward the right. What is electric potential energy? Electric potential energy is the energy that is needed to move a charge against an electric field. The work done by an E field as it act on a charge q to move it from point A to point B is defined as Electric Potential Difference between points A and B: Clearly, the potential function V can be assigned to each point in the space surrounding a charge distribution such as parallel plates.

The above formula provides a simple recipe to calculate work done in moving a charge between two points where we know the value of the potential difference. The above statements and the formula are valid regardless of the path through which the charge is moved.

A particular interest is the potential of a point-like charge Q. It can be found by simply performing the integration through a simple path such as a straight line from a point A whose distance from Q is r to infinity. Path is chosen along a radial line so that becomes simply Edr. Note that potential function is a scalar quantity as oppose to electric field being a vector quantity. Now, we can define the electric potential energy of a system of charges or charge distributions.

Suppose we compute the work done against electric forces in moving a charge q from infinity to a point a distance r from the charge Q. The work is given by: Note that if q is negative, its sigh should be used in the equation!

Therefore, a system consisting of a negative and a positive point-like charge has a negative potential energy. A negative potential energy means that work must be done against the electric field in moving the charges apart!

Now consider a more general case, which deals with the potential in the neighborhood of a number of charges as depicted in the picture below: When a Coulomb of charge or any given amount of charge possesses a relatively large quantity of potential energy at a given location, then that location is said to be a location of high electric potential.

And similarly, if a Coulomb of charge or any given amount of charge possesses a relatively small quantity of potential energy at a given location, then that location is said to be a location of low electric potential. As we begin to apply our concepts of potential energy and electric potential to circuits, we will begin to refer to the difference in electric potential between two points.

This part of Lesson 1 will be devoted to an understanding of electric potential difference and its application to the movement of charge in electric circuits. Consider the task of moving a positive test charge within a uniform electric field from location A to location B as shown in the diagram at the right. In moving the charge against the electric field from location A to location B, work will have to be done on the charge by an external force.

The work done on the charge changes its potential energy to a higher value; and the amount of work that is done is equal to the change in the potential energy. As a result of this change in potential energy, there is also a difference in electric potential between locations A and B. By definition, the electric potential difference is the difference in electric potential V between the final and the initial location when work is done upon a charge to change its potential energy.

In equation form, the electric potential difference is The standard metric unit on electric potential difference is the volt, abbreviated V and named in honor of Alessandro Volta. One Volt is equivalent to one Joule per Coulomb. If the electric potential difference between two locations is 1 volt, then one Coulomb of charge will gain 1 joule of potential energy when moved between those two locations. If the electric potential difference between two locations is 3 volts, then one coulomb of charge will gain 3 joules of potential energy when moved between those two locations.

And finally, if the electric potential difference between two locations is 12 volts, then one coulomb of charge will gain 12 joules of potential energy when moved between those two locations. Because electric potential difference is expressed in units of volts, it is sometimes referred to as the voltage.

## Electric potential, voltage

Electric Potential Difference and Simple Circuits Electric circuits, as we shall see, are all about the movement of charge between varying locations and the corresponding loss and gain of energy that accompanies this movement. In the previous part of Lesson 1, the concept of electric potential was applied to a simple battery-powered electric circuit. In that discussionit was explained that work must be done on a positive test charge to move it through the cells from the negative terminal to the positive terminal.

This work would increase the potential energy of the charge and thus increase its electric potential. As the positive test charge moves through the external circuit from the positive terminal to the negative terminal, it decreases its electric potential energy and thus is at low potential by the time it returns to the negative terminal.

If a 12 volt battery is used in the circuit, then every coulomb of charge is gaining 12 joules of potential energy as it moves through the battery. And similarly, every coulomb of charge loses 12 joules of electric potential energy as it passes through the external circuit.

• Electric potential energy
• Electric Potential Difference

The loss of this electric potential energy in the external circuit results in a gain in light energy, thermal energy and other forms of non-electrical energy.