Electric Potential
Electric potential refers to the amount of electric potential energy per unit charge at a specific point within an electric field. It is defined as the work required to move a charge against the electric field from a reference point to the specified location. This concept is crucial in understanding how electric charges interact and is closely related to voltage, which is the difference in electric potential between two points. Electric potential is measured in volts, and its calculation involves parameters like the electrostatic constant, the charges involved, and the distance separating them.
In practical applications, electric potential plays a significant role in electrical circuits, where it influences the flow of current—defined as the movement of electric charges over time. The relationship between voltage, current, and resistance is encapsulated in Ohm's Law. Energy dissipation in these circuits, often through components like resistors, transforms electric potential energy into other forms, such as heat and light. In medical devices such as pacemakers and defibrillators, capacitors leverage electric potential to provide necessary shocks that can restore normal heart rhythms, emphasizing the critical role of electric potential in both everyday technology and essential medical applications.
Electric Potential
FIELDS OF STUDY: Classical Mechanics; Electronics; Electromagnetism
ABSTRACT: Electric charge is a property of atomic particles. As charged particles move, they generate electric currents. By properly storing these currents, electric potential energy can be stored in devices such as batteries and capacitors later to be released to serve a purpose. The relations that affect electric charges are described in this article.
Principal Terms
- conductor: a material that has a low resistance to electric charges, allowing them to move through it easily.
- coulomb: the basic unit of charge in the International System of Units (SI).
- current: the movement of electric charges from one place to another.
- insulator: a material that has a high resistance to electric charges, preventing them from moving through it easily.
- joule: the SI derived unit of energy, equal to one kilogram–square meter per second squared (kg·m2/s2).
- voltage: the work done per unit charge when moving a charge against an electric field.
- work: the use of energy to move an object over a distance by means of the application of force.
Electric Potential Energy
As a rainstorm gathers in the atmosphere, a dance and motion of charges begins to take place. As the storm gets stronger, it creates faster updraft winds. These updraft winds pick up water droplets and raise them high in the clouds. At these high altitudes, the temperatures are extremely low, and the water freezes to form ice. As more water droplets are carried up by the updrafts, they start to collide with some of these ice particles. During these collisions, electrons are taken away from the ice. The electrons remain lower in the cloud. Eventually enough electrons build up to produce a lightning strike. These electrons travel through the air, which is typically an insulator. However, when enough electrons build up, they can break through the insulator, turning it into a conductor. During the buildup of charges at the base of the cloud, an interesting effect takes place. Electrons at the base of the cloud start attracting positive particles on the ground. This interaction builds up the electric potential energy in the system.
The electric potential energy between the clouds and ground is due to the configuration of electrons and protons, which are treated as point charges, or idealized dimensionless charged particles. Electric potential is defined as electric potential energy per unit charge, or the electric potential energy of a single point charge at any point in an electric field. It is equal to the amount of work that would be necessary to carry the charge to that point when moving against the electric field.
Calculating Electric Potential
The electric potential energy (Ue) between two point charges is a function of the electrostatic constant (k), also called Coloumb’s constant; the values of the individual point charges (Q1 and Q2); and the distance between the two charges (d), measured in meters (m):
The electrostatic constant is measured in newton–square meters per coulomb squared (N·m2/C2) and is equal to 8.99 × 109 N·m2/C2. Any physical energy is measured in the International System of Units (SI) unit of energy, the joule (J). The charges are measured in SI units of coulombs (C). In a system of more than two charges, the total electric potential energy is the sum of the electric potential energy of each pair of charges.
The equation to calculate the electric potential (V) of one of the two point charges is similar to the equation for electric potential energy. It, too, is a function of the charge amount (Q), the electrostatic constant (k), and the distance to the charge (d):
Electric potential is measured in volts (V), an SI derived unit named in honor of the Italian physicist Alessandro Volta (1745–1827). This equation calculates the electric potential generated by one point charge. Electric potential is simply electric potential energy per unit charge. Therefore, it can also be defined in as electric potential energy (Ue) per unit of charge (Q):
When dealing with accumulations of charges, a different technique must be used. Imagine two horizontal charged plates separated by a certain distance. The charges in these plates create a uniform electric field between them. Finding the electric potential using the equation above for point charges would take a great deal of time, because the number of individual charges can be very large. Instead, we turn to the electric field. The electric potential at any point in a uniform electric field with a strength of E newtons per coulomb (N/C), generated by two plates separated by a given distance (d), is
V = Ed
On its own, the electric potential of a single point charge is not a meaningful quantity. However, the difference in electric potential between two points (ΔV) is a very useful quantity. This quantity, called potential difference, is more commonly known as voltage. It is the amount of work, measured in units of electric potential (i.e., volts), that would be necessary to move a charge between the two points in the opposite direction of the electric field.
Electric potential due to a uniform electric field generated by parallel plates is something that affects the world daily. Electronic devices are made with a collection of smaller circuit parts. One of these parts is a capacitor, or a pair of parallel conductive plates that store electric potential energy between them. The electric potential energy (Ue) stored by a single capacitor in a circuit is a function of the capacitance (C) of the capacitor, measured in farads (F), and the potential difference or voltage (ΔV) between the two plates:
Imagine a capacitor of 6 microfarads (µF) is placed in a circuit and achieves a potential difference of 5 V. The electric potential energy stored in that capacitor can be calculated thus:
Currents and Circuits
Although charged particles run through them, circuits do not work using individual charges. They run on a current, a series of charges moving as a function of time. In a circuit there is a voltage that is supplied by a power source, for example a battery. The voltage supplied by the battery depends on the amount of resistance and the current allowed by the resistance. This relation is given by Ohm’s law, which states that the voltage (ΔV) in a circuit is a function of current (I), measured in amperes (A), and the resistance (R), measured in ohms (Ω):
ΔV = IR
Solving this equation for current shows that it is equal to voltage divided by resistance:
Resistors work by slowing down or stopping the electrons from moving through a circuit. That is, the more resistance, the less current will flow. A good example of how resistors dissipate potential energy is an incandescent lightbulb. They are made out of a filament that has very high resistance properties. As electrons flow through the filament, they are slowed down or stopped by the filament. The electric potential energy the electrons carry cannot just disappear. It changes form into thermal energy, which is emitted as light and heat.
The energy in an electrical circuit is directly related to the work done by the charges in the circuit, the current. Work is the energy used by a force to move an object over a distance. A simple circuit can be made using a battery, which provides the voltage, and one resistor. The work done by the system (W) is a function of the voltage supplied by the battery (ΔV), the current in the circuit (I), and the amount of time the current stays flowing (t):
W = ΔVIt
In this same circuit energy is being dissipated by the resistor. There is a limited amount of energy in the battery. Eventually the battery will stop working. The resistor has slowly used up all the energy. The power (P) at which the resistor works and dissipates energy is a function of the voltage (ΔV), the current (I), the resistance (R):
All of these versions of the power equation can be used to calculate the power dissipated by the resistor.
Sample Problem
A 1.0 nanocoulomb (nC) point charge is located at a point 2 m away from another charge, Q. The electric potential at this location is 4.5 V. If the 1.0 nC charge is moved to 4 m from charge Q, what is its new electric potential?
Answer:
In order to calculate the electric potential (V2) at a distance (d2) of 4 m from charge Q, begin by defining the electric potential at the original point (V1), at a distance (d1) of 2 m from charge Q. This value was already given as 4.5 V.
Note that the second point is twice as far from charge Q as the original point:
d2 = 2d1
Now, to calculate V2, use the same equation as for V1:
Replace d2 with 2d1:
This new equation can be rewritten as
Solve:
At twice the distance from charge Q, the electric potential is 2.25 V, one-half of the electric potential at the original point.
Charging Circuits
Hearts beat because of an electrical discharge that makes the heart contract, thereby pushing blood into the arteries. Unfortunately, like most circuits, the circuit that makes the heart beat sometimes fails. It can fail in many ways. Sometimes it gets out of control. Sometimes it stops working altogether. In each of these cases, scientists have developed a device that can help the heart beat normally again. Pacemakers and defibrillators make use of capacitors. They supply a charge or current that gets stored in a capacitor. When the capacitor stores as much charge as it can, no more charge flows through this circuit. As soon as the pacemaker detects that the heart has stopped beating or is beating at different pattern, it releases the charge. At this point it begins to charge the capacitor again. In many ways these capacitors work like batteries that supply the shock needed to keep the heart beating.
Bibliography
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