what is the relation between potential difference and electric potential energy
Answers
Electric potential is potential energy per unit charge. An electron volt is the energy given to a fundamental charge accelerated through a potential difference of 1 V. In equation form, Mechanical energy is the sum of the kinetic energy and potential energy of a system, that is, This sum is a constant.
Answer:
When a free positive charge q is accelerated by an electric field, such as shown in [link], it is given kinetic energy. 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. Let us explore the work done on a charge q by the electric field in this process, so that we may develop a definition of electric potential energy.
A charge accelerated by an electric field is analogous to a mass going down a hill. In both cases potential energy is converted to another form. Work is done by a force, but since this force is conservative, we can write W=-\Delta \text{PE}.
A charge plus q moves from a positive to a negative sheet of charge. The change in the electric potential energy equals the change in kinetic energy. This is similar to the change from gravitational potential energy to kinetic energy when an object of mass m rolls downhill.
The electrostatic or Coulomb force is conservative, which means that the work done on q is independent of the path taken. 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.
We use the letters PE to denote electric potential energy, which has units of joules (J). The change in potential energy, \text{Δ}\text{PE}, is crucial, since the work done by a conservative force is the negative of the change in potential energy; that is, W=\text{-Δ}\text{PE}. For example, work W done to accelerate a positive charge from rest is positive and results from a loss in PE, or a negative \text{Δ}\text{PE}. There must be a minus sign in front of \text{Δ}\text{PE} to make W positive. PE can be found at any point by taking one point as a reference and calculating the work needed to move a charge to the other point.
Potential Energy
W=\text{-ΔPE}. For example, work W done to accelerate a positive charge from rest is positive and results from a loss in PE, or a negative \text{ΔPE}. There must be a minus sign in front of \text{ΔPE} to make W positive. PE can be found at any point by taking one point as a reference and calculating the work needed to move a charge to the other point.
Gravitational potential energy and electric potential energy are quite analogous. 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 much more common, for example, to use the concept of voltage (related to electric potential energy) than to deal with the Coulomb force directly.
Potential Difference
The potential difference between points A and B, {V}_{B}-{V}_{A}, is defined to be the change in potential energy of a charge q moved from A to B, divided by the charge. 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 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.
In summary, the relationship between potential difference (or voltage) and electrical potential energy is
Potential Difference and Electrical Potential Energy
The relationship between potential difference (or voltage) and electrical potential energy is given by