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  • Define electric potential and electric potential energy.
  • Describe the relationship between potential difference and electrical potential energy.
  • Explain electron volt and its usage in submicroscopic process.
  • Determine electric potential energy given potential difference and amount of charge.

When a free positive charge q size 12{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 size 12{q} {} by the electric field in this process, so that we may develop a definition of electric potential energy.

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.
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 = –Δ PE size 12{W= - ?"PE"} {} .

The electrostatic or Coulomb force is conservative, which means that the work done on q size 12{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, Δ PE size 12{?"PE"} {} , is crucial, since the work done by a conservative force is the negative of the change in potential energy; that is, W = –Δ PE size 12{W"=-"?"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 Δ PE size 12{?"PE"} {} . There must be a minus sign in front of Δ PE size 12{?"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 = –ΔPE size 12{W" = -"?"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 ΔPE . There must be a minus sign in front of 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.

Calculating the work directly is generally difficult, since W = Fd cos θ and the direction and magnitude of F size 12{F} {} can be complex for multiple charges, for odd-shaped objects, and along arbitrary paths. But we do know that, since F = qE size 12{F= ital "qE"} {} , the work, and hence ΔPE , is proportional to the test charge q. size 12{q} {} To have a physical quantity that is independent of test charge, we define electric potential     V size 12{V} {} (or simply potential, since electric is understood) to be the potential energy per unit charge:

Questions & Answers

does the force in a system result in the energy transfer?
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Practice Key Terms 4

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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