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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

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. Calculating the work directly may be difficult, since W = F · d and the direction and magnitude of F can be complex for multiple charges, for odd-shaped objects, and along arbitrary paths. But we do know that because F = q E , the work, and hence Δ U , is proportional to the test charge q . 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:

Electric potential

The electric potential energy per unit charge is

V = U q .

Since U is proportional to q , the dependence on q cancels. Thus, V does not depend on q . The change in potential energy Δ U is crucial, so we are concerned with the difference in potential or potential difference Δ V between two points, where

Δ V = V B V A = Δ U q .

Electric potential difference

The electric 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 .

1 V = 1 J/C

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.

Potential difference and electrical potential energy

The relationship between potential difference (or voltage) and electrical potential energy is given by

Δ V = Δ U q or Δ U = q Δ V .

Voltage is not the same as energy. Voltage is the energy per unit charge. Thus, a motorcycle battery and a car battery can both have the same voltage (more precisely, the same potential difference between battery terminals), yet one stores much more energy than the other because Δ U = q Δ V . The car battery can move more charge than the motorcycle battery, although both are 12-V batteries.

Questions & Answers

if 6.0×10^13 electrons are placed on a metal sphere of charge 9.0micro Coulombs, what is the net charge on the sphere
Rita Reply
18.51micro Coulombs
Is it possible to find the magnetic field of a circular loop at the centre by using ampere's law?
Rb Reply
Is it possible to find the magnetic field of a circular loop at it's centre?
Rb Reply
The density of a gas of relative molecular mass 28 at a certain temperature is 0.90 K kgmcube.The root mean square speed of the gas molecules at that temperature is 602ms.Assuming that the rate of diffusion of a gas in inversely proportional to the square root of its density,calculate the density of
Gifty Reply
A hot liquid at 80degree Celsius is added to 600g of the same liquid originally at 10 degree Celsius. when the mixture reaches 30 degree Celsius, what will be the total mass of the liquid?
what is electrostatics
Yakub Reply
Study of charges which are at rest
Explain Kinematics
Glory Reply
Two equal positive charges are repelling each other. The force on the charge on the left is 3.0 Newtons. Using your notes on Coulomb's law, and the forces acting on each of the charges, what is the force on the charge on the right?
Nya Reply
Using the same two positive charges, the left positive charge is increased so that its charge is 4 times LARGER than the charge on the right. Using your notes on Coulomb's law and changes to the charge, once the charge is increased, what is the new force of repulsion between the two positive charges?
A mass 'm' is attached to a spring oscillates every 5 second. If the mass is increased by a 5 kg, the period increases by 3 second. Find its initial mass 'm'
Md Reply
a hot water tank containing 50,000g of water is heated by an electric immersion heater rated at 3kilowatt,240volt, calculate the current
Samuel Reply
what is charge
Aamir Reply
product of current and time
Why always amber gain electrons and fur loose electrons? Why the opposite doesn't happen?
Mohammed Reply
A closely wound search coil has an area of 4cm^2,1000 turns and a resistance of 40ohm. It is connected to a ballistic galvanometer whose resistance is 24 ohm. When coil is rotated from a position parallel to uniform magnetic field to one perpendicular to field,the galvanometer indicates a charge
Palak Reply
Using Kirchhoff's rules, when choosing your loops, can you choose a loop that doesn't have a voltage?
Michael Reply
how was the check your understand 12.7 solved?
Bysteria Reply
LOAK Reply
he's the father of 3 newton law
he is Chris Issaac's father :)
Practice Key Terms 4

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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