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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

What mass of steam of 100 degree celcius must be mixed with 150g of ice at 0 degree celcius, in a thermally insulated container, to produce liquid water at 50 degree celcius
Emmanuel Reply
sorry I dont know
thank you
What is the pressure?
To convert 0°C ice to 0°c water. Q=M*s=150g*334J/g=50100 J.......... Now 0° water to 50° water... Q=M*s*dt=150g*4.186J/g*50= 31395 J....... Which adds upto 81495 J..... This is amount of heat the steam has to carry. 81495= M *s=M*2230J/g..therefore.....M=36.54g of steam
This is at 1 atm
If there is change in pressure u can refer to the steam table ....
instrument for measuring highest temperature of a body is?
brian Reply
how does beryllium decay occur
Sandy Reply
state the first law of thermodynamics
Kansiime Reply
Its state that "energy can neither be created nor destroyed but can be transformed from one form to another. "
what about the other laws can anyone here help with it please
The second law of thermodynamics states that the entropy of any isolated system always increases. The third law of thermodynamics states that the entropy of a system approaches a constant value as the temperature approaches absolute zero.
The first law is very simple to understand by its equation. The law states that "total energy in thermodynamic sytem is always constant" i.e d¶=du+dw where d¶=total heat du=internal energy dw=workdone... PLEASE REFER TO THE BOOKS FOR MORE UNDERSTANDING OF THE CONCEPT.
what is distance.?
Ali Reply
what is physics?
Physics is a scientific phenomenon that deals with matter and its properties
physics is the study of nature and science
Physics is branch of science which deals with the study of matters in relation with energy.
What is differential form of Gauss's law?
Rohit Reply
help me out on this question the permittivity of diamond is 1.46*10^-10.( a)what is the dielectric of diamond (b) what its susceptibility
a body is projected vertically upward of 30kmp/h how long will it take to reach a point 0.5km bellow e point of projection
Abu Reply
i have to say. who cares. lol. why know that t all
is this just a chat app about the openstax book?
Lord Reply
kya ye b.sc ka hai agar haa to konsa part
MPL Reply
what is charge quantization
Mayowa Reply
it means that the total charge of a body will always be the integral multiples of basic unit charge ( e ) q = ne n : no of electrons or protons e : basic unit charge 1e = 1.602×10^-19
is the time quantized ? how ?
What do you meanby the statement,"Is the time quantized"
Can you give an explanation.
there are some comment on the time -quantized..
time is integer of the planck time, discrete..
planck time is travel in planck lenght of light..
it's says that charges does not occur in continuous form rather they are integral multiple of the elementary charge of an electron.
it is just like bohr's theory. Which was angular momentum of electron is intral multiple of h/2π
determine absolute zero
The properties of a system during a reversible constant pressure non-flow process at P= 1.6bar, changes from constant volume of 0.3m³/kg at 20°C to a volume of 0.55m³/kg at 260°C. its constant pressure process is 3.205KJ/kg°C Determine: 1. Heat added, Work done, Change in Internal Energy and Change in Enthalpy
Opeyemi Reply
U can easily calculate work done by 2.303log(v2/v1)
Amount of heat added through q=ncv^delta t
Change in internal energy through q=Q-w
please how do dey get 5/9 in the conversion of Celsius and Fahrenheit
Gwam Reply
what is copper loss
timileyin Reply
this is the energy dissipated(usually in the form of heat energy) in conductors such as wires and coils due to the flow of current against the resistance of the material used in winding the coil.
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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