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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

Why does the lines of force not touch each other 🇲🇲
Gbemisola Reply
what is unit
Rayyanu Reply
Please canu get more questions on electric field and electric flux please
Gbemisola
is electric field directly proportional to the squared of a distance
Benjamin Reply
No electric field is inversely proportional to the squared distance between the charges
Gbemisola
lets treat linear expansivity please
Ujah Reply
The bullet 2.00cm long is fired at 420/s and passes straight through a 10.0 cm thick board existing at 280 m/s.What is the average acceleration of the bullet through the board?
FAUSTINA
an unstretched spring is 12cm long .A load of 5N stretched it to 15cm .how long will it be under a load of 15N?
Morapeli
hi
Africa
hi
Benjamin
Benjamin how are u are u a freshman in the university
Africa
like 100 level
Africa
yes sir
Benjamin
l need a physics tutor
Benjamin
I think the best tutor is God and organic tutor in YouTube that guy is good
Africa
me too 100level
Africa
wow nice
Benjamin
from Nigeria and u
Africa
I am from Nigeria and u wow nice that something I use to always say
Africa
am from Ghana
Benjamin
ok
Africa
studying what
Africa
Compare the electric flux through the surface of a cube of side length a that has a charge q at its center to the flux through a spherical surface of radius a with a charge q at its center.
Shari Reply
please I want to know how to solve increase in length
Ujah
Why a charged capacitor has potential difference but not emf
Gideon Reply
what is the dimension symbol of temperature?
Keren Reply
what is the dimension symbol of temperature?
Keren
what's the meaning of enthalpy in terms of latent heat, internal energy, phase change
Anthony Reply
Enthalpy is the degree ofdisorderlinessof a substance
Gbemisola
how to convert Kelvin to centigrade
Sangeetha Reply
what is the s, p, d, f in this table
Sangeetha
s, p, d, f in this table
Sangeetha
what kind of table this
Vengata
Periodic table
Gbemisola
what are waves
KENNETH Reply
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities
Abdikadir
Discuss how would orient a planar surface of area A in a uniform electric field of magnitude E0 to obtain (a) the maximum flux and (b) the minimum flux through the area.
KARAN Reply
I'm just doing the first 3 with this message. but thankyou for the time your obviously intending to support us with. viva la accumulation
Marcel
Find the net capacitance of the combination of series and parallel capacitors shown belo
jean Reply
what is ohm?
Sharafat Reply
calculate ideal gas pressure of 0.300mol,v=2L T=40°c
Viola Reply
what is principle of superposition
Jyoti Reply
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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