# 7.2 Electric potential and potential difference

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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 $W=\stackrel{\to }{\text{F}}·\stackrel{\to }{\text{d}}$ and the direction and magnitude of $\stackrel{\to }{\text{F}}$ can be complex for multiple charges, for odd-shaped objects, and along arbitrary paths. But we do know that because $\stackrel{\to }{\text{F}}=q\stackrel{\to }{\text{E}}$ , the work, and hence $\text{Δ}U,$ 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

$V=\frac{U}{q}.$

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

$\text{Δ}V={V}_{B}-{V}_{A}=\frac{\text{Δ}U}{q}.$

## 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 .

$1\phantom{\rule{0.2em}{0ex}}\text{V}=1\phantom{\rule{0.2em}{0ex}}\text{J/C}$

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

$\text{Δ}V=\frac{\text{Δ}U}{q}\phantom{\rule{0.2em}{0ex}}\text{or}\phantom{\rule{0.2em}{0ex}}\text{Δ}U=q\text{Δ}V.$

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 $\text{Δ}U=q\text{Δ}V.$ The car battery can move more charge than the motorcycle battery, although both are 12-V batteries.

define electric image.obtain expression for electric intensity at any point on earthed conducting infinite plane due to a point charge Q placed at a distance D from it.
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pls. explain the lack of symmetry in the field of the parallel capacitor
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does your app come with video lessons?
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equivalent capacitance is 9nf nd pd across each capacitor is 500v
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because you can't fit the boundary conditions.
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the study of heat an other form of energy.
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it is a low studied the force between 2 charges F=q.q`\r.r
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Total number of field lines crossing the surface area
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Basically flux in general is amount of anything...In Electricity and Magnetism it is the total no..of electric field lines or Magnetic field lines passing normally through the suface
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process whereby the degree of hotness of a body (or medium) changes
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Q=mcΔT
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where The letter "Q" is the heat transferred in an exchange in calories, "m" is the mass of the substance being heated in grams, "c" is its specific heat capacity and the static value, and "ΔT" is its change in temperature in degrees Celsius to reflect the change in temperature.
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what was the temperature of the soft drink when it was removed ?
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15 degree Celsius
Celine
15 degree
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ok I think is just conversion
Salim
15 degree Celsius to Fahrenheit
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0 degree Celsius = 32 Fahrenheit
Salim
15 degree Celsius = (15×1.8)+32 =59 Fahrenheit
Salim
I dont understand
Celine
the question said you should convert 15 degree Celsius to Fahrenheit
Salim
To convert temperatures in degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.
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what is d final ans for Fahrenheit and Celsius
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it said what is temperature change in Fahrenheit and Celsius
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the 15 is already in Celsius
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So the final answer for Fahrenheit is 59
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what is d final ans for Fahrenheit and Celsius
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what are the effects of placing a dielectric between the plates of a capacitor
increase the capacitance.
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besides increasing the capacitance, is there any?
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mechanical stiffness and small size
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so as to increase the capacitance of a capacitor
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