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Section summary

  • The voltage between points A and B is
    V AB = Ed E = V AB d (uniform E - field only),
    where d size 12{d} {} is the distance from A to B, or the distance between the plates.
  • In equation form, the general relationship between voltage and electric field is
    E = Δ V Δ s , size 12{E= - { {ΔV} over {Δs} } } {}
    where Δ s size 12{Δs} {} is the distance over which the change in potential, Δ V size 12{Δ`V} {} , takes place. The minus sign tells us that E size 12{E} {} points in the direction of decreasing potential.) The electric field is said to be the gradient (as in grade or slope) of the electric potential.

Conceptual questions

Discuss how potential difference and electric field strength are related. Give an example.

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What is the strength of the electric field in a region where the electric potential is constant?

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Will a negative charge, initially at rest, move toward higher or lower potential? Explain why.

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Problems&Exercises

Show that units of V/m and N/C for electric field strength are indeed equivalent.

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What is the strength of the electric field between two parallel conducting plates separated by 1.00 cm and having a potential difference (voltage) between them of 1 . 50 × 10 4 V size 12{1 "." "50" times "10" rSup { size 8{4} } `V} {} ?

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The electric field strength between two parallel conducting plates separated by 4.00 cm is 7 . 50 × 10 4 V/m size 12{7 "." "50"´"10" rSup { size 8{4} } " V/m"} {} . (a) What is the potential difference between the plates? (b) The plate with the lowest potential is taken to be at zero volts. What is the potential 1.00 cm from that plate (and 3.00 cm from the other)?

(a) 3 . 00 kV size 12{3 "." "00"" kV"} {}

(b) 750 V size 12{"750"" V"} {}

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How far apart are two conducting plates that have an electric field strength of 4 . 50 × 10 3 V/m size 12{4 "." "50" times "10" rSup { size 8{3} } `"V/m"} {} between them, if their potential difference is 15.0 kV?

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(a) Will the electric field strength between two parallel conducting plates exceed the breakdown strength for air ( 3.0 × 10 6 V/m size 12{3 times "10" rSup { size 8{6} } `"V/m"} {} ) if the plates are separated by 2.00 mm and a potential difference of 5.0 × 10 3 V size 12{5 times "10" rSup { size 8{3} } `"V"} {} is applied? (b) How close together can the plates be with this applied voltage?

(a) No. The electric field strength between the plates is 2.5 × 10 6 V/m, size 12{2.5 times "10" rSup { size 8{6} } `"V/m"} {} which is lower than the breakdown strength for air ( 3.0 × 10 6 V/m size 12{3 times "10" rSup { size 8{6} } `"V/m"} {} ).

(b) 1.7 mm

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The voltage across a membrane forming a cell wall is 80.0 mV and the membrane is 9.00 nm thick. What is the electric field strength? (The value is surprisingly large, but correct. Membranes are discussed in Capacitors and Dielectrics and Nerve Conduction—Electrocardiograms .) You may assume a uniform electric field.

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Membrane walls of living cells have surprisingly large electric fields across them due to separation of ions. (Membranes are discussed in some detail in Nerve Conduction—Electrocardiograms .) What is the voltage across an 8.00 nm–thick membrane if the electric field strength across it is 5.50 MV/m? You may assume a uniform electric field.

44.0 mV

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Two parallel conducting plates are separated by 10.0 cm, and one of them is taken to be at zero volts. (a) What is the electric field strength between them, if the potential 8.00 cm from the zero volt plate (and 2.00 cm from the other) is 450 V? (b) What is the voltage between the plates?

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Find the maximum potential difference between two parallel conducting plates separated by 0.500 cm of air, given the maximum sustainable electric field strength in air to be 3.0 × 10 6 V/m size 12{3 times "10" rSup { size 8{6} } `"V/m"} {} .

15 kV size 12{"15 kV"} {}

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A doubly charged ion is accelerated to an energy of 32.0 keV by the electric field between two parallel conducting plates separated by 2.00 cm. What is the electric field strength between the plates?

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An electron is to be accelerated in a uniform electric field having a strength of 2 . 00 × 10 6 V/m size 12{2 "." "00" times "10" rSup { size 8{6} } `"V/m"} {} . (a) What energy in keV is given to the electron if it is accelerated through 0.400 m? (b) Over what distance would it have to be accelerated to increase its energy by 50.0 GeV?

(a) 800 KeV size 12{"800"" KeV"} {}

(b) 25.0 km size 12{"25" "." 0" km"} {}

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Questions & Answers

how lesers can transmit information
mitul Reply
griffts bridge derivative
Ganesh Reply
below me
please explain; when a glass rod is rubbed with silk, it becomes positive and the silk becomes negative- yet both attracts dust. does dust have third types of charge that is attracted to both positive and negative
Timothy Reply
what is a conductor
Timothy
hello
Timothy
below me
why below you
Timothy
no....I said below me ...... nothing below .....ok?
dust particles contains both positive and negative charge particles
Mbutene
corona charge can verify
Stephen
when pressure increases the temperature remain what?
Ibrahim Reply
what is frequency
Mbionyi Reply
define precision briefly
Sujitha Reply
CT scanners do not detect details smaller than about 0.5 mm. Is this limitation due to the wavelength of x rays? Explain.
MITHRA Reply
hope this helps
what's critical angle
Mahmud Reply
The Critical Angle Derivation So the critical angle is defined as the angle of incidence that provides an angle of refraction of 90-degrees. Make particular note that the critical angle is an angle of incidence value. For the water-air boundary, the critical angle is 48.6-degrees.
dude.....next time Google it
okay whatever
Chidalu
pls who can give the definition of relative density?
Temiloluwa
the ratio of the density of a substance to the density of a standard, usually water for a liquid or solid, and air for a gas.
Chidalu
What is momentum
aliyu Reply
mass ×velocity
Chidalu
it is the product of mass ×velocity of an object
Chidalu
how do I highlight a sentence]p? I select the sentence but get options like copy or web search but no highlight. tks. src
Sean Reply
then you can edit your work anyway you want
Wat is the relationship between Instataneous velocity
Oyinlusi Reply
Instantaneous velocity is defined as the rate of change of position for a time interval which is almost equal to zero
Astronomy
The potential in a region between x= 0 and x = 6.00 m lis V= a+ bx, where a = 10.0 V and b = -7.00 V/m. Determine (a) the potential atx=0, 3.00 m, and 6.00 m and (b) the magnitude and direction of the electric ficld at x =0, 3.00 m, and 6.00 m.
what is energy
Victor Reply
hi all?
GIDEON
hey
Bitrus
energy is when you finally get up of your lazy azz and do some real work 😁
what is physics
faith Reply
what are the basic of physics
faith
base itself is physics
Vishlawath
tree physical properties of heat
Bello Reply
tree is a type of organism that grows very tall and have a wood trunk and branches with leaves... how is that related to heat? what did you smoke man?
algum profe sabe .. Progressivo ou Retrógrado e Acelerado ou Retardado   V= +23 m/s        V= +5 m/s        0__>              0__> __________________________>        T= 0               T=6s
Claudia
Practice Key Terms 2

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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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