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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

the range of objects and phenomena studied in physics is
Bethel Reply
what is Linear motion
Hamza Reply
straight line motion is called linear motion
then what
Amera
linear motion is a motion in a line, be it in a straight line or in a non straight line. It is the rate of change of distance.
Saeedul
Hi
aliyu
your are wrong Saeedul
Richard
Linear motion is a one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension
Jason
what is the formula to calculate wavelength of the incident light
David Reply
if a spring is is stiffness of 950nm-1 what work will be done in extending the spring by 60mmp
Hassan Reply
State the forms of energy
Samzy Reply
machanical
Ridwan
Word : Mechanical wave Definition : The waves, which need a material medium for their propagation, e.g., Sound waves. \n\nOther Definition: The waves, which need a material medium for their propagation, are called mechanical waves. Mechanical waves are also called elastic waves. Sound waves, water waves are examples of mechanical waves.t Definition: wave consisting of periodic motion of matter; e.g. sound wave or water wave as opposed to electromagnetic wave.h
Clement Reply
correct
Akinpelu
what is mechanical wave
Akinpelu Reply
a wave which require material medium for its propagation
syed
The S.I unit for power is what?
Samuel Reply
watt
Okoli
Am I correct
Okoli
it can be in kilowatt, megawatt and so
Femi
yes
Femi
correct
Jaheim
kW
Akinpelu
OK that's right
Samuel
SI.unit of power is.watt=j/c.but kw.and Mw are bigger.umots
syed
What is physics
aish Reply
study of matter and its nature
Akinpelu
The word physics comes from a Greek word Physicos which means Nature.The Knowledge of Nature. It is branch of science which deals with the matter and energy and interaction between them.
Uniform
why in circular motion, a tangential acceleration can change the magnitude of the velocity but not its direction
Syafiqah Reply
reasonable
Femi
because it is balanced by the inward acceleration otherwise known as centripetal acceleration
MUSTAPHA
What is a wave
Mutuma Reply
Tramsmission of energy through a media
Mateo
is the disturbance that carry materials as propagation from one medium to another
Akinpelu
mistakes thanks
Akinpelu
find the triple product of (A*B).C given that A =i + 4j, B=2i - 3j and C = i + k
Favour Reply
Difference between north seeking pole and south seeking pole
Stanley Reply
if the earth Suddenly contract s then
Swami Reply
please formula for density is what
Akinpelu
mass/volume
Jaja
what is motion
Nelson Reply
In physics, motion is the change in position of an object with respect to its surroundings in a given interval of time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, time, and speed. ... Momentum is a quantity which is used for measuring the motion of
Karthi
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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