<< Chapter < Page Chapter >> Page >

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.

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Problems&Exercises

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

Got questions? Get instant answers now!

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} {} ?

Got questions? Get instant answers now!

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"} {}

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

(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

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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"} {}

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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"} {}

Got questions? Get instant answers now!

Questions & Answers

What interference
Moyinoluwa Reply
What is a polarized light called?
Moyinoluwa
what is a half life
Mama Reply
the time taken for a radioactive element to decay by half of its original mass
ken
what is radioactive element
mohammed
Half of the total time required by a radioactive nuclear atom to totally disintegrate
Justice
radioactive elements are those with unstable nuclei(ie have protons more than neutrons, or neutrons more than protons
Justice
in other words, the radioactive atom or elements have unequal number of protons to neutrons.
Justice
state the laws of refraction
Fabian
state laws of reflection
Fabian
Why does a bicycle rider bends towards the corner when is turning?
Mac
When do we say that the stone thrown vertically up wards accelerate negatively?
Mac
Give two importance of insulator placed between plates of a capacitor.
Mac
Macho had a shoe with a big sole moving in mudy Road, shanitah had a shoe with a small sole. Give reasons for those two cases.
Mac
when was the name taken from
Biola Reply
retardation of a car
Biola
when was the name retardation taken
Biola
did you mean a motion with velocity decreases uniformly by the time? then, the vector acceleration is opposite direction with vector velocity
Sphere
Atomic transmutation
Basirat Reply
An atom is the smallest indivisible particular of an element
mosco Reply
what is an atomic
Awene Reply
reference on periodic table
Titus Reply
what Is resonance?
Mozam Reply
phenomena of increasing amplitude from normal position of a substance due to some external source.
akif
What is a black body
Amey Reply
Black body is the ideal body can absorb and emit all radiation
Ahmed
the emissivity of black body is 1. it is a perfect absorber and emitter of heat.
Busayo
Why is null measurement accurate than standard voltmeter
Neemat Reply
that is photoelectric effect ?
Sabir Reply
It is the emission of electrons when light hits a material
Anita
Yeah
yusuf
is not just a material
Neemat
it is the surface of a metal
Neemat
what is the formula for time of flight ,maxjmum height and range
agangan Reply
what is an atom
Awene
how does a lightning rod protect a building from damage due to lightning ?
Faith Reply
due to its surface lustre but due to some factors it can corrode but not easily as it lightning surface
babels
pls what is mirage
babels
light rays bend to produce a displaced image of distant objects; it's an natural & optical phenomenon......
Deepika
what is the dimensional formula for torque
Otto Reply
L2MT-2
Jolly
same units of energy
Baber
what is same units of energy?
Baber
Nm
Sphere
Ws
Sphere
CV
Sphere
M L2 T -2
Dokku
it is like checking the dimension of force. which is ML2T-2
Busayo
ML2T-2
Joshua
M L2 T-2
Samuel
what is the significance of moment of inertia?
study
an object of mass 200g moves along a circular path of radius 0.5cm with a speed of 2m/s. calculate the angular velocity ii period iii frequency of the object
Faith Reply
w = 2/(0.005) period = PIE(0.005) f = 1/(PIE(0.005)) assuming uniform motion idk..
Georgie
w=2/(0.005)×100
isaac
supposed the speed on the path is constant angular velocity w (rad/s) = v (m/s) : R (m) period T (s) = 2*Pi * R : v frequency f ( Hz) = 1: T
Sphere
a=w.w.r=mv.v/r,w=mv/r=0.2×2/0.005=80rads-s
Mac
Practice Key Terms 2

Get the best College physics course in your pocket!





Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask