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The voltages in both of these examples could be measured with a meter that compares the measured potential with ground potential. Ground potential is often taken to be zero (instead of taking the potential at infinity to be zero). It is the potential difference between two points that is of importance, and very often there is a tacit assumption that some reference point, such as Earth or a very distant point, is at zero potential. As noted in Electric Potential Energy: Potential Difference , this is analogous to taking sea level as h = 0 size 12{h=0} {} when considering gravitational potential energy, PE g = mgh size 12{"PE" rSub { size 8{g} } = ital "mgh"} {} .

Section summary

  • Electric potential of a point charge is V = kQ / r size 12{V= ital "kQ"/r} {} .
  • Electric potential is a scalar, and electric field is a vector. Addition of voltages as numbers gives the voltage due to a combination of point charges, whereas addition of individual fields as vectors gives the total electric field.

Conceptual questions

In what region of space is the potential due to a uniformly charged sphere the same as that of a point charge? In what region does it differ from that of a point charge?

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Can the potential of a non-uniformly charged sphere be the same as that of a point charge? Explain.

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Problems&Exercises

A 0.500 cm diameter plastic sphere, used in a static electricity demonstration, has a uniformly distributed 40.0 pC charge on its surface. What is the potential near its surface?

144 V

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What is the potential 0 . 530 × 10 –10 m size 12{0 "." "530" times "10" rSup { size 8{ - 10} } `m} {} from a proton (the average distance between the proton and electron in a hydrogen atom)?

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(a) A sphere has a surface uniformly charged with 1.00 C. At what distance from its center is the potential 5.00 MV? (b) What does your answer imply about the practical aspect of isolating such a large charge?

(a) 1.80 km

(b) A charge of 1 C is a very large amount of charge; a sphere of radius 1.80 km is not practical.

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How far from a 1 . 00 µC size 12{1 "." "00" mC} {} point charge will the potential be 100 V? At what distance will it be 2.00 × 10 2 V ? size 12{2 "." "00" times "10" rSup { size 8{ 2} } `V} {}

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What are the sign and magnitude of a point charge that produces a potential of –2.00 V at a distance of 1.00 mm?

–2 . 22 × 10 13 C size 12{2 "." "22" times "10" rSup { size 8{ - 13} } `C} {}

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If the potential due to a point charge is 5 . 00 × 10 2 V size 12{5 "." "00" times "10" rSup { size 8{ 2} } `V} {} at a distance of 15.0 m, what are the sign and magnitude of the charge?

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In nuclear fission, a nucleus splits roughly in half. (a) What is the potential 2 . 00 × 10 14 m size 12{2 "." "00" times "10" rSup { size 8{ - 14} } `m} {} from a fragment that has 46 protons in it? (b) What is the potential energy in MeV of a similarly charged fragment at this distance?

(a) 3 . 31 × 10 6 V size 12{3 "." "31" times "10" rSup { size 8{6} } `V} {}

(b) 152 MeV

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A research Van de Graaff generator has a 2.00-m-diameter metal sphere with a charge of 5.00 mC on it. (a) What is the potential near its surface? (b) At what distance from its center is the potential 1.00 MV? (c) An oxygen atom with three missing electrons is released near the Van de Graaff generator. What is its energy in MeV at this distance?

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An electrostatic paint sprayer has a 0.200-m-diameter metal sphere at a potential of 25.0 kV that repels paint droplets onto a grounded object. (a) What charge is on the sphere? (b) What charge must a 0.100-mg drop of paint have to arrive at the object with a speed of 10.0 m/s?

(a) 2 . 78 × 10 - 7 C size 12{2 "." "78" times "10" rSup { size 8{-7} } `C} {}

(b) 2 . 00 × 10 - 10 C size 12{2 "." "00" times "10" rSup { size 8{-10} } `C} {}

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In one of the classic nuclear physics experiments at the beginning of the 20th century, an alpha particle was accelerated toward a gold nucleus, and its path was substantially deflected by the Coulomb interaction. If the energy of the doubly charged alpha nucleus was 5.00 MeV, how close to the gold nucleus (79 protons) could it come before being deflected?

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(a) What is the potential between two points situated 10 cm and 20 cm from a 3 . 0 µC size 12{3 "." 0 mC} {} point charge? (b) To what location should the point at 20 cm be moved to increase this potential difference by a factor of two?

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Unreasonable Results

(a) What is the final speed of an electron accelerated from rest through a voltage of 25.0 MV by a negatively charged Van de Graaff terminal?

(b) What is unreasonable about this result?

(c) Which assumptions are responsible?

(a) 2.96 × 10 9 m/s

(b) This velocity is far too great. It is faster than the speed of light.

(c) The assumption that the speed of the electron is far less than that of light and that the problem does not require a relativistic treatment produces an answer greater than the speed of light.

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Questions & Answers

Pls guys am having problem on these topics: latent heat of fusion, specific heat capacity and the sub topics under them.Pls who can help?
hamidat Reply
Thanks George,I appreciate.
hamidat
this will lead you rightly of the formula to use
Abolarin
Most especially it is the calculatory aspects that is giving me issue, but with these new strength that you guys have given me,I will put in my best to understand it again.
hamidat
you can bring up a question and let's see what we can do to it
Abolarin
the distance between two suasive crests of water wave traveling of 3.6ms1 is 0.45m calculate the frequency of the wave
Idris Reply
v=f×lemda where the velocity is given and lends also given so simply u can calculate the frequency
Abdul
You are right my brother, make frequency the subject of formula and equate the values of velocity and lamda into the equation, that all.
hamidat
lExplain what happens to the energy carried by light that it is dimmed by passing it through two crossed polarizing filters.
Christoper Reply
When light is reflected at Brewster's angle from a smooth surface, it is 100% polarizedparallel to the surface. Part of the light will be refracted into the surface.
Ekram
What is specific heat capacity?
hamidat Reply
Specific heat capacity is the amount of heat required to raise the temperature of one (Kg) of a substance through one Kelvin
Paluutar
formula for measuring Joules
Rowshan Reply
I don't understand, do you mean the S.I unit of work and energy?
hamidat
what are the effects of electric current
ADAMS Reply
What limits the Magnification of an optical instrument?
Naeem Reply
Lithography is 2 micron
Venkateshwarlu
what is expression for energy possessed by water ripple
Prabesh Reply
what is hydrolic press
Mark Reply
An hydraulic press is a type of machine that is operated by different pressure of water on pistons.
hamidat
what is dimensional unite of mah
Patrock Reply
i want jamb related question on this asap🙏
sharon Reply
What is Boyles law
Pascal Reply
it can simple defined as constant temperature
Muhammad
Boyles law states that the volume of a fixed amount of a gas is inversely proportional to the pressure acting on in provided that the temperature is constant.that is V=k(1/p) or V=k/p
FADILAT
what is motion
Mua Reply
getting notifications for a dictionary word, smh
Anderson
what is escape velocity
Shuaibu Reply
the minimum thrust that an object must have in oder yo escape the gravitational pull
Joshua
what is a dimer
Mua
what is a atom
ADAMS
how to calculate tension
Deena Reply
what are the laws of motion
Mua

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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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