What is Potential: Definition and 1000 Discussions

Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple release of energy by objects to the realization of abilities in people. The philosopher Aristotle incorporated this concept into his theory of potentiality and actuality, a pair of closely connected principles which he used to analyze motion, causality, ethics, and physiology in his aPhysics, Metaphysics, Nicomachean Ethics and De Anima, which is about the human psyche. That which is potential can theoretically be made actual by taking the right action; for example, a boulder on the edge of a cliff has potential to fall that could be actualized by pushing it over the edge. Several languages have a potential mood, a grammatical construction that indicates that something is potential. These include Finnish, Japanese, and Sanskrit.In physics, a potential may refer to the scalar potential or to the vector potential. In either case, it is a field defined in space, from which many important physical properties may be derived. Leading examples are the gravitational potential and the electric potential, from which the motion of gravitating or electrically charged bodies may be obtained. Specific forces have associated potentials, including the Coulomb potential, the van der Waals potential, the Lennard-Jones potential and the Yukawa potential. In electrochemistry there are Galvani potential, Volta potential, electrode potential, and standard electrode potential. In the
thermodynamics, the term potential often refers to thermodynamic potential.

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  1. K

    I Retarded potential of a moving point charge

    Potential of a moving point charge is given as ##V (\mathbf r,t)= \frac{1}{4\pi\epsilon_0}\int \frac{\rho (\mathbf r',t_r) }{|\mathbf{ (r-r')}|}d\tau'## Griffiths says: " It is true that for a point source the denominator ## |\mathbf{(r-r')}|## comes outside the integral..."Why does it come...
  2. Salmone

    I Separable Hamiltonian for central potential

    In a central potential problem we have for the Hamiltonian the expression: ##H=\frac{p^2}{2m}+V(r)## and we use to solve problems like this noting that the Hamiltonian is separable, by separable I mean that we can express the Hamiltonian as the sum of multiple parts each one commuting with the...
  3. LCSphysicist

    Potential vector of a oscilating dipole:

    I am passing through some difficulties to understand the reasoning to derive the electric potential of an oscilating dipole used by Griffths at his Electrodynamics book: Knowing that ##t_o = t - r/c##, What exactly he has used here to go from the first term after "and hence" to the second term...
  4. link223

    Calculating the point where potential V = 0 (due to 2 charges)

    Apparently, there are two solutions where the electric potential is zero which I don't understand, can I get some input on how this is possible? I have one thing in mind (which I just thought of and might solve it), the equipotentiality i.e. when I draw a circle for V = 0 around the negative...
  5. Green dwarf

    I Exploring Energy in Astronomy: Kinetic, Potential & Mass?

    I am planning to teach a school astronomy group about energy. Most people seem to accept that there are two types: kinetic energy, resulting from movement; potential energy, resulting from position in a force field with a potential gradient (convertible to KE if the object is allowed to move...
  6. breadlover98

    Runge-Lenz vector with perturbation potential

    For the case that there is only a potential ##\sim 1/r##, I have already proven that the time derivative of the Lenz vector is zero. However, I'm not sure how I would "integrate" this perturbation potential/force into the definition of the Lenz vector (as it is directly defined in terms of the...
  7. G

    Potential difference metallic sphere

    a) We know that ##Q_1=1,2\, \textrm{nC}## and ##Q_2=6\, \textrm{nC}##. By the TOTAL influence theorem: $$-Q_1=Q_{2i}=-1,2\, \textrm{nC}$$ $$Q_2=Q_{2i}+Q_{2e}\rightarrow Q_{2e}=7,2\, \textrm{nC}$$ b) Electric potential difference crust: $$V_A-V_\infty=$$ How was this potential difference thing...
  8. Ahmed1029

    I Exact electrostatic potential of a pure dipole using multipole expansion

    If I have a physical dipole with dipole moment p. Now, this formula for potential (V) is a good approximation when r is much larger than both r1 and r2 in the picture below. It's however said that for a pure dipole for which the separation between charges goes to zero and q goes to infinity, the...
  9. G

    Potential difference of an electric circuit

    The figure is: I have the solution to this problem: We have two distinct branches $$V_a-V_b=\overbrace{(V_a-V_c)}^{\textrm{INI}-\textrm{FIN}}+\overbrace{(V_c-V_b)}^{\textrm{FIN}-\textrm{INI}}$$ They have different intensities: ##3\, \textrm{mA}## and ##2\, \textrm{mA}## ##V_A-V_C\rightarrow##...
  10. ajaymohan251

    Is Time-Dependent Electric Current Simulation Possible in COMSOL?

  11. guyvsdcsniper

    Rectangular Box with two non zero potential faces

    I believe what I have to do to solve this problem is find the potential at each end face and then use the super position principle to find the net potential. So my boundary condition v and iv will give the potential at each respective position. Im just a bit confused about my boundary V...
  12. MatinSAR

    Problem about electric potential

    Can anyone help me how to solve this problem ?! I am sure that my answer is not right :
  13. shivajikobardan

    Unlocking the Potential of Electric Vehicle Energy Storage: Exploring V2G

    How can electric vehicle deliver energy to grid? This is the one of the few block diagrams that I could see in google. Do you have better one or can you explain this one? If I am not wrong. V2G is basically giving excess charge in your EV back to the grid.
  14. F

    I A question about potential in the periodic lattice of a solid

    In 3D period lattice, can we separate variable and write potential as V=V(x)+V(y)+V(z)?Then we can reduce the 3D problems into 1D problems. I ask this question because in Solid State Physics books they often consider the 1D problems.
  15. coolpoke0908

    I Can someone explain why momentum does not commute with potential?

    My assumption is that knowing potential can lead to knowing the position, but I don't know how this can be.
  16. V

    B How is capacitor energy the same as electrostatic potential energy?

    The energy stored in a capacitor is derived by integrated the work needed to move charge dQ from one plate to another. I'm confused on how this energy is the same as electrostatic potential energy, the energy needed to assemble this configuration from infinity. In the case of capacitor energy...
  17. J

    Find largest potential energy difference between 2 loop orientations

    I thought the largest PE difference would be when the loop's area vector is in the same direction as the magnetic field, hence cos(0) =1, minus when the loop's area vector in perpendicular to the field, cos(pi/2) = 0. Just plug in the variables and you get 0.126 joules. Did I make a mistake?
  18. J

    Find the Potential energy of a system of charges

    There are six pairs. three turn out to be negative and three turn out to be positive (3q^2 - 3q^2) which nets zero when you add them together with the equation. But zero was the incorrect answer. Did I do something wrong? Thank you
  19. Mr_Allod

    Quantum Harmonic Oscillator with Additional Potential

    Hello there, I am trying to solve the above and I'm thinking that the solutions will be Hermite polynomials multiplied by a decaying exponential, much like the standard harmonic oscillator problem. The new Hamiltonian would be like so: $$H = - \frac \hbar {2m} \frac {d^2}{dx^2}\psi + \frac...
  20. guyvsdcsniper

    Finding Potential inside a hollow sphere

    I am currently reading Griffiths book for electrodynamics and having trouble making a jump in one of the problems. I have attached the problem (3.6) in question. In the part that is highlighted, I don't see how we go from (1-cosθ) to (P0cosθ-P1cosθ)? I can see that from the Legendre...
  21. J

    Velocity of two masses due to electric potential energy

    We can find the potential energy by finding the potential difference between the two masses. the minimum distance between the two masses is 10 cm. The maximum is 30 cm because they can be 3 string lengths apart as they repulse each other once the string is cut. So, to get potential difference...
  22. A

    I How to interpret this definition of potential energy?

    Hello everyone, I'd like to share a doubt I am currently struggling with. So we know that ΔU=−W, where ΔU is the difference of potential energy and Wthe work done by the force to move the body from point A to point B. When analyzing this for the gravitational force, since we have U=−GmM/R, with...
  23. Salmone

    I Derivative of the retarded vector potential

    In a problem of an oscillating electric dipole, under appropriate conditions, one can find, for the potential vector calculated at the point ##\vec{r}##, the expression ##\vec{A}=\hat{k}\frac{\mu_0I_0d}{4\pi}\frac{cos(\omega(t-r/c))}{r}## where: ##\hat{k}## is the direction of the ##z-axis##...
  24. MevsEinstein

    Admissions Win a Davidson Institute Fellowship: Unlock the Potential of Your Math Project

    If you didn't know, there is something called the Davidson Institute Fellow Scholarship for middle and high school students. To get a scholarship (which come in 10,000 dollars, 25,000 dollars, and 50,000 dollars (if I remember correctly)), you will need to share a research project in the...
  25. G

    Potential on the axis of a uniformly charged ring

    We know that $$V_Z=\int_{\textrm{ring}} E\cdot dl$$ We therefore consider ##E=\dfrac{\lambda}{2\pi \varepsilon_0}\cdot \dfrac1r##. Then, $$V_Z=\int_{\textrm{ring}} \dfrac{\lambda}{2\pi \varepsilon_0}\cdot \dfrac1r\, dl = \dfrac{\lambda}{2\pi \varepsilon_0}\dfrac1r \int_{\textrm{ring}}dl=$$...
  26. K

    I Form of potential operator of two interacting particles

    Considering two interacting particles in 3d, the corresponding Hilbert space ##H## is the tensor product of the two individual Hilbert spaces of the two particles. If the particle interaction is given by a potential ##V(\mathbf r_1 -\mathbf r_2)## ,what is the corresponding potential operator...
  27. rudransh verma

    Potential energy in case of Atwood machine

    ##T-2mg=2ma_1## (acceleration of heavier mass) ##T-mg=ma_2## (##-a_1=a_2##) On solving the eqns, ##a_1=-g/3=-a_2## ##s=1/2at^2## ##s=-g/6## , distance covered by heavier mass. ##s=g/6## , covered by lighter mass. Edit: ##\Delta U_1=mgh=-2mg^2/6## (decrease in U of heavier mass) ##\Delta...
  28. A

    Electric Potential Difference -- Conceptual Question

    I am able to get V1 = kq/a - 4kq/b and V2 = kq/b + -4kq/b For some reason the solution says it is V1-V2 as opposed to V2-V1. Maybe has something to do with positive shell in the center and negative outer shell? I know the electric field goes from positive to negative, but I don't know how...
  29. guyvsdcsniper

    Finding the quantum number using Morse Potential

    This problem had me take the taylor series of the Morse Potential, until I got the first non zero term. My result was U(x)=Aα2(x-x0)2. I know to find the quantum number I can use En=(n+1/2)ℏω and I know I can relate that to the potential energy of a harmonic oscillator, 1/2kx2. So if this...
  30. Haorong Wu

    I Coefficients in expansions of a vector potential

    I have seen two expansions of a vector potential, $$\mathbf A=\sum_\sigma \int \frac{d^3k}{(16 \pi^3 |\mathbf k|)^{1/2}} [\epsilon_\sigma(\mathbf k) \alpha_\sigma (\mathbf k) e^{i \mathbf k \cdot \mathbf x}+c.c.],$$ and $$\mathbf A=\sum_\sigma \int \frac{d^3k}{ (2 \pi)^3(2 |\mathbf k|)^{1/2}}...
  31. S

    Potential difference of a ring rolling in magnetic field

    I don't understand why there is potential difference between point A and O. Is there any change in magnetic flux experienced by the ring? I think the magnetic field passing through the ring's cross sectional area is constant Thanks
  32. B

    Potential Energy of the Atmosphere

    Summary:: I have been trying to do this question for a while using the hydrostatic relationship to put rho and z in terms of p, however, I can not seem to end up with an answer. Can anyone suggest where to start. The question is as follows:
  33. Danny_aero

    Change in potential energy of expanded air in piston-cylinder

    Air is heated in a vertical piston–cylinder assembly fitted with an electrical resistor. The volume of the air slowly increases by 1.6 ft^3 while its pressure remains constant. The area of the piston is 1 ft^2. The mass of the air is 0.6 lb. The local acceleration of gravity is g = 32.0 ft/s^2...
  34. K

    I How to apply potential operator ##V(\hat{x})##

    I want some clarification on the potential operator ##V(\hat{x})##. Can you please help me ------------------------------ Is the action of ##V(\hat{x})## defined by its action on the position kets as ##\hat{V}(x)|x\rangle=V(x)|x\rangle##? Then we'd have for any ket ##|\psi\rangle## that...
  35. Dario56

    I Potential Energy of an Electron-Nuclei Interaction in DFT

    In density functional theory (DFT), electron density is a central quantity. Because of this, we want to calculate electron - nuclei potential energy as functional on electron density. If we know how potential energy varies across space, we can calculate this functional with plugging particular...
  36. Dario56

    I Kinetic Energy and Potential Energy of Electrons

    Time indepedendent Schrödinger equation for a system (atom or molecule) consisting of N electrons can be written as (with applying Born - Oppenheimer approximation): $$ [(\sum_{i=1}^N - \frac {h^2} {2m} \nabla _i ^2) + \sum_{i=1}^N V(r_i) + \sum_{i < j}^N U(r_i,r_j)] \Psi = E \Psi $$ Terms in...
  37. H

    I Is the scalar magnetic Potential the sum of #V_{in}# and ##V_{out}##

    Hi, I'm wondering if I have an expression for the scalar magnetic potential (V_in) and (V_out) inside and outside a magnetic cylinder and the potential is continue everywhere, which mean ##V^1 - V^2 = 0## at the boundary. Does it means that ##V^1 - V^2 = V_{in} - V_{out} = 0## ?
  38. Anmoldeep

    Time dependant Potential Energy in ion trap

    Ion traps are very complex, but one of my Physics Olympiad textbooks presents a simplified model of a resonating charged particle in an ion trap A tuned circuit consists of an inductor and a parallel plate capacitor (capacitance C and plate separation d). It has a resonating frequency ##\nu...
  39. nmfowlkes

    Potential Difference over Capacitors in Series

    V1 = Q/30 In parallel: C = C1 + C2 V2 = Q/(60 + 90) V1/V2 = 3 V1 = 3V2
  40. S

    Gravitational Field and Potential at certain point

    The removed mass is ##\frac{1}{8}M## My idea is to find ##g## from large sphere then minus it with ##g## from small sphere (because of the removed mass): ##g## at A = $$\frac{GM}{R^3}\left(\frac{1}{2}R\right)-\frac{G\left(\frac{1}{8}M\right)}{R^2}$$ Is this correct? Thanks
  41. S

    Work done on dipole and potential energy in uniform electric field

    I encountered a problem regarding the appropriate sign needed to be taken for the work done on a dipole when it rotates in a uniform electric field and would appreciate some help. The torque on a dipole can be defined as τ=PEsinθ The work done on a dipole to move it from an angle ##\theta_0##...
  42. potatonecromancer

    What factors affect stopping and directional control in basketball shoes?

    - Change DV to velocity and measure it with motion sensor - create separate table/graph of friction coefficient using velocities and other information
  43. S

    Finding potential at a point in capacitor

    I tried solving the part (a), and got I =1.82 A for the current value using Kirchoff's law. Next, I want to use Ohm's law to calculate the voltage at point a. Va = IR In this equation, will resistance R correspond to 4.4Ω or 8.8Ω? How do you determine which resistance to use when solving this...
  44. S

    Relativistic correction to Coulomb Potential in SQED

    I have derived the Coulombian potential as an effective potential between two spinless charged particle taking the non-relativitic approach on the scattering amplitude obtained in terms of the Feynman rules in SQED. The scattering amplitudes are: I'm using the gauge in which xi = 1. How could...
  45. iochoa2016

    The electric field from its electric potential: semicircle

    According to theory I should be able to get the Electric Field (E) from its pOtential (V) by doing the grad (V) so E = -grad(V), however, V is contant V = k*lambda* pi which results having E =0, but this is not right. What I am missing?? see figure below The answer should be Ex = 2*k*lambda / r...
  46. L

    A disconnected capacitor with two dielectrics in parallel

    I considered the capacitor as two capacitors in parallel, so the total capacitance is ##C=C_1+C_2=\frac{\varepsilon_0\varepsilon_1 (A/2)}{d}+\frac{\varepsilon_0\varepsilon_2 (A/2)}{d}=\frac{\varepsilon_0 A}{2d}(\varepsilon_1+\varepsilon_2).## Since the parallel component of the electric field...
  47. P

    Scattered State Solutions of a Repulsive Dirac Delta Potential

    I feel that this problem can be directly answered from the E>0 case of the attractive Dirac delta potential -a##\delta##(x), with the same reflection and transmission coefficients. Can someone confirm this hunch of mine?
  48. L

    Potential due to a finite charged wire

    Considering a reference frame with ##x=0## at the leftmost point I have for the leftmost piece of wire: ##\int_{x=0}^{x=2R}\frac{\lambda dx}{4\pi\varepsilon_0 (3R-x)}=\frac{\lambda ln(3)}{4\pi\varepsilon_0}##. The potential at O due to the semicircular piece of wire at the center is...
  49. NoahCygnus

    Potential difference between two points in an electric field

    So I have been given a uniform electric field ##\vec{E}=20 V/m## in the direction as show in the image. I have been told to calculate the potential difference ##VC - VA##. According to the teacher (on YouTube) the potential difference ##VC - VA = -10\sqrt{2}V##. But I say it's ##-20 V## as...
  50. V

    Kinetic & Potential Energy of a Pendulum

    When the pendulum is released, the Kinetic Energy should be 0. When the pendulum is at the bottom/hits the rod, it should have 0 potential energy. However, I don't quite understand what happens after it hits the rod.
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