# Questions tagged [potential]

Scalar and vector potentials in electromagnetism. The scalar potential is potential energy per unit charge. For potential energy, use the [potential-energy] tag.

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Say we have a positive point charge located somewhere. Then the electric field due to this point charge is $\vec{E} = \frac{1}{4\pi \epsilon_0}\frac{Q}{r^2}\hat{r}$ , now considering potential is $V =... • 119 0 votes 1 answer 44 views ### Surface charge density within a parallel plate capacitor on different voltages I need a way to vary the surface charge density without changing the electric field. My idea is to use two large conducting parallel plates close to each other in vacuum enclosed in a grounded vessel (... • 1 0 votes 1 answer 57 views ### Thermodynamic work and potential functions I was reading about the maximum thermodynamic work of a system (Z) that is going to equilibrium. $$dZ = dU + p_0 + T_0dS$$ I then came across the thermodynamic potential ... • 31 1 vote 1 answer 24 views ### Electric field at any point in the region between two capacitors is proportional to the magnitude of charge on each conductor This is a statement from Young and Freedman's University Physics Section 24.1 on Capacitors. Suppose we have any two conductors with charges$-Q$and$+Q$on each charged with a battery. Then this ... 1 vote 2 answers 67 views ### Potential of an electric dipole I'm currently working my way through Griffith's Introduction to Electrodynamics (4th ed). In chapter 3 section 4, he shows that we can take the equation for the electric potential of a continuous ... 0 votes 0 answers 44 views ### Is there a deeper relationship between symmetry and gravitational potential comparing Newton's and Einstein's gravity? In this question, see Why is general relativity in (2+1) dimensions different from cylindrical systems in (3+1) dimensional GR?, it is mentioned "The gravitational potential Φ of an infinite rod ... • 1,589 0 votes 3 answers 98 views ### How do charges on two conductors charged by the same battery relate to each other? Let’s consider 2 neutral conducting spheres, L and R, with different radii. There is a battery somewhere in the middle between these spheres. The battery has potential$\phi_{B-}$on its negative ... • 119 1 vote 1 answer 77 views ### Potential on conducting shell without image charge Edit 2: I know how image charges work. But I'm still trying to rationalize without it. Edit 1: scrap this, realized what I needed was image charges. This entire question is sort of a jury-rig ... • 73 0 votes 1 answer 66 views ### How to describe the dynamics of a magnetic monopole charge in the external EM field using a Lagrangian in terms of the EM potentials? The equation of motion of a magnetic charge in the fixed external electromagnetic field$\mathbf{E},\mathbf{B}$is $$\frac{d}{dt}(\gamma m \mathbf{v})=q_m(\mathbf{B}-\mathbf{v}\times\mathbf{E}),$$ ... • 21 0 votes 1 answer 70 views ### A General Analysis of Charge Distribution inside conductors I'll go ahead and present my question straight-forward and then talk about the calculation details.My Question is: how do you define a conductor in Electrostatics? What are the basic(minimum) set of ... 5 votes 2 answers 120 views ### Long-range approximations of the Uehling interaction A common approximation to the U(\vec{r})=-m\frac{\alpha(Z\alpha)}{\pi} \int_1^\infty\mathrm{d}u\frac{\sqrt{u^2-1}\left(2u^2+1\right)}{3u^4}\frac{\exp(-2mur)}{mr} \tag{$\star$} \end{... • 2,385 0 votes 6 answers 140 views ### What is electromotive force? What's its relationship to Voltage? + clarification of confusion So first of all, yeah I know that the electromotive force is not a force (the name was coined by Alessandro Volta I think). About Power and dissipated power The power with wich a battery provides the ... • 11 0 votes 0 answers 28 views ###$\pi$phase shift upon reflection in quantum wells Is there a similar phenomenon to the$\pi$phase shift experienced by light upon reflection from a medium of lower to higher refracted index for particles in different potentials? For instance, does a ... 0 votes 3 answers 53 views ### How is electric potential the work done on a unit charge? I recently read that electric potential at a point is defined as work done in bringing a positive unit charge from infinity (or any other reference point) to that point. How can electric potential be ... 2 votes 0 answers 118 views ### What are the limitations of Nodal Analysis? Yea, that's the question basically. What are the limitations of Nodal Analysis? Like, for example take the following case, we have to find out the net capacitance between A and B. Now I want to solve ... • 374 1 vote 0 answers 61 views ### Vector potential of Weird loop I have to calculate the vectorpotential of a current flowing through the loop at the origin: where the current is given by$I(t)=kt$for some$k>0$. Given equations $$\mathbf{A} = \frac{\mu_0}{4\... -1 votes 1 answer 48 views ### How does 1D Schrödinger equation arise out of the postulated 3D Schrödinger equation and solving 1D particle using 3D Schrödinger equation? I've stumbled upon this question when I was trying to solve the Schrödinger equation for a particle confined to a 1D line with some given time independent potential V(x). The energy eigenstates ... • 109 0 votes 0 answers 44 views ### Hydrogen atom energy: n vs l (QM) I've come across a problem that states the following: let two (separate) particles be subject to a central potential V(r). Their reduced radial function is depicted in the following image: Which ... • 1,624 1 vote 1 answer 86 views ### Method of images and the zero potential of the conductor I was reading the method of images in Griffiths' electrodynamics book. He uses the classic image problem to explain the significance of the uniqueness theorem suppose a point charge q is held a ... • 73 4 votes 1 answer 174 views ### Series Solution of Laplace Equation in Spherical Coordinates I was recently Studying Griffiths Electrodynamics after a long time and there I saw the Laplace equation. Because it was my second time going over Griffiths so I thought maybe I should try to derive ... 2 votes 0 answers 52 views ### Time evolution of scalar potential using Huygens principle Huygens principle states that every point in space acts as a source of spherical waves. The amplitude for potential (scalar and vector) will be given by V(r,t)=f(t-r/c)/r, where f is a function ... • 63 1 vote 5 answers 91 views ### The electrostatic potential due to a pair of oppositely charged infinite thin conducting plates The electric field in region A and C (outside the pair of sheets) is 0. The electric field in region B (between the plates) is given by:$$E = \frac{\sigma}{\varepsilon}.$$The distance between the ... 1 vote 0 answers 24 views ### Electric field due to plane at constant potential and a cylinder with no flux on surface There is a plate at a constant potential V and potential equal to zero far away. the problem is two-dimensional. For this case, the electric field lines will simply be straight lines. Now let there be ... • 107 0 votes 2 answers 27 views ### Potential attained by a sphere under illumination A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are ... 1 vote 2 answers 66 views ### Potential on concentric shells not making sense? Suppose you have 2 concentric spherical shells, radius A (inner) and B (outer). Now suppose the inner shell has +Q charge and the outer one has -Q charge. Through integration, we get that the ... • 11 10 votes 2 answers 916 views ### Is work done by a charged particle not gauge invariant? Work done by a charged point particle with charge q in an external electric field derived from a scalar potential \phi is given by$$W=q \phi.$$Even if we add a magnetic field the definition ... 1 vote 1 answer 97 views ### What is the potential of a conductor between two eletrically-charged plates? Let's say I have two plates. One is at +20V, the other is at +10V, and they are separated a meter apart. I place an uncharged conductor that's 10cm wide into the gap between them, 20cm from the plate ... • 21.5k 0 votes 2 answers 48 views ### It's possible to have different potentials (boundary conditions) in the surface of a cylindrical conductor? Edit I realized that my problem is not clearly stated. In general, I can solve the Laplace equation for boundary conditions$V(r,\phi, z=0) = f(r,\phi)$(bottom of the cylinder),$V(r,\phi, z=L) = g(r,...
I am having some trouble with problem 3.15 from Griffith's Electrodynamics. It states the following: A rectangular pipe, running parallel to the $z$-axis (from $-\infty$ to $+\infty$), has three ...