Potential Definition and 1000 Threads

Using the generating function for the legendre polynomial: $$ \sum_{n=0}^{\infty} P_{n}(x) t^{n}=\frac{1}{\sqrt{1-2 x t+t^{2}}} $$ It's possible to expand the coulomb potential in a basis of legendre polynomials (or even spherical harmonic ) like this: $$ \begin{aligned} &\frac{1}{\left.\mid...

If the book had said that electrical potential energy is the negative of work done by electrical force on a charge, then the definition would be very clear and easy to understand. So, why should the book give this confusing definition instead.

Hi, What would happen if I set L in this equation to zero? I can have an L that is zero right?

Here is my solution, which is correct. The tilt of the water at the top can be described in terms of ##x## and ##y## as ##y = \frac{2y_0}{L}x##. The height of the water at any given x is then equal to ##h + \frac{2y_0}{L}x## where ##x \in [-\frac{L}{2}, \frac{L}{2}]##. So the potential...

It is my second "energy state diagram problem" and I would want to know if I am thinking correctly. First I have done some function analysis to get a glimpse of the plot: - no roots but ##\lim\limits_{x\to-\infty}U(x)=\lim\limits_{x\to+\infty}U(x)=0## - y interception: ##U(0)=-U_0## - even...

There is a formula for the potential ##\varphi## outside of a homogenous ellipsoid of density ##\mu## in Landau\begin{align*} \varphi = -\pi \mu abck \int_{\xi}^{\infty} \left(1- \dfrac{x^2}{a^2 + s} + \dfrac{y^2}{b^2 + s} + \dfrac{z^2}{c^2+s} \right) \frac{ds}{R_s} \ \ \ (1) \end{align*}where...

What do we think re the most powerful sci-fi weapons are that we could realistically envision becoming reality one day. I am wondering if we will ever be able to build anything more powerful than matter / anti-matter explosions like Star Trek's Torpedo's.

In orbital mechanics, the effective potential is given by ##\frac {1} {2} m r^2 w^2##, which can be expressed in terms of angular momentum ##L## which is conserved. Yet, https://web.njit.edu/~gary/321/Lecture17.html apparently shows the centrifugal potential as the negative of the above...

Good afternoon to everybody. I have may be a stupid question according to the tangential part of the electric field near the surface of the conductor. Why is it zero? The normal part is zero on the distance of Debye cause of screening. But is this situation the same for horizontal direction...

Hello, I'm seriously confused on several things around how concretely batteries create potential difference in order to force the electrons circulate trought the circuit wire. Almost all explanations I found (wikipedia, diverse tutorials, intro scripts, etc.) explain it in nearly the same...

I have tried to solve the problem through the use of a rotating reference frame, since I should have as a solution an orbit given by the Kepler potential, but I haven't come up with anything. Any ideas ?

Good evening, I got a seriously problem at understanding the membrane potential for ions in a cell. Particulary, i don't understand the case for example for ions with a charge of 2 or higher. I take a look on two scenarios: If you got an ion like calium and got a concentration ratio of 1:10...

Hello there. Do you know any paper that derive the Lennard Jones potential ##V = \epsilon [(\delta / r)^{12}-2(\delta / r)^6]## theorically? If you know a book instead, let me know. Thank you

I understand that potential energies are energies relative to reference points. For example, gravitational/electrical potential energy is relative to a point at infinity. What is the reference point for centrifugal potential energies? In the case of planetary orbits, must the reference point...

The equation below allows us to calculate the potential energy of a continuous distribution of electric charge. $$U=\frac {\epsilon_0} 2 \iiint\limits_\text{Entire electric field}\vec E^2\,dV$$ In my textbook, the author states $$U=\frac 1 {8\pi\epsilon_0}\iiint\limits_\text{Entire electric...

Molecular potential energy of hydrogen in dependence with atomic distance for bonding orbital is given by picture below. We can see that at large distances force between atoms is attractive and potential energy drops to minimum which corresponds to bond energy and length. This part of the...

LJ potential is an empirical potential function used between 2 neutral atoms. Is there any classical/empirical potential for electron-ion interactions as well? Different from Coulomb potential, this one if any should be able to capture the mechanism of a valence electron leaving an atom and of...

From hyperphysics, "The unique point in the case of the traveling wave in the string is the element of the string that is at the maximum displacement as the wave passes. That element has a zero instantaneous velocity perpendicular to the straight string configuration, and as the wave goes "over...

is this method accepted? 2V is split equally between the 2 5kohms resistor because they are of equal resistance. 2V=5kohms 2kohms= 0.8V 3kohms=1.2V. p.d across P and Q= 1V-0.8V=0.2V

Potential inside is given as in ,https://en.wikipedia.org/wiki/Method_of_image_charges, which is the sum of excitation and induced potential. When the charge is outside it is easy to argue potential is zero in the sphere. But when we have charge inside and image outside, what is potential...

Hello, I have a particle at point A with charge ##q_A##, and an unmovable sphere of radius ##R_B## at point B with a volumic charge density ##\rho##. The distance from particle A to the centre of the sphere in B is ##r##. Both objects have opposed charges, so, the particle in A, initially at...

The potential contribution from R > 0 is simple. My next step is to integrate from R to r. With regards to the integration from R to r, the 2nd method gives a potential contribution that is the negative of the 1st method. What is the reason?

Hey guys, I have two questions: 1) I thought absolute electrode potential is galvani potential difference at the interface. However, it is given by this equation in John Bockris - Modern Electrochemistry: $$ E(abs) = ^M\Delta^S\phi - \mu_e^M/F $$ First term is galvani potential difference on...

Voltmeter is an instrument which measures electric potential difference between two points. When measuring electrode potential of some redox system (vs SHE for example), it is said that voltmeter reading contains sum of all potential differences present in a cell. This includes all...

A ramp rises 10cm for every 80cm along the sloping surface. A box of mass 50 kg slides down the ramp starting from rest at the top of the ramp. The coefficient of friction between the ramp and the box is 0.03 and no other resistance acts. The box is traveling at 2 m/s when it reaches the bottom...

A tile of mass 1.2 kg slides 3m down a roof that makes an angle of 35 degree to the horizontal. Find the decrease in potential energy. Iam getting the ans 24.8J PE = mgh= 1.2× 12 sin 35 ×3 The ans in the textbook is 20.6J

I was wondering, we constantly assume the reference of zero potential is the surface of the Earth. But if we consider the reference to be the infinity, what would be the electric potential of the Earth? As Faraday says, the Earth is charged with a -580 kC of negative charge. If we consider...

I understand phase voltage (phase to neutral) well, but I'm still confused by what exactly the potential difference is between any 2 phases in 3 phase power. If you were to try to find the potential difference where 2 sine wave phases cross, then at that instantaneous point, the potential...

When we have a resistor in electronic conductors, potential difference is created via surface charges which accumulate on conductor surface. What about electrolytes? I am not sure if electrolytes can create potential difference in the same way since surface in electrolytic conductors isn't as...

I have a problem with finding the energy of an electron in an FCC lattice using the weak potential method. We did that for a one-dimensional lattice during class, and I know that there was a double degeneration at the boundaries of the first Brillouin Zone. However, I'm not sure what...

I got (a) but have no idea about b. Potential fields aren't just additive all the time are they?

Let's say a mass is gently laid on top of a massless spring. The spring compresses. There is a change in the height of the mass. Therefore, there is a change in the gravitational potential energy: a decrease. The compressed spring now has potential energy (it has gained energy). The change...

If I hold a ball above the ground, it has potential energy. Once gravity pulls on it, it becomes kinetic. What is gravity and how does it convert one kind of energy to another?

Potential energy in a two-dimensional crystal Consider the potential energy of a given ion due to the full infinite plane. Call it##U_{0}##. If we sum over all ions (or a very large number##N##) to find the total##U##of these ions, we obtain##N U_{0}##. However, we have counted each pair twice...

Knowing that ##F(x)=-\mathrm{d}V(x)/\mathrm{d}x##, I found that ##F(x)=-2.4x^3+1.35x^2+8x-3##. But it was the only thing I could find. How can I analyze what will be the type of movement with the information presented by the question statement?

The answer given states that: The entire x-y plane is obviously at the same potential since all the fields are strictly perpendicular to it (draw a diagram if youre confused). Since we choose the sphere to be at potential zero, the point on the sphere which cuts the x-y plane is also at zero...

If I have a force that behaves according to the formula ##F(x)=\alpha x-\beta x^3##, how can I get the potential energy from it? I know that: $$-\frac{\mathrm{d}V(x)}{\mathrm{d}x}=F(x),$$ but what about the limits of the integration?

So I have a ring(red) of uniform charge ##\lambda## per unit length, and I want to calculate the electric potential at the origin (actually on any point of the ring). It is clear that the ring is given by the equation $$r=2 R \sin \theta$$, in polar coordinates, where R is the radius of the...

General state of the infinite potential well is that ##L^2[0,L]##, where ##L## is well width, or ##C^{\infty}_0(\mathbb{R})##?

Hello! So I need to find the potential function of this Vector field $$ \begin{matrix} 2xy -yz\\ x^2-xz\\ 2z-xy \end{matrix} $$ Now first I tried to check if rotation is not ,since that is mandatory for the potentialfunction to exist.For that I used the jacobi matrix,and it was not...

hi guys i came across this question about the maximum and minimum number of bound states that can be confined in these potential wells 1- infinite potential well 2- semi infinite potential well (from one side) 3 - finite potential well i think i have a good idea about the minimum number of...

We can write the Newtonian metric in the form of $$ds^2 = -(1 - 2M/r)dt^2 + (1+2M/r)[dr^2 + r^2d\Omega^2]$$ In order to obtain the orbit equation I have written the constant of motion, $$e = (1 - 2M/r)(\frac{dt}{d\tau})$$ and $$l = r^2sin^2(\theta)(\frac{d\phi}{d\tau})$$ I can divide the...

Under the Lorentz Gauge the Einstein Field Equations are given as $$G^{\alpha \beta} = -\frac{1}{2}\square \bar{h}^{\alpha \beta}$$ Then the linearized EFE becomes, $$\square \bar{h}^{\mu\nu} = -16 \pi T^{\mu\nu}$$ For the later parts, I ll share pictures from the book I have couple of...

Hi, If we are standing on the ground, the Earth applies a force equal to our weight to us, but why do we feel a greater force when we fall to the ground from a certain height? Our weight is the same along this small height because our mass and acceleration are the same and, even so, the normal...

My understanding is at the level of Griffiths's Introduction to quantum mechanics or Robinson's Symmetry and the standard model, i.e., using the phi^4 potential to explain the effects of global and local symmetry breaking, Goldstone and Higgs bosons. These books and others use a potential of...

Good day, If I consider my system to be an object and the earth, and the object is on the surface of the earth, then the system will have gravitational potential energy. Why couldn't I say that only the object (considering it as my system) has gravitational potential energy? Thanks

I am reading Planck 2015 results. In particular, I focused on "Power law potentials" subsection. The issues I have are 1. I do not understand why the validity of the model can be determined by the value of the ##B## mode. 2. Why the ##B## mode values ##\ln B = −11.6## and ##\ln B = −23.3## for...