Potential Definition and 1000 Threads

I tried to make the kinetic energy of the first electron equal to the electric potential work. mv^2/2=ke^2/d We have to solve for the minimum distance between them: d=2ke^2/mv^2=5.05*10^-10 m The force is: F=ke^2/d^2=9*10^-10 N, which is not correct.

I am given an initial vector potential let's say: \begin{equation} \vec{A} = \begin{pmatrix} g(t,x)\\ 0\\ 0\\ g(t,x)\\ \end{pmatrix} \end{equation} And I would like to know how it will transform under the Lorenz Gauge transformation. I know that the Lorenz Gauge satisfy...

Are lost volts the difference between EMF and terminal pd?

Greetings, in one of the exercise sheets we were given by our Prof, we were supposed to draw the trajectory of a patricle that moves toward a bounded spherical potential that satisfies ## V(\vec{r}) = \begin{cases} V_0 & | \vec{r} | \leq a \\ 0 & else \\ \end{cases} ## for...

For this part(b) of this problem, The solution is However, I tried solving (b) like this: Since ##Q_{total} = 363 \times 10^{-6} C## then ##Q_1 = 181.5 \times 10^{-6} C ## since the equivalent upper capacitor is in series with the equivalent bottom capacitor so should store the same amount...

Hello everyone, All living things have a growth cycle in which they gain mass and volume. These elements are obviously and undoubtedly taken from the environment in which these creatures live. Therefore, it is undeniable that the amount of potassium, for example, in the body increases during...

For 2D charge distribution ρ(x,y)=Ne PDF(x,y), where PDF is the normalized probability density function with its peak on (0,0) and has standard deviations σ x. and σ y. Are the contours with the equal probability "PDF(x,y)=const" the same as the equipotiential contours?, I tend to think that...

Can anyone explain to me why grounded means zero electric potential. I confuse what's the relation between infinite ground conducting plane and its electric potential (the method of images). I have a several question: 1. Why the conductor plane must be infinite, while in reality there's no...

Can anyone explain to me why grounded means zero electric potential. I confuse what's the relation between infinite ground conducting plane and its electric potential (the method of images). I have a several question: 1. Why the conductor plane must be infinite, while in reality there's no...

For A.1 of this problem, The solution is However, I have a doubt about the linear charge density ##\lambda##. I don't understand how ##\lambda = \frac {q}{2\pi R} ## since this is not a thin ring, but has a non-negligible width of ##2a## I think that the toroid has a larger area than thin...

The solution chooses the centre wire to determine the potential difference, where Va−(0.909 A)(2.00 Ω)=Vb and Vb - Va = -1.82 If I choose the top wire (passing through the 12 V battery and 4 Ω resistor), Va - 12 + (1.636 A)(4.00 Ω)=Vb, and Vb - Va is different (= -5.46 V). Why would this path...

I don't understand why the Uranium 238 ions are accelerated I think ##\Delta V = -2000 V## to accelerate since the ion would be accelerated by more postive charges so ## V_i > V_f ##

For part (a) of this problem, The solution is However, my solution is Am I correct? In the solutions that don't appear to plot the electric potential as units of ## \frac {k_eQ} {a} ## like I have which the problem statement said to do. Many thanks!

Assume you have a two particle system, A, which has a mass and gravitational pull of g, and B, an object with low mass, The system starts at time 0 with the distance between A and B being 0, A being at rest and B having enough kinetic energy to move it a distance r away from A, until time t all...

Hello, guys! I have a question. How can I prove the behavior of a particle subjected to an infinite potential? Will the wave function exist?

Hello, so we have two potitions right, if we take ##\theta = 90## as the first position (i.e. both rods are flat) and then the second position at ##\theta = 0##. I totally understand the exercise, not difficult. The only issue I am having is the torsional spring... it says that it is uncoiled...

I want to follow the Lienard-Wiechert potential derivation in Robert Wald's E-M book, page 179. I do not understand $$dX(t_\text{ret})/dt$$ on the right side. I assume the chain rule is applied, but I can't see how. $$ \frac{\partial[x'^i - X^i(t - |\mathbf x - \mathbf x'|/c)]}{\partial x'^j} =...

"Heat is the transfer of kinetic energy between molecules. If the velocity is more, the kinetic energy will be more so that the heat is more." "As an object's speed increases, the drag force from the fluid increases exponentially. For example, when you drive at high speeds, the frictional force...

when you do a multipole expansion of the vector potential you get a monopole, dipole, quadrupole and so on terms. The monopole term for a current loop is μI/4πr*∫dl’ which goes to 0 as the integral is over a closed loop. I am kinda confused on that as evaulating the integral gives the arc length...

It is to my understanding that if the spring was compressed 10cm, it is due to the Work of the Weight Force of the stone. So: Work done on the spring by the stone = m.g.x = 7.84 J The work done on the spring will be stored as potential energy of the spring, so: Us = W Us = (1/2).k.x² k =...

Hi Unfortunately, I can't get on with the following task. The system looks like this it is divided in such a way that the same number of particles is present in each ##\epsilon## section. I am now to determine the energy ##E(P_h,V_h,N)## at the height h using the energy ##h=0## i.e...

1. To find the solution simply integrate the e_r section by dr. $$\nabla g = A$$ $$g = \int 3r^2sin v dr = r^3sinv + f(v)$$ Then integrate the e_v section similarly: $$g = \int r^3cosv dv = r^3sinv + f(r)$$ From these we can see that ##g = r^3sinv + C## But the answer is apparently that there...

I have wrote all feilds and potentials and I want to find the constants. My first question is " when we say in the a<x<2a the potential is V(x)" then the potential in the a is V(a) or V(0) ( cause it is 0 in our new area) ? Second one is " when I want to write the gausses law for the point x=a I...

Hello! I am trying to use the wavefunctions of a Morse potential as defined in the link provided. They define a parameter ##z## and the wavefunctions are in terms of z. In my particular case, given their definitions, I have ##\lambda = 132.19377##, ##a=1.318 A^{-1}## and ##R_e = 2.235 A##. I am...

I am trying to reproduce the results from this paper. On page 10 of the paper, they have an equation: $$ \frac{S}{T}=\int dt\sum _{n=0,1} (\dot{c_n}{}^2-c_n^2 \omega _n^2)+11.3 c_0^3+21.5 c_0 c_1^2+10.7 c_0 \dot{c_0}{}^2+3.32 c_0 \dot{c_1}{}^2+6.64 \dot{c_0} c_1 \dot{c_1} \tag{B12} $$ where they...

Hello everyone, I was looking at the light matter interaction Hamiltonian and I worked out a simple calculation where I was surprised to see that I had to introduce an explicitly non-local vector potential if I want to go further: $$\langle\psi|...

Hi, I'm working on a problem where I need to find the different energies allowed for a potential, and I found this link https://quantummechanics.ucsd.edu/ph130a/130_notes/node151.html, which is similar of what I'm doing. I'm using mathematica to find the values of E. However, I'm not sure how...

I have a nanoparticle of cadmium selenide with a diameter d. When it emits a photon with a wavelenght lambda, it happens because an electron jumps from the conduction band to the occupied band across a forbidden band. I can suppose that jump as a jump from a higher energy level (the conduction...

Part (a) was simple, after applying $$Q=\int_{\mathbb{R}^3}^{}\rho \, d^3\mathbf{r}$$ I found that the total charge of the configuration was zero. Part (b) is where the difficulties arise for me. I applied $$V(\mathbf{r})=\frac{1}{4\pi \epsilon _0}\int_{\Gamma }^{}\frac{\rho...

Ki + Ui = Kf + Uf 1/2)kx2 = (1/2)mvf2, but W = (1/2)mvf2 = F∆d, so 1/2)kx^2 = F∆d. The solution says that I should just substitute v as d/t. But could anyone explain why my reasoning is wrong? Thanks.

This is the diagram provided in the question: The ring is made of conducting material. I was originally asked to find the potential difference between ##a## and ##b##. I did so using the Hall effect (and assuming it would work as per normal in this situation). This got me ##\Delta V = vBl##...

I don't understand where I went wrong, the formula and calculations which I have attached are correct...please do help if anyone can spot the mistake.

I am currently studying to solve Maxwell's equations using FEM. I have a question about Maxwell's equations while studying. I understood that the magnetic potential becomes ▽^2 Az = -mu_0 Jz when the current flows only in the z-axis. I also understood the effect of the current flowing in a...

I can calculate the electric field strength at any point above the plane with Gauss' Law (##E = \frac{\eta}{\varepsilon_0}##) and so the electric potential at any point a perpendicular distance ##z## above the conducting plane (##V=−\frac{\eta}{\varepsilon_0}z##). But I'm having trouble taking...

I have attached my attempt and proof that my attempts were incorrect.

I solved laplacian equation. and got the solution of V(r, phi) = a. +b.lnr + (summation) an r^n sin(n phi +alpha n ) + (summation) bn r ^-n sin( n phi +beta n)

The context: I created an educational resource, a set of interactive diagrams that allow the user to see how Hamilton's stationary action arrrives at the true trajectory. There is a diagram for each of the following three cases: - Uniform force, hence the potential increases linear with...

In the case motional emf, there is a static magnetic field and a rectulgular loop that goes into the field region, then current is produced. There is no electric field, but there is an emf. However, Griffiths states that emf is equal to the potential difference between the source endpoints. But...

The Lagrangian for a massless particle in a potential, using the ##(-,+,+,+)## metric signature, is $$L = \frac{\dot{x}_\mu \dot{x}^\mu}{2e} - V,$$ where ##\dot{x}^\mu := \frac{dx^\mu}{d\lambda}## is the velocity, ##\lambda## is some worldline parameter, ##e## is the auxiliary einbein and...

If I start with two, otherwise isolated, masses M and m initially together and do work to separate them then the work done, I assume, goes into the gravitational binding energy between them. Will the system of mass M and m have increased in mass due to this in accordance with e=mc^2? I...

So, I am able to calculate the electric potential in another way but I know that this way is supposed to work as well, but I don't get the correct result. I calculated the electric field at P in the previous exercise and its absolute value is $$ E = \frac {k Q} {D^2-0.25*l^2} $$ This is...

The vectorfield is $$A = grad \Phi$$ $$A = x^2 + y^2 + z^2 - (x^4 + y^4 + z^4 + 2x^2y^2 + 2x^2z^2 + 2y^2z^2)$$ The surface with maximum flux is the same as the volume of maximum divergence, thus: $$div A = 6 - 20(x^2 + y^2 + z^2)$$ This would suggest at the point 0,0,0 the flux is at maximum...

I have a little doubt about Morse potential used for vibration levels of diatomic molecules. With regard to the image below, if the diatomic molecule is in the vibrational ground state, when the oscillation reaches the maximum amplitude for that state the velocity of the molecule must be zero so...

Suppose there is a pressurized gas canister in space, at rest. With a mass "m" of gas inside of it at a pressure "P". Next the valve of the canister is opened. The canister will accelerate in the opposite direction to the valve opening. When all the gas has left the canister, it will be moving...

I am trying to derive radial and axial magnetic fields of a current carrying loop from its magnetic vector potential. So far, I have succeeded in deriving the radial field but axial field derivation gives me trouble. My derivation of radial field (eq 1) can be found here. Can anyone point out...

While reading this thread on Stack Exchange... https://physics.stackexchange.com/questions/113092/why-does-a-system-try-to-minimize-potential-energy ... a question came to mind : - Say an object is launched away from Earth at a velocity greater than the escape velocity. This system will not end...

The Higgs mechanism is an ingenious mechanism inspired by condensed state physics. The famous Mexican hat potential ensures a VEV value of about two times the mass of the Higgs particle (which, as an aside, is of comparable order as the W and Z vector bosons, the difference though is that its a...

Hello everyone! I noticed in the derivation of potential energy, Mr Lewin defined the gravitational potential energy of a mass m at point P relative to a much larger mass M. He says the potential energy of m at point P is equal to the work he would have to do to move the mass m from infinity to...