Potential Definition and 1000 Threads

If both S1 and S2 are switched on, then the charge on the leftmost and rightmost surfaces will be zero. Also, we may assume that a charge q would appear on the left surface of Y, and a charge Q-q on the right surface of the same. due to this, there will be a charge q-Q on the left surface of Z...

I am very confused, all i have thought about right now is that, in that isolated branch connecting A, B and C, the net charge would be conserved. Not sure how to proceed. I feel that, if there is a charge ## -Q ##at A, and a charge ##-Q_1 ## at B, then the charge at C MUST be ## Q+Q_1 ## maybe...

In the article https://arxiv.org/abs/1112.1682 effective potential in equation 16 is approximated for early universe and obtained equation 21 and for later time in equation 26. Some constraints are given in equation 4 and 5. Can anyone explain how this approximations are made? I was trying to...

My interpretation of this equation is "how much does the electrical potential energy changes when I move the particle a little bit"? Suppose that I have some arrangement of charges, with Q at x and q at x'. Then I move the charge q a little bit in the direction of Q (dx), it will require some...

Here is my line of thinking: I know A and B aren't correct since the work done would be negative since the electric force and displacement are in opposite directions. When calculating the electric potential energies to consider options C and D, I thought the initial electric potential energy of...

Hello. Help me understand the energies. The energy of a particle in a potential well, formula 1. An electron in the field of a nucleus, as an example of a particle in a potential well, and it turns out according to this formula that the further from the nucleus, the more energy is needed. And...

For (a), I got ##V(r)=0## For (b), using Gauss law I get the electric field in the region to be ##\vec E=\frac{kQ}{r^2}\hat r##, then: $$V(r)-V(b)=-\int^{r}_{b} \left(\frac{kQ}{r^2}\hat r\right) . (-dr ~\hat r)$$ $$V(r)-0=\int^{r}_{b} \frac{kQ}{r^2} dr$$...

At first I tried using U1 = 1/2kx^2 from -x to zero then U2 from zero to +x but I don't know shall I add U1 and U2 or subtract them?

Hi I have problems with the following task I now wanted to try to calculate the vector potential, which according to my professor's script is defined as follows: $$\mathbf{A}(\mathbf{x}) = \frac{1}{c} \int d^3\mathbf{x}' \frac{\mathbf{j}(\mathbf{x}')}{|\mathbf{x} - \mathbf{x}'|}$$ I have...

The answer says it decreases but shouldn't it increase? according to the kinetic model, KE accounts for particle vibrations. PE accounts for the attractive forces between particles. Since condensation means gas -> liquid, it means the particles become closer and hence the attractive forces...

In r<a the potential is V_o. I don't understand why in a<r<2a, V(r)=V_o-\int^r_a E*dl. I would write V(r)=\int^r_a E*dl+\int^2a_\infty E*dl I dont know how to write math symbols here but I wrote question here...

Homework Statement: circuits - terms Relevant Equations: - How exactly can the electric potential be constant between two points in a wire; (assuming that it is electron current); if the electron is moving from a region of high electric potential to a low electric potential because of the...

Hello, I am having some confusions in what should be basic pointwise Newtonian mechanics, and would like to get some help with that. It is all about changing coordinates in potential energies. Let us start by considering a point particule in a 2d world with an axis x (left-right) and an axis z...

Theres a picture of the circuit attached. I did not understand how to start the problem since we dont know the distance between the terminal A and the sphere to write the absolute potential at terminal A. So I looked at the solution and im afraid I dont understand it at all. The teacher took...

My understanding of this question is that, if you have a proton standing against a positive electric field, and move it in the opposite direction of the field, you're putting in work and therefore should have greater electric potential energy. But that idea breaks down when you consider a...

I was doing a problem with this one detail. It says that the electric potential energy of an uniformly charged hollow sphere and a point charge is (at the surface of the hollow sphere; both positive): $$U = k \frac{q_1 q_2}{r}$$ I guess this assumes that the hollow sphere is a point charge. Now...

This comes from Griffiths' Electrodynamics and is problem 2.51 or 2.52, the disk has a surface charge density and my usual approach to solving these problems is to pick an area element and find a way to create a vector to the point(s) at which the potential is evaluated at. I sent a picture of...

We take out "formulas" for electric potential from the relation $$V=\int E.dx$$ Some general formulas are : For a hollow sphere : ##\frac{Q} {4π\epsilon_0 x}## when x>R, x =distance of that point from the center And the problem is we just input the distance in sums to calculate absolute...

I'm confused on this problem, as I feel they state two completely contradictory things in the explanation of how to solve it. The first statement that I feel contradicts the second is this: "We can see that the bullet’s speed v must determine the rise height h. However, we cannot use the...

Hello there, I'm training with some exercises in view of the July test, so I will post frequently in the hope that someone can help me, since the teacher is often busy and there are no solutions to the exercises. A particle of mass m in one dimension is subject to the potential: ##V(x) =...

In the last page of this image, the formula for the transmission coefficient, i'm not sure exactly what it means. The page says there is no reflection when the sine term is 0 cuz T=1), but for scattering states E>0 anyways? So won't it always pass through? Or is there a chance for a particle...

We know that in electrostatics, there is path independency for line integral of E, so E is a conservative field and thus we have E=-gradV. Integrating this from ro(reference point of our choice) to the point r we are studying, along a random path, we get the solution of the above equation...

Here is the exercise: And these are my attempts: This is for the first question about the electric field. (I know I'm missing the drawing, which is a drawing of the plane layer of thickness 2e with a cylinder on it as a GAUSS SURFACE ). As for the second question, I'm not sure about it, so I...

I expanded ET1=ET2 to get (Total energy at top) 1/2mv^2+mgh = 1/2kx^2 (Total energy at bottom) Rearanged i got k = (mv^2+2mgh)/x^2 so [(73)(20)^2+2(73)(9.8)(52)]/0.465^2 =479137.945N/m

I'm trying to follow the proof given in Box 5.3, page 235, of the MCP book regarding the Van der Waals grand potential. It seems to me that there is a missing factor (2l−1)!/(l−1)! in the last term of Equation (8). What am I doing wrong?

I originally thought that this problem was simple, and it still seems like it is, but there are conflicting solutions and I don't know which is correct. So I first solved for R1 and R2 using V=kQ/r where R1 is 0.514 and R2 is 0.54. My original thought was volume is conserved so V1 + V2 = V3 and...

So I understand that I have to integrate the negative of the force function to get the change in PE. I get -(20x^2 - 2x^3) and when I evaluate it from 0 to 2, I get -64N. But, of course, the change is positive. What am I missing? Thank you.

Hi PF, long time no see. Hope you are all well. Recently I have come into a mental conundrum of a cosmological physical nature. After doing some napkin calculations about the energy of celestial bodies and transforming them into mass via E=mc^2 I've found that said energy is by no means small...

I believe that this is due to context of application, but now, I'm starting to doubt myself. For example, a helicopter lifting itself has positive PE change. I really don't intuitively understand how this works. Can someone kindly explain this to me?

The book wanna show how to find potential of a dielectric. The problem arises when it uses a vector identity. Still there is no problem. My problem is that I cannot understand why ##\rho_P= -div P##? I think it should be ##-div' P##. The book is wrong? In next page it uses ##-div'## In...

Picture of question: Part (a) : ##\nabla \times \vec F = 0## so a Potensial exists. I don't have problem with this part. Part (b) : what I've done : First experssion is 0 because ##\theta = \dfrac {\pi} {2}##. I don't know how to integrate over ##\theta ## when it is a constant.

A homework thread, https://www.physicsforums.com/threads/point-charge-with-very-thin-metal-sheet-along-a-spherical-surface.1057702/, references https://arxiv.org/pdf/1007.2175.pdf. There is an uncharged conductor and a point charge. In the paper referenced, ##\bar\phi_y(x)## is defined as the...

I've been looking at a practice test for an introductory class in quantum physics, and I've found a really weird question. It asks for an estimation of the force that an electron exerts on the walls of a box of known length during a collision. This seems like an entirely nonsense thing to ask...

Given the potential energy, the force is obtained as F = -∇U(r). A conservative force field F is associated with a potential f by F = ∇f. Does the first expression arise from this last one? If so, with -∇U(r), would one obtain the electric field E instead of the force F?

This question is from Collection of Problems in Classical Mechanics by Kotkin & Serbo, here, the answer is given as the following: However, the graph of ##-Ax^4## looks like: so shouldn't the trajectory be just ##x(t)=0##?

Attaching the image of the problem as an image. Somehow text is not copied from the book. Somehow, I can't imagine the picture in my head. We can do it in 2D plane. I know, it mentions the solution, but need to see the drawing, otherwise, my logic fails. I thought that maybe, first half space...

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I am bit confused with voltage potential terminology again to basics When it is referred as Voa it is Voltage of "o" wrt "a". Is it correct? But other major question is as per the document I would have written KVL as Voa - I1 * Z = Vn. I am really confused with notation used.

Looking at the image, I see that due to symmetry, the bottom-left negative charge and the bottom-right positive charge cancel out, leaving me with a triangle around the center. I'm not entirely sure how to solve for potential at the origin specifically, but I believe that the potential energy of...

In the given circuit, a transient current will flow and when this current finally stops at equilibrium, the charges ##q_1## and ##q_2## are assumed to deposit at the capacitor plates as shown below. The dashed line indicates an isolated system that will have it's total charge conserved. If I...

Hey all, I am looking equations (13.24),(13.25) in Peskin & Schroeder's QFT book and I am confused about how they change from the Callan-Symanzik equation for the Effective Action to the Effective Potential. I thought the relation for constant ##\phi_{cl}## was ##\Gamma[\phi_{cl}] = -(VT)\cdot...

In some cases, photons can be produced in "back to back" (BTB) conditions. For example, electron-positron annihilation produces two photons, each at 0.511 MeV, with equal and opposite momentum. Or pretty close, up to the original velocities of the electron and positron. Start with a source of...

Problem: I have done part a) in spherical polar coordinates. For part b) I thought it would be just: $$\sigma = -\epsilon_0 \frac{\partial V}{\partial r}$$ But I got confused by "You may want to use different coordinate systems .." So I assume partial derivative w.r.t to r is the spherical...

(a) I know some of the apparatus needed for the experiment, such as DC power supply, ammeter, voltmeter, maybe rheostat. But I don't know how to change the temperature of diode. What is the correct and safe way to change the temperature of diode? Thanks

Electric potential = "absolute potential" Textbooks usually connect both ends of two capacitors, of different voltages, in parallel. What would happen if we only connect one end of the capacitors? Perhaps we would have to solve for Maxwell's coefficients of potential for these two cases (to...

I am struggling with how to go about this; in particular, I'm not sure I understand what state is being alluded to when Ballentine says "For an electron that approaches the surface from the interior, with momentum ##\hbar k## in the positive ##x## direction, calculate the probability that it...

Hello everybody, I consider two electrons that have enough kinetic energy to reach their respective classical electron radius. This would be: 2.0514016772310431402e-13 J The corresponding speed is v = 287336682 m/s. The electric field is E = \frac{k_{e}}{R_e^2} = 1.8133774657059088443 ×...

Here is a depiction of the problem a) The potential at any point P due to a charge q is given by ##\frac{kq}{r}=\frac{kq}{\lvert \vec{r}_s-\vec{r}_P \rvert}##, where ##r## is the distance from the charge to point P, which is the length of the vector difference between ##\vec{r}_s##, the...

I got answer for (a), which is 0.51 m For (b), loss of potential energy = 35 x 9.81 x 0.51 = 175 J Rate of loss of potential energy = 175 J / 1 s = 175 W But the answer key is 80 W. Where is my mistake? Thanks