Potential Definition and 1000 Threads

Hi. At age 70 having retired and now having time to study I am just completing my first-year physics degree at the open university with good results. It is I think healthy and good to have an ongoing ambition, mine to get a job with the ESA before I am 80, maybe but clearly optimistically to be...

My attempt was to consider spherical shells of radius ##r## (##r\leq R##))and thickness ##dr## and then the potential energy of this shell would be in the field only of the "residual" sphere of radius ##r## (a result also known as shell theorem) $$U_{dr}=G\frac{\rho\frac{4}{3}\pi r^3 \rho 4\pi...

In generic terms and expressions without going into specificity or nature of fields/forces in order to highlight the same, how exactly could we characterise the distinction between 'Potential' & 'Potential Energy'?

I've already tried to calculate the potential with respect to the 3 segments and then apply superposition (V1+V2+V3). However, I was not very successful. My error I think is in the calculation of the radii, mainly of the line segment that is on the z axis. Can anybody help me? I need some light...

= -3.7298538168*10^13, -2.0594767123*10^13 Ive tried this equation with both masses and my homework keeps coming back with the wrong answer. I've tried checking my arithmetic but I cannot find anything wrong with it please help haven't gotten the chance to try B but I am pretty sure it will be...

I could try to apply the Liénard-WIechert equations immediatally, but i am not sure if i understand it appropriately, so i tried to find by myself, and would like to know if you agree with me. When the information arrives in ##P##, the particle will be at ##r##, such that this condition need to...

Suppose a charged particle is in an electric field and feels an electric potential. Then the particle travels through a wormhole to another electric field and the particle feels a different electric potential. The potential energy of the particle will change. So what will that part of potential...

I think the answer is that the elastic potential energy will be a 1/16th of the original value. This is my reasoning: 1) If the diameter doubles, the cross sectional area is 4 times the original value. (from A= πr2). 2) F= stress/area. Force (load is the same). If cross sectional area...

Hamilton’s principle minimises kinetic energy minus potential energy, that is, with a fixed kinetic energy, Hamilton's principle maximises potential energy. What if we consider the limit that the kinetic energy or the mass/the inertia can be ignored then the lagrangian is solely the negative of...

I've heard in this video that the voltage is the electrical potential difference, for two points (A, and B) you measure their voltage and you subtract to find the difference. If you measure the voltage at A isn't that a 'electrcal potential difference' between two points? So is the voltage at...

Hi, if the force is the derivative of potential energy, does it mean that the force is equal to mg and with a constant gravity, it will be the same at any height? But in real life, F (or mg) would be different on the Earth's surface and 400 km above it (~8 m/s^2). So, this formula is used to...

Suppose I have some interaction potential, u(r), between two repelling particles. We will name them particles 1 and 2. I want to find the force vectors F_12 and F_21. Would I be correct in saying that the x-component of F_12 would be given by -du/dx, y-component -du/dy etc? And to find the...

So the potential energy of an object in a gravitational field is pe=hmg where h is the height of the object in the gravitational field in meters m is the mass in kilograms and g is the acceleration in meters per second per second I read on an answer to a question that the force to lift an...

1. Golf ball initial potential energy uncertainty (110-5kg 0.01 m 0.01m/s2)= 110-9J4.31210-5=4.31210-14j 2. Golf ball initial potential energy calculation (4.4 x10-4kg 9.8 m/s2 0.609 m)= 4.31210-54.31210-14j 3.Golf ball final potential energy uncertainty ( 110-5kg 0.0 m0.01 m/s2)= 0.0 J 4...

I was thinking about the vacuum airship concept that was conceived a long time ago. For example: I think the main problem is the required structural strength of the container, and also being light weight. I have not run any numbers, what do you think the potential issues with the following...

I am thinking about the reason why we cannot probe the built-in potential across a diode with a voltmeter. Obviously, a diode is not an energy source, so it is impossible for it to show a voltage reading. After doing some research, I found some explanations and some questions about them. 1. The...

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...

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...

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...

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...

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...

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...

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...

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...

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##...

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...

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

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.

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.

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

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...

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?

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

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...

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...

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...

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...

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##...

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...

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

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...

##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...

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...

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...

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}}...

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

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:

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...

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...