Potential Definition and 1000 Threads

Homework Statement Homework Equations Thermodynamic Identity The Attempt at a Solution While I was able to work out the problem with the help of the hint, I couldn't completely understand the implication of said hint. The hint suggests that the equations for Chemical Potential in a process...

I am tasked with finding the path a particle takes through this potential field. $$U(x,y) = x^2+xy+y^2$$ I then took the gradient, and this produced a pair of differential equations. $$\frac{d^2x}{dt^2}=\frac{1}{m}(-2x-y)$$ $$\frac{d^2x}{dt^2}=\frac{1}{m}(-2y-x)$$ I have yet to encounter set of...

Homework Statement (a) What voltage will accelerate electrons to a speed of ##6.00 \times 10^{-7} m/s## ? (b) Find the radius of curvature of the path of a proton accelerated through this potential in a 0.500-T field and compare this with the radius of curvature of an electron accelerated...

Homework Statement Four protons (each with mass 1.7 10-27 kg and charge 1.6 10-19 C) are initially held at the corners of a square that is 7.1 10-9 m on a side. They are then released from rest. What is the speed of each proton when the protons are very far apart? (You may assume that the...

My textbook doesn’t go into it, can someone tell me why Taylor expansion is used to express spring potential energy? A lot of the questions I do I think I can just use F=-Kx and relate it to U(x) being F=-Gradiant U(x) but I see most answers using the Taylor expansion instead to get 1/2 kx^2...

Homework Statement Homework EquationsThe Attempt at a Solution ## V(r) = \frac 1{r^3} \left( A - Br^2 \right )## At the bottom of the well, r is verry small. So, ## V(r) = \frac A{r^3}## Assuming the validation of Equipartition of energy theorem, since the degrees of freedom is 1, the...

In fact I am not sure if this is the right place to ask such a question but I'm going to ask anyways, just tell me if I am in the wrong place. So I doing a little experiment with the Schröndinger's equation, but the problem is I can't find a certain function. You all know the Schrödingers...

Homework Statement I want to derive the expansion of ##\Phi(x)## in rectangular coordinates: $$ \Phi(\vec{x}) = \frac{1}{4\pi \epsilon_0} \bigg[ \frac{q}{r}+\frac{\vec{p}\cdot \vec{x}}{r^3}+\frac{1}{2}\sum_{i,j} Q_{ij} \frac{x_ix_j}{r^5}+\ldots\bigg]$$ Homework Equations $$\vec{p}= \int...

Homework Statement I have a particle of mass m. The particle is moving in direction of axis z because of the gravitational force of a homogeneous circular disk of mass M and radius a. There is a formula for gravitational force of the disk on the picture. Task: 1) Find the formula of...

I've read that two electrons can become entangled in a "potential well," which is a point where potential energy is lowest compared to its surroundings. Is this correct? What does this have to do with entangling particles?

Hello guys, came across some Analytical Physics lectures (http://www.physics.rutgers.edu/ugrad/227_f11/classes/lect08.pdf) that got me confused. It is described in the lecture the problem of determining the force between capacitor plates for a constant voltage (ie. connected to a battery). For...

Homework Statement Posting here because it was over a previous homework assignment and I don't understand the solution that was given out. For reference, the problem is 2.27 is Griffiths' Introduction to Electrodynamics. It reads "Find the potential on the axis of a uniformly charged solid...

Homework Statement A particle with charge q1 = -6.75x10^-6 is located at (0,3.25x10^-2 m ) and a second particle with charge 3.2x10^-6 is located at (0,-2.75x10^-2 m) what is the electric potential due to the two charges at the origin? Homework Equations V = kq/r The Attempt at a Solution So...

Homework Statement Given an isolated system of 2 particles in space, we can express the motion of both particles as follows: $$m_1\ddot{\vec{x_1}}=-\frac\partial{\partial \vec{x_{1}}} V(\vec{x_1},\vec{x_2})\\ m_2\ddot{\vec{x_2}}=-\frac\partial{\partial \vec{x_2}} V(\vec{x_1},\vec{x_2}),$$ where...

Homework Statement A beam of particles of mass m and energy E is incident from the right unto a square well potential given by ##V(x)=-V_0## for ##-a<x<0##, and ##V(x)=0## otherwise. Solve the Schrodinger equation to determine the wave function which describes this situation. Determine the...

In class while learning about electromagnetism, I was given the following two equations: U=-μ⋅B τ=μ×B where μ=IA First of all, what does μ stand for? How should I interpret the relationship between potential energy (U) and torque? Can someone explain this in terms of μ and B?

Homework Statement Homework EquationsThe Attempt at a Solution a. ##{ P }_{ avg }=\frac { 1 }{ 2 } \mu v{ \omega }^{ 2 }{ A }^{ 2 }=\frac { 1 }{ 2 } 0.075\frac { 10 }{ 3 } { 0.35 }^{ 2 }{ (10\pi ) }^{ 2 }=15.1W## b. Not sure how to calculate that... I'm guessing it'd be some integral over 1...

I have a discussion going on with some friends. The discussion goes like this: We have two identical tanks. One is empty. One is full of water. Both placed on the ground. They are connected with a hose at the bottom. There is a ball valve in line with the hose. The full tank has a given...

Homework Statement The volume charge density for some charge configuration is given as ## \rho (x,y,z) = \lambda \delta(x) \delta(z) [\theta(y+L)-\theta(y-L)]## where ## \theta(x)## is the step function, defined as ##\theta(x)=1## for x>0 and 0 for x<0. a) Calculate V(x,y,z), the potential...

Homework Statement I was going through a worked example in my textbook to gain a better understanding but after I had a go myself it is the opposite to what I have calculated. I have attached the worked example which asks you to calculate the gain in gravitational potential moving from a point...

Homework Statement A disc of radius R lying in the xy-plane is composed of an inner disc of radius R/2 carrying a uniform surface charge density +σ and an anulus (inner and outer radii of R/2 and R) carrying a uniform surface charge density -σ. Assume that the inner disc and the annulus are...

Homework Statement ( The following problem is taken from kleppner's " Introduction to mechanics" ) ( The question in the book talks about the velocity but my confusion is related to the Energy ) Homework Equations Conservation of Mechanical energy : Ef - Ei = 0 Consevation of Momentum : Pf -...

Homework Statement Find the potential at points P1, P2, P3, and P4 in the diagram due to the two given charges. Homework Equations VP =k∑qi/ri p = q ⋅ d The Attempt at a Solution I'm not sure how to approach the problem. I thought about using that given equation four times and adding it all...

Homework Statement What is the strength of the electric field between two parallel conducting plates separated by 1.00 cm and having a potential difference (voltage) between them of 1.50×104 V? Homework Equations ΔV = qΔU ΔV = -∫E⋅dl E = kq/r2 The Attempt at a Solution I am not sure where to...

I've been studying PEM fuel cells for a while and wondered if they could be used for electrolysis. I was surprised at first to find out the technique had been used for decades, but after watching this animation the dynamics make much more sense...

If we had a a sample of atoms in thermal equilibrium at a temperature, T, it would approximately follow a Maxwell-Boltzmann distribution and be isotropic. But if we now subject these atoms to a force in one direction (e.g. gravity, perhaps near a dense object), it will take the system out of...

Homework Statement A particle with mass m and spin 1/2, it is subject in a spherical potencial step with height ##V_0##. What is the boundary conditions for this eigenfunctions? Find the degeneracy level for the energy, when it is ##E<V_0## Homework Equations Radial equation \begin{equation}...

In the case of lifting a box, I know potential energy is negative because negative work is done by gravity. What does the negative part of -PE denote? Does it denote the direction of the energy or does it mean that energy is being lost? But how is energy being lost if the box gains more...

My book says: "Let us derive an expression for the potential energy associated with an object at a given location above the surface of earth. Consider an external agent lifting an object of mass ##m## from an initial height ##y_{i}##above the ground to a final height ##y_{f}##. We assume the...

Is the potential energy of a symmetric planar (x,y) charge distribution lower than any non symmetric distribution ? from the discussion on Gauss's law and symmetric charge distributions I would think so because the electric field could only be normal to the (x,y) plane in the symmetry case but...

Hi guys! I was wondering about the relation between the Gradient, Electric Potential, and Electric Field. I know that if you take the Gradient of a scalar field, you get a resultant vector field in which the vector points in the direction of greatest increase when you take a infinitesimally...

Homework Statement I have a few questions I'd like to ask about this example. (C1 was already derived before the second part) 1. What does the line "The rest of the coefficients make up the difference" actually mean? 2. What does "As one might expect...because of the admixture of the...

Homework Statement Determine the potential difference across the plates of the capacitor of the network shown in the figure. Homework Equations kirchoff's loop rule q=vc 3. The attempt at a solutio applying kirchhoffs law starting at bottom right point, q/c2-E1+q/c1+E2=0 =>E2-E1=-q/c1-q/c2...

work done in taking positive charge from A to B in electric field E= potential energy at B - potential energy at A OR potential at A-potential at B Am i correct in both formula?

1. Homework Statement A particle with mass m and spin 1/2, it is subject in a spherical potencial step with height ##V_0##. How is the general form for the eigenfunctions? What is the boundary conditions for this eigenfunctions? Find the degeneracy level for the energy, when it is ##E<V_0## 2...

How can I find the potential energy of a string of mass m and length L that has a block of mass M attached to it? The string is uniform, so I know its center of mass is at L/2.

Homework Statement When calculating the Fourier coefficients of the potential of the following lattice (the potential is a sum of deltas at the atom sites): I get the wrong coefficients if I choose the following primitve cell, with primitve vectors a1,a2: And the right coefficients if I...

From CNN: Powerful Hurricane Irma is rapidly intensifying in the open Atlantic and poses a major threat to the Caribbean and potentially to the United States next week. With the storm still five days away from the outermost Caribbean islands and at least a week away from any potential US...

My textbook states that an alternative definition of the change in potential energy is the work required of an external force to move an object without acceleration between two points. I am confused on why it says acceleration. Wouldn't that mean that the acceleration is 0 and therefore the...

Why there is the term ##\frac{3}{5}## in the formula of the electrostatic potential of a nucleus $$U_e = \frac{3}{5} \cdot \frac{(Ze)^2}{4 \pi \epsilon_0 R}$$

Homework Statement Two concentric spheres have radii a and b with b>a. The region between them is filled with charge of constant density p. The charge density is zero everywhere else. Hence, find the electric field of all points , then find the electric potential. 2. Homework Equations [/B]The...

Homework Statement In Fig. 26-5, how large must R be if the potential drop from A to B is 12 V? (The figure has been pasted into the attached file). The answer to this problem is 3.0 ohms. I keep trying to solve this problem but I get a wrong answer. The answer I get from my calculations does...

Homework Statement A molecule of nitrogen has a diameter of 3.2 x 10-8 cm and can be ionized upon absorbing 14.5 eV. what potential must be applied to a parallel-plate ion chamber operating at a pressure of 50mm of mercury, and with an electrode separation of 3.0 cm, in order to produce...

Homework Statement An electron that accelerates from a point near a collection of negative source charges toward a point near a collection of positive source charges experiences A) a decrease in electric potential energy as it moves toward a region at a lower electric potential B) a decrease...

Homework Statement A point charge of + 2.0 μC is placed at the origin of coordinates. A second, of − 3.0 μC, is placed on the x-axis at x = 100 cm. At what point (or points) on the x-axis will the absolute potential be zero? Homework Equations V= ko*∑ (q/r) The Attempt at a Solution My work...

Here is the Wikipedia page on electrode potentials. Here's how I'm reading it, which makes no sense: If a singly ionized atom of strontium donates an electron to the hydrogen in the standard hydrogen electrode, this will emit 4.101 eV of heat (395.68 kJ/mol). If cesium is used, there will be...

This might be either an obvious one, or I might be totally off track. I haven't seen, or been able to find neural action potentials being referenced as signal transductions. Aren't they signal transductions? And if not (say if action potential is only referenced to the change in potential)...

Potential of a body is defined as the amount of work done in bringing that body from infinity up to some point divided by its charge. The Earth has zero net charge, so the work done in bringing any charge from infinity till the Earth is zero. So what do statements like, "The potential of this...

when the external electrical potential difference is applied across the conductor ,electrons flow in the direction opposite to the current.Whether the number of free electrons in the conductor decrease?

Homework Statement I want to find the charge and potential drop across each capacitor Homework EquationsThe Attempt at a Solution I know both the capacitors are in series and hence have the same charge on them. However I don't know how to calculate the potential drop across the capacitors...