Potential energy is the energy of a body or a system due to the position of the body or the arrangement of the particles of the system.

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Interaction between magnetic moments and magnetic field

Consider a particle with a magnetic moment $\vec{m}$. For simplicity, suppose that this particle is a circle in the plane $xy$ which can rotate around its center of mass along the $z$ axis. If this ...
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Electric potential energy of a charge

Potential energy is the work done by the particle against a conservative force. Isn't it? when a charge is fixed on a free space and then when we bring another charge from infinity to a distance r ...
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Total potential energy in electric field?

if there are 2 charges generally potential energy of the system should be the sum of individual potential energy. but why the potential energy is half of the sum of every individual charge's potential ...
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61 views

Why do a conservative force try to reduce potential energy?

Mathematically I understood the reason why, for a conservative force, $\vec{F}=-\vec{\nabla}U$. Physically this means that a conservative force is always oriented in the direction of greatest ...
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61 views

Why is the longitudinal term removed to form the Lorentz force equation?

Beginning with the expression for interaction energy, and deriving the potentials form for the force on a test charge moving at velocity $\vec v$ yields: $$\vec F = q(-\nabla\phi - {D\vec A \over ...
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Directional derivative of the potential energy in the direction of the displacement in three dimensions

For a conservative force $\vec{F}=-\vec{\nabla } U \implies \mathrm dW= -\vec{\nabla} U \cdot \mathrm d\vec{s} $ Where $\mathrm d\vec{s}$ is the infinitesimal displacement. For a differentiable ...
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Physical meanings of kinetic energy

While studying energy on Sears & Zemansky's University Physics, I came up with a doubt on the meaning of kinetic energy. The book gives two possible physical interpretations of this quantity. ...
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About Electric potential

when we bring a unit positive charge from infinity to a point in the electric field EF does work on the charge and external work is also done on the charge in same amount but in opposite sign. then ...
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42 views

Mechanical energy $E<0 \implies $ the system is in a bound state?

In a gravitational field if a body has negative mechanical energy, then the system body-planet (or star) is in a gravitationally bound state. The explanation that I have in mind for that is: since ...
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Binding energy of a galaxy?

I'm a novice in physics and new to the forms, so please forgive me if this is a dumb question or if this is in the wrong section to be posted, but how would one find the gravitational binding energy ...
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Interpretation of a case of the double square well

Consider a 'double square well' potential (where $E < 0$) defined as: $$V(x) :=\begin{cases} -V_0~~~~~~~~~~~~~\text{for }\frac{b}{2} < x < \frac{b}{2} + a \text{ and } -a - \frac{b}{2} < ...
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Potential energy (in lifting an object)

When a man of mass 60 kg lifts a mass of 20 kg upto height of 20m. The energy spent by him will be $mgh$. My question is should we add the masses of both the man and the object?. (Competetive ...
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Confusion about Conservation of Mechanical Energy

I'm having a bit of difficulty understanding how to apply the idea of conservation of mechanical energy to a problem. One of the questions on my homework reads: A physics student shoves a 0.50-kg ...
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Difference between potential centrifugal energy and rotational/kinetic energy

I'm having troubles to understand the difference between kinetic energy and potential centrifugal energy in some situations. I make an example where I am confused. A object moves on a rod attached ...
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45 views

Are ALL vibrations an exchange of kinetic and potential energy?

I'm taking a course on mechanical vibrational analysis and this is what I was told by my professor, but I'm curious if there are any counter-examples.
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89 views

How much the notion of force is discarded in modern physics? [closed]

Suppose that we are not allowed to use the notion of force to describe nature. My understanding of general relativity says that won't be a problem because the Einstein field equation doesn't involve ...
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49 views

Wave function for step potential

Given the step potential $$V(x)=\begin{cases} 0~~~~~~~~\text{if }~~x \leq 0 \\ V_0~~~~~~\text{if }~~x > 0 \end{cases}$$ Consider the case where $E < V_0$. In this region $x \leq 0$ we have ...
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34 views

Why potential at infinity is 0? (sphere of constant electrostatic potential)

Suppose I have a sphere of radius $R$ with potential $V_o$. Since the volume inside the sphere is bounded, then the lack of curvature of the potential (i.e. $\nabla^2\phi = 0$) gives a potential ...
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Energy potential of a cold sink inside the sun

An answer in this question discusses using a fusion engine in a theoretical spaceship within a star. ...
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Elastic potential energy and equilibrium position when mass changes in vertical mass-spring system

I'm a bit stuck with this situation: Suppose that an object $A$ with mass M=8 kg at 10 mt above the floor falls from rest tied to an 2 mt elastic rope, which does not exert any force since $A$ falls 2 ...
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Would this be a practical way to convert tidal energy into electrical energy?

Imagine a structure that is held above the water by pylons that are grounded on the ocean floor. In between these pylons is a pontoon that, when tides are rising holds and lifts a heavy weight. When ...
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Prove that gravitational potential energy of a body of mass m at a height h is mgh

Many introductory physics books just write that potential energy of a body of mass $m$ at a height $h$ as $U_g=mgh$. However, they never show how this was derived. I'm interested in knowing this ...
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How to find speed of rotation of gears from kinetic energy of falling body?

A pulley is fitted to the first driven shaft of compund gear train. Last driven shaft of gear train(gear 8) is fitted to the 12V DC generator (6W).Now to the rope extension at the one end of the ...
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Deriving the formula for energy stored in a spring without using geometry (determining the area under a curve)?

Using Hooke's Law, we know that the force applied is proportional to the extension of the spring. Therefore by plotting a graph of force against extension, through the area under the curve we are able ...
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Is this thought regarding work and potential energy correct?

I am really confused about this. The potential energy acquired by an object is equal to $mgh$, if we are on any planet, where $g$ is the planet's gravitational acceleration, which directly comes from ...
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Period on the phase plane (small oscillations)

I have this formula to calculate the period of a motion in the phase space (plan, in this case) along a phase curve. \begin{equation} T(E)=\int_{x_1}^{x_2}\frac{dx}{\sqrt{2(E-U(x))}} \end{equation} ...
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Energy of a body in circular motion?

I'm confused about energy of a body in circular motion. In particular I'm having trouble to find the correct answer to this question. Consider the body in the picture that is set in motion from ...
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Relation between gravitational field and gravitational potential

gravitational field is the negative differential of gravitational potential . now gravitational potential due to a particle at a distance r is -Gm/r where m is the mass of the particle . If i take the ...
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50 views

Electric Potential from separating charges [closed]

Say there are 2 charges, one of charge C, and the other with a charge of -2C. C=1.5*10^-6 C. Initially, they are right next to each other. I pull them apart to a distance of 15 cm. So I can use the ...
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79 views

Gravitational potential energy lost by an object falling on the earth [closed]

I am stuck on this simple question: g is the strength of the gravitational field at the surface of the Earth; R is the radius of the Earth. Show an equation describing the potential energy ...
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43 views

Potential Elastic Energy between two carts [closed]

I have a problem in which two carts are attached by a compressed spring. I have found that cart $A$ moves at $1.1~\mathrm{m/s}$ to the right and has a mass of $0.39 ~\textrm{kg}.$ Cart $B$ has a mass ...
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66 views

Calculating Potential Energy

I'm familiar with the potential energy equation, but I'm concerned with the value of 'g' in it. I know that, at sea level, earth's gravitational acceleration is 9.81 m/s/s. So I know that within the ...
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electric potential and other potentials

We know that without potential difference no electric current can flow.If two conductors carrying positive and negative charge respectively then the first one will have positive and the rest one will ...
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Does a potential of interaction produce also torque?

I have a system of particles (spheres with masses and radii), with $6$ degree of freedom (they are free to move and rotate as they wish). Between each couple there is an interaction potential $V(d)$, ...
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When we write that $F = -\nabla V$ , what would happen if we ommit the (-) minus sign

I have had this question for a long time. In classical mechanics, if we choose $\mathbf F = -\mathbf \nabla \, V,$ with the minus sign, we can proof the work - kinetic energy theorem. What are the ...
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Understanding parallel plate capacitors [closed]

I need help with understanding this assignment. I originally though of using the equation of Eo*A/D = Q/ΔV but I don't know how to answer this without actual numbers to plug in besides the epsilon-not ...
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184 views

Where Potential increase gets it's energy from?

Imagine there are two particles: A,B; of which, we observe A to be stationary, while B is moving towards A at velocity v. A,B has same mass; and they are charged both positive. B has a potential wrt ...
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is the potential energy of a black hole infinity

It appears like black holes posses an escape velocity greater than the velocity of light. It takes an atom infinity energy to travel at speed of light.Do black holes posses that energy to retain ...
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How does the gradient operator pick up a minus sign when the reference frame is switched from one particle to another? [closed]

A potential between two particles, $i$ and $j$, is given as a function only of the separation distance, $$V_{ij} = V_{ij}(|r_i − r_j|)$$ It should follow that the force by $j$ on $i$ is equal and ...
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Gravity well and constant total energy in circular orbit [closed]

According to this question, the total energy of an object in a circular orbit in a $1/r^2$ potential does not depend on the radius of the orbit. However, if you look at "circular orbits" in a gravity ...
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Why the force acting on a particle is the negative gradient of a scalar potential? [closed]

For conservative forces we can proof that it is a gradient of a scalar potential, but why we use the negative sign? In every book I searched, it said that it is like an agreement between physicists, ...
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How to efficiently cool down simulated gas by time-dependent potential?

I'm trying to simulate condensation of a highly diluted gas (a model gas, not any real one). For simplicity I restrict the simulation to 2 dimensions. To setup the simulation I take some interparticle ...
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176 views

How can energy be negative in a finite square well?

Say if the potential $V(x) < 0$ in the well but the sides or the scattered states its zero potential, anyways How is that the energy in the well is less than zero? Is it because the potential ...
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Confusion with $F=-\nabla V$, $F$ conservative

I am rather confused by the relationship $F=-\nabla V$. If a pen drops from a height it loses potential energy so $\nabla V$ is negative. From the above equation this means that the gravitational ...
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Mechanical energy of a body

What is the total mechanical energy of an air-plane flying in the sky? Does it possess both kinetic energy and potential energy,taking the zero potential energy at ground? As it is moving it will ...
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131 views

Charging by induction [closed]

When we charge an conductor by induction and grounding, we first bring a negative charge to the conductor. As a result the mobile electrons of the conductor get repelled and stay far from the negative ...
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Equivalence between principle of least action and minimum potential energy

Are the principle of least action and the principle of minimum potential energy equivalent? How does one show that? Also, are Newton's laws of motion equivalent to the principle of least action? How ...
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Why is the potential energy minimal when the repulsion and attraction force between molecules is 0?

According to this potentialcurve and the other curve(?) the potential energy is minimal when the intermolecular forces equal zero. Why? How should I interprete negative potential energy in this ...
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How does potential energy relate to kinetic energy on a rollercoaster?

This is appearantly how the potential and kinetic energy are in the different positions of the rollercoaster, if I am not mistaking. However I don't understand why the total energy is energy and ...
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Electrical energy in a piezoelectric material

How do we define the electrical energy stored in a piezoelectric material? I'm confused about both the naming and the meaning. Are "electrostatic energy density", "dielectric energy density" and ...