Questions tagged [approximations]

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Can there be tension in an inextensible string?

In physics, tension describes the pulling force exerted by each end of a string, cable, chain, or similar one-dimensional continuous object, or by each end of a rod, truss member, or similar three-...
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3answers
266 views

Why is current not 0 in a regular resistor - battery circuit immediately after you closed a circuit?

In regular open circuits with either a capacitor or inductor element, (when capacitor is uncharged) with a battery, when a switch is closed to complete the circuit the current is said to be 0 because ...
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3answers
103 views

How strict are the boundaries that divide dimensions? Is a single-layer sheet of graphene 2D or 3D? [closed]

I would like to know if there is any theory that describes a set of rules that define the boundaries of dimensions. For example, does a single layer sheet made of graphene considered a two or a three ...
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2answers
127 views

Why can large objects at greater distance be treated as a point particle?

Why can large objects at greater distance be treated as a point particle? "The bodies of our solar system are so far apart compared with their diameters that they can be treated as particles to an ...
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3answers
70 views

Electric field generated by a small object

I've just begun to study electrostatics and I've read the coulomb law, it describes the electric field generated by a point charge as characterized by a spherical shape. I think it is due to the fact ...
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1answer
79 views

Models in physics [closed]

As I said in another question I am just a physics enthusiast so I am sorry for my very poor knowledge. What is meant by models in physics? what is their function and why physicists imply them? Are ...
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1answer
56 views

Why is it intuitively unreasonable for this transition probability to grow quadratically in $t$?

In Sakurai's "Modern Quantum Mechanics" section 5.6, there is a seemingly simple statement made that I do not understand the logic of. The author is considering a physical situation in which we "turn-...
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1answer
367 views

How can we consider charge to be continuous? [duplicate]

In electrostatics, we usually consider charge to be continuous on any body, to calculate the electric field of the body. For eg. I had proved the Shell Theorem taking an infinitesimal charge of $dq$ ...
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5answers
185 views

Which type of conductors don't follow Ohm's law? [closed]

Which type of conductors don't follow Ohm's law? I know that semiconductors and superconductors don't follow them, but why? And what about ideal conductors. What are they? Do they follow ohm's law? ...
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2answers
83 views

Are continuous densities only good approximations?

In a number of situations, continuous densities (e.g. for mass, electric charge, etc.) are used in calculations. However, for example, as far as I know, matter is not continuous. Also, for example, ...
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1answer
402 views

Post-Newtonian approximation for binary gravitating system

I have been studying gravitation waves radiated by a binary source. I have linearised Einstein's field equation and approximated the source to a Quadrupole moment to get the power radiated by the ...
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1answer
97 views

Electron electric field

As we know the fundamental unit of charge in our universe at the time of electrodynamics was an electron, and in any frame of reference, its radius is a finite number and assuming uniform charge ...
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2answers
829 views

Negligible Mass of String

I've recently been working through a lot of physics problems and a lot of them say to assume that the mass of the string used in a problem involving a pulley, for example, is negligible. Why is this ...
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1answer
64 views

What exactly does Ohm's law say?

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, R ...
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1answer
154 views

Coulomb's Law Question

The presentation of Coulomb's Law in various books occasionally has a note that the test charge, q2, must be small enough that it doesn"t alter the field of the first charge, q1. The same limitation ...
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1answer
107 views

Non-conservative forces in Lagrangian mechanics

In the Lagrangian formalism with a dissipative frictional force $F$, we can write $$\frac{d}{dt}\frac{\partial\mathcal{L}}{\partial\dot{q}_{k}}-\frac{\partial\mathcal{L}}{\partial q_{k}}=Q^{(nc)}_{k}...
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1answer
93 views

When and why are we allowed to treat a rigid body as a point mass?

When the subject Mechanics first taught, it is common that we explicitly state that the Newton's laws are valid only for point masses, and then we give examples of rigid bodies colliding with each ...
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2answers
161 views

Electric field charged disc and L'Hôpital's rule

I have been looking at the electric field of a charged disk and have a question about the use of l'Hopital's rule for the limiting case of electric field at points along the axis $z\gg$ disc radius $R$...
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1answer
49 views

An approximation question from “Nuclear Models” by Judah Eisenberg and Walter Greiner

I'm looking at page 311 of the book "Nuclear Theory" by Judah Eisenberg and Walter Greiner. Now for identity (49) which is: $$\omega_{1,2}^2=\frac{\omega_\alpha^2+\omega_\zeta^2-2bc\omega_\alpha\...
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2answers
1k views

Point object, Kinematics

I am very new to physics. This evening, I was reading about the concept of objects to be considered as point objects under some circumstances. And I was trying to think of circumstances under which ...
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1answer
135 views

conservation of momentum? [closed]

At hyperphysics I got this image, with the same description in text as is in this image It says that when a massive particle (say $A$) moving with a velocity collides with an object having a ...
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1answer
270 views

Born approximation and dipole approximation

I'm having some trouble really understanding when it's okay to use these approximations and why. I've been looking myself blind on equations, but I'm not even sure I understand it qualitatively. So I ...
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2answers
464 views

Taylor series: Epsilon not differentiated? [closed]

Why isn't epsilon differentiated with respect to time? (see my question on the right)
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1answer
1k views

How to use the WKB approximation to find wave functions?

I'm trying to learn how to apply WKB. I asked a similar question already, but that question was related to finding the energies. Here, I would like to understand how to find the wave functions using ...
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1answer
2k views

How to apply the WKB approximation in this case?

I'm trying to learn how to apply the WKB approximation. Given the following problem: An electron, say, in the nuclear potential $$U(r)=\begin{cases} & -U_{0} \;\;\;\;\;\;\text{ if } r < ...
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2answers
435 views

Discrete approximation of charge density

Given the electric potential $\Phi(r)$ and the Poisson's equation: $$ \nabla^2 \Phi(r) = - 4\pi \rho(r)$$ Consider the 2-dimensional case and let's say that I want to discretize this using a square ...
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1answer
342 views

Reference for understanding characteristic length and time scales in a system (in particular electronic transport)

I am working on the transport properties of two dimensional electron gas in semiconductor heterostructures and am interested in the characteristic length and time scales of the system like elastic ...
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1answer
48 views

Theoretical justification for the range of validity of the approximation $R(T)\approx R(T_0)[1+\alpha (T-T_0)]$

In the experiment for calibrating a platinum resistance thermometer, we are always approximating the resistance of the platinum thermometer by $$R(T) \approx R_0 (1+T),$$ taking the reference at $0^o ...
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1answer
62 views

Why is the Earth not an inertial frame of reference?

From many sources I have found the explanation that the Earth is not an inertial frame of reference because it rotates around its axis. However, nobody mentions the rotation about the Sun. What I ...
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2answers
83 views

Thick vs thin lens

What is the criteria to know whether a lens is thin or thick ? Suppose we have a lens of r1= 10 mm , r2= -10 mm and thickness is 5 mm. So, with this information what can we say about the lens whether ...
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3answers
153 views

Why we often approximate a wave function of a particle to Gaussian wave function?

I was solving problem of two particle system. We were taking wave function generally $\psi$. Later we approximated this wavefunction of two-particle system to double Gaussian wave function. My ...
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1answer
42 views

Approximating mechanical systems with high friction

I remember to have read (a long time ago) that if I have a mechanical system $\ddot x=\frac1mF(x)$ with a high friction, then I can instead study the other system $$\dot x\sim F(x)$$ to get an ...
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1answer
187 views

Nearly circular orbits (and their angular frequency)

In 'nearly' circular motion, the radius is not constant. If the force is central the and the angular momentum is still conserved, we have a central force: where $r_0$ is equilibrium position. For ...
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1answer
163 views

Two-source interference in the perpendicular direction and small-angle approximations

In the following setup, we have two point sources of light producing monochromatic, spherical light waves in-phase of wavelength $\lambda$, and a screen positioned in a plane prependicular to the line ...
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1answer
52 views

Approximations in general

In analysis, a statement like $f(x) \ll g(x)$ (as $x\to x_0)$, has a very precise meaning: $$ \lim_{x\to x_0}\dfrac{f(x)}{g(x)}=0. $$ I was wondering, when physicists write $L_1 \ll L_2$, for, say, ...
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128 views

Gravitational Field of a Photon compared to that of Massive Matter

[I'm aware relativistic mass is an outdated term, but I'm not sure what term to use in place of it] How is it that [as I've heard, perhaps incorrectly] photons can contribute to the stress-energy ...
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1answer
38 views

Entropy of two interacting spins with strong magnetic field

I want to calculate for two interarcting spins and an applied magnetic field the entropy. The values for the spins are $s_1= \pm 1$ and $s_2 = \pm 1$ and the Hamiltonian is given by \begin{align} H =...
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2answers
215 views

Quantum Gravity In Particle Accelerators

It is my understanding that we have no fully working model for Quantum Gravity. However, I imagine one would need to take quantum gravity into account when making discoveries in, say, particle ...
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3answers
141 views

Wave speed derivation

The wave speed derivation approximates the wave as a circle. It uses that to know that $$a=\frac{v^2}{R}$$However, numerous functions can approximate the wave. A straight line, $x^2$, $x^3$, etc. If I ...
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1answer
64 views

The Energy Equation

I've been studying the energy equation in relativistic motion $E= \frac{mc^2}{\sqrt{1-v^2/c^2}}$, which can be expanded as $$E = mc^2 + \frac{1}{2} mv^2\text{ + some other terms.}$$ I'm curious ...
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70 views

Am I using the variatonal method correctly conceptually?

Given A particle in a potential well: $V=-V_0 \exp(-x^2 / L^2)$ Goal Use the variational method to approximate the ground state energy My proposal The well (For $L=1$ and $V_0=10$) has the following ...
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1answer
4k views

Hartree-Fock: Coulomb integral [closed]

Today I was wondering how to better understand the Coulomb integral in the Hartree-Fock approximation. Extracted from: Szabo & Ostlund, Modern Quantum Chemistry, p. 112 The Coulomb term has a ...
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1answer
161 views

Magnetization $\ M$ of a ferromagnet as a function of temperature $T$, nearby $T=0$

Using mean-field theory, the magnetization per spin, $M$, for a ferromagnet always obeys the equation: $M=\frac{g \mu_{\mathrm{B}}}{2}\mathrm{tanh} \left( \frac{2}{g \mu_{\mathrm{B}}} \frac{T_{\...
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1answer
211 views

How to reconcile these two approximations?

I'm working on what should be a simple problem (Taylor Classical Mechanics problem 6.23.), but I'm having a tough time reconciling the many ways it can be tackled. An aircraft whose speed is $v_0$ ...
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1answer
2k views

Field from non-conducting plate?

For a non-conducting sheet, the electric field is given by: $$E = \frac{\sigma}{2\epsilon_0}$$ where $\sigma$ is the surface charge density. This equation holds well for a finite ...
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1answer
139 views

A sphere, a simple object?

In this video, the woman says that a sphere is a pretty simple object. What intrigues me is the use of a sphere for such a calculation. First of all, the sphere wouldn't be perfect as a perfect sphere ...
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1answer
93 views

semiclassical exact expression (in one dimension only)

let be $ N(x)= \sum_{n} H(x-E_{n}) $ the eingenvalue 'staircase' function and let be a system so $ V(x)=V(-x)$ and $ V^{-1}(x)=\sqrt \pi \frac{d^{1/2}}{dx^{1/2}} N(x) $ then would it be true that ...
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34 views

How to find the terms of Post-Newtonian approximation?

I am studying the Damour paper on the Post-Minkowskian approximation to the 2 bodies problem in General Relativity (paper) but can't really understand the explanation of the previous state of the art, ...
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0answers
51 views

High Temperature Expansions and Cumulants

In this paper the authors perform a high-temperature expansion of the correlation functions for a Heisenberg model on a lattice. Starting from $$\left<\mathbf{S}_i\cdot\mathbf{S}_j\right>_\beta ...
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29 views

What is the mathematical approximation for uniform gravitational field in Newtonian Mechanics? [duplicate]

When measuring the local gravitational field using a simple pendulum, one of the core assumptions is that the gravitational field is homogeneous. But the theory itself (Classical/Newtonian Mechanics) ...