# Questions tagged [approximations]

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### Why can the equation of adiabatic process $P_1 V_1^\gamma=P_2 V_2^\gamma$ be written as $\Delta P/P=-\gamma \Delta V/V$?

Why can the equation of adiabatic process $P_1 V_1^\gamma=P_2 V_2^\gamma$ be written as $$\frac{\Delta P}{P}=-\gamma \frac{\Delta V}{V},$$ where $P_2-\Delta P=P_1$ and $V_2+\Delta V=V_1$ as in ...
153 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 ...
37 views

### Working on Newton's Gravitational Law and cannot understand this approximation

Working through some questions in a text book and came across one which I did not quite understand how to find the solution. I looked up the solution in the manual and was unable to understand how ...
123 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 ...
61 views

### Taylor approximation vs setting to zero

I was recently solving a problem where I had to find the velocity of a particle. The correct result is the following: v^2 = v_0^2 + \frac{k\delta^2}{m}\left(1-e^{-\frac{\Delta^2}{\...
61 views

### Is it possible to approximate the motion under a V-shaped potential as harmonic motion?

Let's assume an $xy$ plane and let there be a force field defined by the potential $$V=F_0|x|$$ Though the potential is not differentiable still its a perfectly realisable system. If we solve the ...
4k views

### Elliptical Trajectory, or Parabolic?

Discuss whether this statement is correct: “In the absence of air resistance, the trajectory of a projectile thrown near the earth’s surface is an ellipse, not a parabola.” Is the above statement ...
23 views

657 views

### Understanding multipole expansion in classical electrodynamics

I am trying to better understand what the multipole expansion means from a phyiscal point of view. Although mathematically, one may say it is just another form of a series expansion, in this case, the ...
58 views

### Linear approximation of time dilation. In what point is it?

I have watched a video about linear approximation and there was an example, exactly here: https://www.youtube.com/watch?v=BSAA0akmPEU&feature=youtu.be&list=PL590CCC2BC5AF3BC1&t=32m50s ...
420 views

### Hartree-Fock decoupling of Hubbard model

Hartree-Fock approximation requires wavefunctions be as separable as possible. I know the basic idea of Hartree-Fock but having some trouble in formalism of second quantization. I am trying to ...
154 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 $R$...
477 views