Questions tagged [conventions]

A convention is a set of agreed, stipulated, or generally accepted norms. It typically helps common efficiency or understanding but is not required, as opposed to a strict standard or protocol.

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129 views

What is the correct form of Dirac equation?

Usually the Dirac equation in curved space is written as $$i\Gamma^{\mu}D _{\mu}\Psi-m\Psi=0,$$ where $\Gamma_{\mu}$ are curved space gamma matrices and $D_{\mu}$ is covariante derivative. This ...
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158 views

How is the Time Derivative of the the Electric Field Equal to the Current Density in Gaussian Units?

The microscopic form of Ampere's law with the Maxwell addition in Gaussian units states, \begin{equation} \nabla \times \vec{B} = \frac{1}{c} \left ( 4 \pi \vec{J} + \frac{\partial \vec{E}}{\partial ...
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35 views

Sign convention for spherical mirrors

What is the sign convention for this formulation of the spherical mirror equation? $$1/i + 1/o = 1/f$$ f is negative for convex mirrors. i is image distance. o is object distance. (How can the ...
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If I were to change the definition of refractive index [closed]

We know that the Refractive Index is just a number that gives an idea of how much velocity of light decreases in comparison to vacuum. So, it makes sense to define a variable, n as: n=c/v where v ...
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1answer
219 views

Why $1 \ \mathrm{fm}$ is often used in modern physics?

In the International System, we all know that a one femto (or one Fermi) is equal to $$1 \ \mathrm{fm}=10^{-15} \ \mathrm{m}$$ What is the historical reason why this unit of measure was adopted as ...
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41 views

Formulas with complete sign conventions for spherical mirrors and thin lenses

I'm looking for two things: Something like the third equation in the chosen answer in the link, but for spherical mirrors, and Something that covers conventions for the radii of curvature and focal ...
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1answer
67 views

Why electric potential energy at a point is the same as amount of work done to bring the charge to that point from infinity?

Let's consider a positive charge at a point in the space. Now, if we want to bring a another positive charge to a point within the electric field of the first charge, then we have to do some work ...
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3answers
194 views

Cross product and handeness

I'm having some difficulties understanding the cross product in a left-handed coordinate system. I want to compute $\hat{i} \times \hat{j}$ for both systems in the picture (the first one is right-...
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448 views

Velocity in circular motion, $v = r × \omega$ or $v = \omega × r$?

I know it might sound silly to ask, but is the relation between linear velocity and angular velocity of an object undergoing circular motion $ v = r × \omega$ or $v = \omega × r$? I didn't notice it ...
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1answer
202 views

Transformation of metric by diffeomorphism: pushforward or pullback?

Let $(M,g)$ be a smooth manifold with a metric tensor of signature $(p,q)$. The signature isn't really important for this question so we leave it general. If $\Phi : M\to M$ is a diffeomorphism we ...
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1answer
70 views

Correct transformation of left-handed Weyl spinor

In the book "Matthew D. Schwartz, Quantum Field Theory and the Standard Model", page 164, it says that a left-handed spinor transforms as $$\psi_L \rightarrow e^{\frac{1}{2}(i\vec{\theta} - \vec{\...
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For the potential difference, how is it that $V=W/Q$=$U/Q$ when $U$ and $W$ are negatives of each other?

I'm currently studying electric potential and am somewhat overwhelmed by all of the different equations and their iterations. For instance, the first definition I learned was that: $$\Delta{V}=V_b-V_a=...
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Electromagnetic field tensor (and other tensors) with different sign conventions

In Wikipedia the components of the EM Field Tensor are listed as $$F^{\mu\nu}=\left( \begin{array}{cccc} 0 & -E_x & -E_y & -E_z \\ E_x & 0 & -B_z & B_y \\ E_y & B_z &...
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1answer
111 views

Why is a Coulomb the charge of $6.24 \times 10^{18}$ electrons? [duplicate]

Where does the $6.24 \times 10^{18}$ number come from? How was it historically derived? I know that $1$ C $=$ $1$ A s but that just pushes the question down another step, and another and another, at ...
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Should the 4D normalization constant $8\pi$ in Einstein field equations (EFE) be changed to $(n-2)S_{n-2}$ in other spacetime dimensions?

Should the 4D normalization constant $8\pi$ in Einstein field equations (EFE) be changed to $(n-2)S_{n-2}$, where $S_{n-2}$ denotes the area of a $n-2$-sphere, in higher dimensions? The reason is that ...
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59 views

What's the point of choosing the reference direction of current to go from low to high potential?

In my textbook the author sometimes chooses the reference direction of the current $I$ to go from low to hight potential, from $-$ to $+$ and sometimes from high to low potential $+$ to $-$. I have ...
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Intuitive explanation why electrons move from low to high electric potential

I know almost nothing about physics but am about to learn some electronics. I have trouble understanding why electrons move from low to high electric potential based on the definition given on the ...
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1answer
58 views

Sign-Conventions for Spinor Transformations

In the literature one encounters a lot of different conventions for how left-handed spinor transforms (rotation angle $\phi$, rapidity $\beta$), among them $M_L = M_{(\frac{1}{2}, 0)} = e^{-i \frac{1}...
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4answers
106 views

Ambiguity between electric potential and voltage?

I understand that electric potential is a location based measure of electric potential energy per unit charge in an electric field, and that voltage is then the difference between two electric ...
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1answer
76 views

What's the most common convention for torsion and contorsion tensor index position?

In Einstein-Cartan theory, the torsion tensor is usually defined as the antisymetric part of the connection: \begin{gather} \nabla_{\mu} \, A^{\lambda} = \partial_{\mu} \, A^{\lambda} + \Gamma_{\mu \...
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63 views

How to decide the number of significant figures? [closed]

When we do calculations involving significant figures with their uncertainties, Which rule/rules do we use to decide the number of significant figures in the result?
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2answers
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Is it reasonable and common to interpret $dt$ as a time point (a point in time)? [duplicate]

I heard some one talked about the instantaneous and average velocities. He was using $\Delta t$ to denote a time frame, $dt$ denote a time point. average velocities $\bar{v} = \dfrac{\Delta s}{\...
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Why define $D_\mu = \partial_\mu -ieA_\mu$ with the electric charge $e$?

If $D_\mu = \partial_\mu - ieA_\mu$ then the QED Lagrangian is invariant under $$A_\mu \to A_\mu + \frac{1}{e}\partial_\mu\alpha(x)$$ $$\psi \to e^{i\alpha(x)}\psi$$ However if $D_\mu = \partial_\mu -...
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1answer
147 views

Why does the parity of a meson have a “+1” in it?

The parity of a meson is defined as $ P = (-1)^{L+1} $ where $L$ is the angular momentum. What does the "1" in the exponent represent?
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115 views

What does $\Delta$ stand for? [duplicate]

Newton’s first law states that $\Delta v=0$ unless acted on by an external force, $F_{\mathrm{net}}\neq0$. Can someone explain to me what the $\Delta v$ symbol means?
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29 views

Why is there a negative sign in the (non-relativistic) bivector formulation of the Lorentz force?

I'm currently trying to update my understanding of basic (Newtonian, non-relativistic) physics to use bivectors and Clifford products instead of pseudovectors and cross products. And I've come up ...
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0answers
55 views

Difference between position of indexes in tensor notation (SR) [duplicate]

I am learning SR, and don't understand the difference between the following notations of a Lorentz transformation $\Lambda$ $$\Lambda_{\mu\nu} , \Lambda_{\mu}\ ^\nu , \Lambda^{\mu\nu}$$ I know that ...
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Conventions for direction of current flow and forming a charge difference

I have explored many videos, postings, and lectures regarding the interaction of electricity, magnetism, and motion, including Fleming's Right Hand Rule and Left Hand Rule. While the explanations of ...
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1answer
78 views

Significance of the negative sign in $V=-\int \vec E · \mathrm d\vec r$ [duplicate]

Why is there a negative sign in the relation $$V=-\int \vec E · \mathrm d\vec r$$ between the electric field and the electric potential? Is this because of some derivation in vector calculus because ...
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92 views

Why am I getting a negative sign in this derivation?

I want to derive a formula for calculating the final velocity of an object that falls from rest as it reaches the surface of the Earth. I want to take the change in acceleration into account and hence ...
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1answer
197 views

Is there a $\pi$ in Planck's Radiation Law?

In Sear and Zemansky's University Physics with Modern Physics 13th edition and other sources like this post, it says the formula for Planck's radiation is given by: $$I(\lambda)=\frac{2\pi hc^{2}}{\...
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2answers
52 views

Potential barrier, vertically shifted

I'm attempting to solve the 1D Schrodinger Equation, approaching a potential barrier defined as follows: $$V(x) = \begin{cases}-V_0&\quad\text{for}\quad x<0 \\0&\quad\text{for}\quad x>0\...
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1answer
198 views

What is the difference between degree celsius and celsius degree? [duplicate]

It seems similar but can you guys please answer it that what is a specific difference between degree celsius and celsius degree?
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1answer
68 views

What's the preferred way of writing units per unit? [closed]

Why do we write units such as meters per second as $\mathrm{m\,s} ^{-1}$ instead of $\mathrm{m/s} $. Is the latter still a valid way of expressing units? Why are there two different ways of expressing ...
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1answer
77 views

Minus sign in perturbative expansion via Green's function (Schwartz QFT)?

In Schwartz's QFT textbook Section 3.5, the Lagrangian for the graviton $$\mathcal{L}=-\frac{1}{2}h\Box h+\frac{1}{3}\lambda h^3+Jh$$ with EOM $\Box h-\lambda h^2-J=0$ is perturbatively expanded in $h$...
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Why time is 4th dimension not 1st? [closed]

Yeah we can not define a line without a point but why time is not 1st. Also time exist in 1st dimension as well doesn't it?
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84 views

Potential and potential energy

I know when a negative charge moves in the direction of a uniform electric field its potential energy increases and its potential decreases. For example, its potential energy changes from $0.9\ \rm{mJ}...
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2answers
57 views

Soft X-rays and Hard X-rays

How to know how much of kilovolts are in soft X-rays, and in hard X-rays? (Ex: 80kV is in soft X-rays or hard X-rays?
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4answers
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Do air conditioner power ratings violate the 2nd law of thermodynamics?

I just got a new AC rated at 6000 BTU and wanted to determine its power consumption. Some research on AC conventions quickly reveals that 6000 BTU really means 6000 BTU/h, where BTU is a measure of ...
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335 views

In the equation $R = R_0 [1+αt(∆T)]$ is $R_0$ the resistance only at 0K/0°C?

For example, we're asked to find the resistance at a temperature 20°C, we know that the resistance at 10°C is 5 ohm, and we know the value of the temperature coefficient of resistance. Can we put Ro ...
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2answers
256 views

Quantizing Klein-Gordon Field: Sign Problem

I'm trying to re-derive the Quantization of the Klein Gordon Field but I'm running into sign problems. My starting point is: $$ \phi(x,t) = \frac{1}{(\sqrt{2 \pi})^3} \int \tilde{\phi}(k,t) e^{i kx}...
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1answer
208 views

Potential - When and when not to use infinity as a reference point?

I'm reading Griffiths' Electrodynamics and having a bit of a problem to understand when we can use infinity as a reference point and when it cannot be used. One question asked to calculate the ...
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37 views

Orientation and sign convention in 2D electrodynamics using differential forms

I've been following this paper for a treatment of electrodynamics using differential forms. In particular, they demonstrate that Maxwell's equations expressed using differential forms are form-...
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2answers
67 views

What is the fundamental reason behind electric potential decreasing in the direction of increasing electric field? Is there any exception to this?

Does this increase and decrease necessarily have to be linear in nature? I have seen this statement being thrown around which states that in direction of increasing electric field the potential ...
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Symbolizing frequency as $v$

In my school textbook $v$ is symbolized to the frequency of the wave. Is that correct? I also saw this convention used in Chemistry: The Central Science By Theodore L. Brown, H. Eugene LeMay Jr
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1answer
40 views

Mars longitude reference?

Platforms like NASA's JPL HORIZONS web-interface for solar system dynamics often have obtainable parameters like sub-solar or sub-terrestrial longitude for a given time and celestial object. (example: ...
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1answer
68 views

Confusion on negative charges, current, and direction

My text book seems to have two contradictory statements about the same subject. Under the electrical potential and capacitance chapter, it says that negative charges move from lower to higher ...
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1answer
77 views

Angle $\phi$ in astronomical coordinate transformations

I was reading about the transformation between horizontal coordinates (Alt-Az) and equatorial coordinates (RA-Dec) from Fundamental Astronomy by H.Karttunen. In the image, one can see the angle $\phi$...
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91 views

Energy Density is expressed in Liters, Liters of What?

When looking at energy density of batteries it is often expressed as Wh/L. For instance, Wikipedia says Lithium Ion batteries have a density of 250–693 W·h/L. Liters is supposed to express the volume ...
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154 views

How does one obtain $\hbar$ as $\frac{h}{2\pi}$?

I'm reading Dirac's Principles of Quantum Mechanics. He defines $\hbar$ to be the real number satisfying the following relation $$ uv - vu = i\hbar[u,v]$$ where $u$ and $v$ are dynamical variables, ...

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