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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Why is the cut off mass for massive stars 8 solar masses? Why can't it be 10-11 solar masses or so?

I know that stars having a mass greater than or equal to 8 solar masses are termed "massive stars". But why is the cut-off 8 solar masses?
2
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1answer
71 views

Wave equation in classical mechanics!

We represent the wavefunction of any wave on the string as $$y=f(x-vt),$$ where $v$ is velocity of the wave and $x$ is distance from origin and $t$ is time taken to reach the given point and $y$ is ...
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1answer
42 views

“Normalisation” in the unitary gauge

I will use the example of the Abelian Higgs model to explain my problem. Consider the Lagrangian: $ \mathcal{L} = - \frac{1}{4} F^{\mu \nu}F_{\mu \nu} + \left(D^\mu \phi\right)^\dagger \left( D_\mu \...
4
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2answers
85 views

Maxwell's equations from differential forms

I found the following in some lecture notes I took some time ago: $$ \mathbf{E}=-\text{grad}\Phi-\partial_t\mathbf{A}\\ \mathbf{B}=\mathrm{rot}\mathbf{A} $$ These are the electromagnetic fields ...
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2answers
85 views

Thought process [closed]

Voltage = Energy/ Charge If voltage comes out of the negative terminal through a wire to do the powering and then end up at the positive terminal, then what is it that comes out the positive terminal....
4
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0answers
65 views

Why are generators defined oppositely in Weinberg's vs. Maggiore's QFT books?

I've been confused about the sign conventions used in Weinberg's QFT book for a long time. Here's my question: The generators $J^{\mu\nu}$ are defined in this book as $$U(1+\omega)=1+\frac{i}{2}\...
0
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1answer
67 views

Does the imperial system have any advantages (besides its wide acceptance in the US)? [closed]

The United States (and one other country, somewhere in Africa I think) uses the imperial system (feet, pounds, etc.), while pretty much everyone else uses the metric system (meters, kilograms). The ...
0
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1answer
98 views

Rocket equation derivation mistake by my professor

In one of my lectures our physics professor gave a derivation of the ideal rocket equation as follows: Let $v_G > 0$ be the velocity at which the gas is emitted from the rocket. Let $m$ and $v$ be ...
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1answer
42 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 $\phi(...
0
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2answers
75 views

Electric Potential of Point Charge (sign problem)

This question has been asked before, but the answers didn't clarify the problem for me, so I thought I might ask again. It's really a simple question. Let's say we're calculating the electric ...
0
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2answers
33 views

Sig Figs, Combined Operations

Using the sig fig rule for addition / subtraction seems to break in certain circumstances. For example (I'm using underlines to show sig figs): $\underline{66}+\underline{66}-\underline{1.3}\times ...
0
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0answers
72 views

Need some help understanding Relativistic Notation

My question originates from what is done in the book on Quantum Field Theory book by Mark Srednicki on page 21 (if anyone has it). So say you have an inertial frame that is represented in the ...
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1answer
55 views

Deep confusion with conventions and signs in geometric optics

This is an equation given in my book. The question is why have they used a negative sign on the LHS? Now, if you try to derive the mirror equation with simple geometry, you get 1/v +1/u =1/f . ...
0
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1answer
26 views

Negative ampere and graphical convention

Since only electron's flow in electricity and electrons have negative charge, then why we don't say —1amps (—1C/s)? Secondly, as conventional way we write down independent variable in $x$ axis and ...
1
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1answer
62 views

Conventions and realities of kinetic energy?

I am having doubts regarding why $1/2$ is present in kinetic energy and if this is conventional why cant we say potential energy is $2mgh$ and kinetic energy $mv^2$. So is this $1/2$ conventional or ...
0
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1answer
75 views

Relation between gravitational field and gravitational potential

The gravitational field is the negative differential of the gravitational potential. Now the gravitational potential due to a particle at a distance $r$ is $-Gm/r$ where $m$ is the mass of the ...
1
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4answers
166 views

The sign of the current flowing in a circuit

I was doing the following problem: And I was asked to find Iy. I found Iy to be 2.64 using KCL. However, the right answer was negative 2.64. Is it negative only because there is a dependant ...
1
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1answer
47 views

Is the net force conventionally shown in a free body diagram?

Is it standard convention to display the net force vector on a free body diagram? Internet searches seem to give mixed results.
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3answers
166 views

Why is the Ricci tensor defined as $R^\mu _{\nu \mu \sigma}$?

The Ricci tensor is defined as the contraction of the Riemann tensor in its upper and the second lower index. I was wondering why it is defined this way. What happens if the Ricci tensor is defined ...
3
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2answers
83 views

Are ergs commonly used in astrophysics? If so, is there a specific reason for it?

I was reading the recent LIGO paper and one passage stuck out to me: The system reached a peak gravitational-wave luminosity of $3.6^{+0.5}_{−0.4}× 10^{56}\:\mathrm{erg/s}$, equivalent to $200^{+...
3
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6answers
156 views

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 ...
3
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2answers
80 views

How can “…electrons flow in metals, but not in the ground…” explain grounding rods?

I really enjoyed Why is the charge naming convention wrong? But, in the comments at the very end, the statement that "...electrons flow in metals, but not in the ground..." left me uneasy. I was ...
3
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2answers
130 views

Can an angle be defined as a vector?

In Classical Mechanics angular velocity, angular acceleration, torque and angular momentum can be defined as vectors with clear advantages such as the possibility to use vector product to simplify ...
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0answers
45 views

Why is surface tension positive?

My book describes surface tension as $e=dW/dA$ and work as being negative when it is done against a force. Therefore, if i increase the surface area of a liquid i am doing work on the liquid against ...
0
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4answers
88 views

When writing a differential equation, when do you take $+\text{d}x$ and when do you take $-\text{d}x$?

When writing a differential equation I'm confused as to when to write $+\text{d}x$ a and when to write $-\text{d}x$ a where $x$ represents some quantity. For example, I wanted to derive the equation ...
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2answers
68 views

Sign of induced EMF and other elements in AC circuit

I am having problems to determine the direction of the induced EMF in AC circuits. For example, we have an inductor of inductance $L$. The induced EMF is given by: $$ \epsilon = - L \frac{di}{dt} $$ ...
0
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1answer
49 views

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, ...
0
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1answer
224 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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0answers
14 views

What is the direction of area vector while calculating flux in AC generators?

I was told that in case of an open surface, the direction of area vector is considered to be in the direction of magnetic field but my doubt is won't the direction of area vector change as armature ...
3
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2answers
85 views

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 ...
6
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2answers
244 views

Performing Wick Rotation to get Euclidean action of scalar field

I'm working with the signature $(+,-,-,-)$ and with a Minkowski space-stime Lagrangian $$ \mathcal{L}_M = \Psi^\dagger\left(i\partial_0 + \frac{\nabla^2}{2m}\right)\Psi $$ The Minkowski action is $$ ...
0
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2answers
86 views

Kirchoff's law, can it tell me the direction of current in this case?

Say I want to find the current Ia in the circuit below: If I use the approach of using kirchoff's voltage law and ohm's law on the left loop, I get $-24V -12k\Omega*1mA -21k\Omega*I_a = 0$ $I_a = -...
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3answers
70 views

Correlation function $\langle s_1(x, t)s_2(x', t')\rangle$ vs $\langle s_1(x, t)s_2(x', t')\rangle-\langle s_1(x, t)\rangle\langle s_2(x', t')\rangle$

The correlation function in statistical mechanics is defined in either of two ways $$g(\mathbf{x}-\mathbf{x}', t-t') = \left\langle s_1(\mathbf{x}, t)s_2(\mathbf{x}', t') \right\rangle$$ $$g(\mathbf{...
0
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1answer
153 views

Two mass spring system

The equations of motion of the spring mass system with, m = 1 $ \ddot{y_1} = -k_1y_1 + k_1(y_2-y_1)$ $ \ddot{y_2} = -k(y_2-y_1) - ky_2$ My question is with the second term in the first equation. I ...
3
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1answer
342 views

How should Christoffel symbols be written (in LaTeX)? [closed]

I'm writing a summary of a lecture on relativity, and we've recently introduced the Christoffel symbols. It seems that the upstairs indices are the "leftmost" and the downstairs indices are somewhat ...
1
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1answer
68 views

Problem arising from quantisation of e.m. field

In my studies on the quantisation of the electromagnetic field I've come across a small calculation that I wasn't able to reproduce. Remember the following: In the Gupta-Bleuler method to quantize ...
1
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0answers
32 views

The sign of a focal length

We know that for converging lens, $f>0$ , for diverging lens, $f<0$. But for many materials I have read so far, it says that: "the focal length of a concave lens is 8 cm." I thought that the ...
4
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2answers
110 views

Does metric signature affect the stress energy tensor?

If one were to derive the stress-energy tensor for a metric with $(+,-,-,-)$ signature would it be different from the stress-energy tensor derived from the same metric but with $(-,+,+,+)$ signature?
3
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0answers
24 views

Conventions in defining spherical harmonics and associated Legendre polynomials

Relevant Background Spherical harmonics are defined with several different conventions: the definition used in quantum mechanics according to Wikipedia is $Y_l^{\,m}(\theta,\phi) = (-1)^m\sqrt{\frac{...
1
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1answer
50 views

What are the right signs? [closed]

This is a question provided in my book: An object of height $2\ \mathrm{cm}$ is placed at a distance of $2.5f$ from a concave mirror where $f$ is the focal length. Find the height of the image. ...
0
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1answer
119 views

Momentum conservation in the one-loop contribution of the photon propagator

The lowest contribution to the photon self-energy is represented by the following diagram (Taken from F.Schwabl, Advanced quantum mechanics, p.365):: ($k$ is the momentum of the photon that decays in ...
1
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1answer
45 views

Velocity-time-distance problem

In my book the formula for the $y$-component of velocity during the upward projectile motion is given: $$V_y=V_{iy}-gt$$ and next to it the formula for $y$-component of velocity during the downward ...
0
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1answer
140 views

Confused regarding sign convention of silvered plano convex lens

I'm totally confused while finding the sign convention of a silvered plano convex lens. I know that equivalent power of such a system can be found by adding the power of the mirror and twice the power ...
2
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3answers
208 views

Complex scalar field theory

For the complex scalar field theory $$L = -\partial_{\mu}\phi^{*}\partial_{\mu}\phi - m^{2}\phi^{*}\phi + J\phi^{*}+J^{*}\phi,$$ Why is there no factor of 1/2 in the lagrangian like in the real ...
0
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1answer
41 views

Integration path with opposite direction from the unit vector

The task is to calculate the voltage between points $M$ and $N$ if the electric field vector is known to be $\vec{E}=\frac{V_0\cdot x^2}{a^3} \cdot \vec{i} + \frac{V_0 \cdot y}{a^2} \cdot \vec{j}$, ...
0
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2answers
139 views

Defining gravitational potential

I recently came across the definition of gravitational potential where ..... Suppose a particle of mass $m$ is taken from a point $A$ to $B$. Let $U(A)$ and $U(B)$ denote the gravitational ...
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1answer
75 views

Why do physicists use a positive sign for the Fourier kernel / outward propagating waves? [closed]

I am not a physicist but rather an engineer / mathematician, so I've always wondered why is it that physicists use the positive sign convention in the forward Fourier transform. That is, in all of my ...
0
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1answer
109 views

Maxwell equations in 2+1 D

I have a problem with the Maxwell equations in (2+1) dimensions using differential form. Following J. Baez "Gauge Fields, Knots and Gravity" page 93 (or any other book), the equations are \begin{...
0
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3answers
109 views

What's the work done by a spring on a block when it moves from extreme to mean position?

I really don't know where am I doing it wrong, but block when it moves towards mean position displacement will be along the force right, so the force acting on block will be $+fxdx$ Integrating we ...
0
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1answer
70 views

Is the unit symbol written twice when using the +\- symbol?

When notating error using the $\pm$ symbol, are the units only ever included at the end? For example: 10.2 $\pm$ 3.2 m rather than 10.2 m $\pm$ 3.2 m This seems to be correct though I ...