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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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 ...
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71 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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52 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 . ...
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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 ...
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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 ...
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74 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 ...
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4answers
165 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 ...
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46 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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164 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 ...
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80 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^{+...
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6answers
155 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 ...
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74 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 ...
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126 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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43 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 ...
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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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65 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: $$ \epsilon = - L \frac{di}{dt} $$ ...
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1answer
48 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, ...
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1answer
190 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 ...
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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 ...
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226 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 $$ ...
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2answers
79 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
69 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{...
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1answer
145 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 ...
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1answer
316 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 ...
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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 ...
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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 ...
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2answers
106 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?
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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{...
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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. ...
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111 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 ...
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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 ...
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1answer
133 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
197 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 ...
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1answer
40 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 $\vec{E}=\frac{V_0\cdot x^2}{a^3} \cdot \vec{i} + \frac{V_0 \cdot y}{a^2} \cdot \vec{j}$, ...
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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
72 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 ...
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1answer
108 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{...
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3answers
101 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 ...
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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 ...
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1answer
60 views

Why is a satellite's GPE negative? [duplicate]

Okay, so the formula for Gravitational Potential Energy (GPE) of satellites is: $$ U=-GmM/d$$ Mass and distance can't be negative, and $G$ is constant that is not negative. Why is a satellite's GPE ...
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1answer
63 views

Work done should be positive but it is coming out to be negative? [closed]

I have described a question in which this problem arises in the image below:
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2answers
123 views

Why specify the state of a particle in terms of position and momentum not velocity?

Often a particle's state is expressed in terms of position and momentum. Why not position and velocity? Momentum has a connection to the particle's mass which I wouldn't say is so important to the ...
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2answers
79 views

Complex conjugation of Weyl Spinors

Let $\chi$ be a left-handed Weyl spinor transforming as $$\delta\chi=\frac{1}{2}\omega_{\mu\nu}\sigma^{\mu\nu}\chi.$$ In my lecture notes it is explicitly stated that complex conjugation interchanges ...
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40 views

Non-linear pendulum (Whittaker's treatise on analytical dynamics of particles)

Reading through Whittaker's "treatise on the analytical dynamics of particles and rigid bodies" I have a question regarding his analysis of the simple nonlinear pendulum at chapter IV. At some point ...
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1answer
250 views

Gradient, divergence and curl with covariant derivatives

I am trying to do exercise 3.2 of Sean Carroll's Spacetime and geometry. I have to calculate the formulas for the gradient, the divergence and the curl of a vector field using covariant derivatives. ...
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2answers
70 views

What is time measured against? [duplicate]

Today I was observing a clock and its movement, every second is an exact second on every clock. I was making a comparison between a second and a meter. I know in France there is a metal stick one ...
2
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1answer
61 views

Definition of primary fields actually leads to a Witt algebra with a minus sign?

Let's take as an example Di Francesco et al. but every source I am aware of is doing the same. First of all, the Virasoro algebra is usually defined as $$[L_m,L_n] = (m - n)L_{m+n} + \frac{c}{12} m (...
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1answer
305 views

Electric field for concentric spheres

I have a couple clarifying questions: (A) in $E=kq/r^2$ for the area between a sphere inside another spherical shell, the sphere inside is considered a point charge. However, the sphere inside has a ...
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2answers
89 views

Why isn't the work minus the potential energy when bringing a charge in from infinity?

This is an example in my physics textbook, and there is just one step that I don't understand. Two point charges are located on the x-axis, $q_1 = -e$ at $x = 0$ and $q_2 = +e$ at $x=a$. Find ...