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We consider for example this image,
which is a polar graph of a naval unit's on-board instrumentation with vector radius (or polar radius) $\rho$ and anomaly $\theta$ or polar angle.
We know that a point $P=(x,y)$ in an orthogonal Cartesian coordinate system may be identified in a polar diagram with coordinates $P\equ... |
If I stir up some liquid helium in a container with an irregular shape, I'd expect to see a vortex break up into smaller and smaller vortices. Since liquid helium has no viscosity, I would also expect that the rotational inertia would be sustained in this process. So what happens as the vortices become vanishingly smal... |
When using Bernoulli's Equation we sometimes assume that the velocity is zero if the tank is very large. Why can we do this? Is it because the pressure is assumed to be zero as well?
|
I am currently building a laser scanning microscope setup. I need to focus the laser on my sample and also place a quarter-wave plate right before the sample so I can control the polarization of the light. Right now I am having a hard time figuring out the solution to the beam drift during continuously rotating the qua... |
Consider a distant observer traveling at .866 c relative to the solar system along the line that is co-linear with the sun's axis of rotation. According to his/her wristwatch the observer measures the earth's orbital period around the sun to be 730.5 days, correct?
But the observer also measures the major and minor axe... |
I'm trying to determine the redshift observed for a light signal between 2 observers (let's call them observers one and two) in a flat matter-dominated universe. Observer one sends a signal ($t_1$) at light speed to observer 2 and she records it as a z of 5 ($t_2$). Observer two then sends a signal directly back. At wh... |
Below is a diagram of a simple pendulum with a 'fixed pivot point' and a rigid spherical mass $m$ attached to the end of a string.
I have shown the forces acting on the mass, its weight $mg$ and the string tension ($T1$ and $T2$) for the 2 snapshot positions.
I have also drawn a red line along the equator of the spher... |
Given that $\hat{r} \psi = r\psi$ where $r$ is the position of a quantum particle, and where $\hat{p}=-i\hbar \nabla$, the notes I have simply state that
$$[\hat{r}_i, \hat{p}_j] = i\hbar \delta_{ij}$$
where $\delta$ is the Kronecker delta.
Is there a proof of this from the fundamental results i.e. the definitions of t... |
The classical way to derive the equation of motion of a pendulum with an isotropic rod is to study its motion with respect to its pivot point, that is, point $A$ in the following figure
Then, given that the moment of inertia with respect to point $A$ is $I^{(A)} = \tfrac{1}{3}mL^2$, we have
\begin{align*}
&-mg\sin \th... |
Quantum wells where the potential varies along only one direction are typically solved assuming that electrons can only move along the direction. What happens when the 'well' is actually an infinite slab and the electron is free to move in any direction? The wavefunction can be broken up as X(x)Y(y)Z(z). If the well po... |
I am currently studying quantum mechanics and statistical mechanics, and I am rather new to QM. I have a question from the following section in the notes:
Systems of many identical particles, such as assemblies of photons or
assemblies of electrons are very important in physics. These systems
require a special treatme... |
For a mechanical wave, the energy transported is directly proportional to the square of its amplitude.
In quantum physics, the energy of a photon is proportional to its frequency.
Will changing the frequency of light also affect its intensity?
|
Suppose I have multiple light sources in a 2 dimension plane (X and Y), for which I only know the real and imaginary component of the electric field in the X and Y directions within the 2D plane.
This image is an example of such a case. There is 3 sources S1,s2,s3 and I only know the electric fields $\vec{Ex}=A+Bi$ an... |
It is generally said that entropy always increases. But after the Big Bang elementary particles came together to form an atom. Isn't that paradoxical ?
|
We know that change in internal energy is equal to heat supplied - work done in a cyclic process. The change in internal energy is zero and work done is non-zero. This implies that the heat given is non zero then how can the enthalpy change be 0?
|
In the Intro to Quantum Mechanics textbook by Griffiths on page 105 equation [3.116], I'm confused about 3 things.
What is $$\hat{Q}$$ supposed to represent? At first they use the variance definition but then they treat it as an operator. In fact, if they really used the variance definition, it should have just been ... |
Two astronauts are in the same circular orbit of radius R around the Earth, 180 deg apart.
Astronaut A has two cheese sandwiches, while Astronaut B has none. How can A throw a
cheese sandwich to B? In terms of the astronaut’s period of rotation about the Earth, how long
does it take the sandwich to arrive at B? What i... |
Given that $$\langle \hat{A} \rangle = \langle \psi|\hat{A}|\psi \rangle$$
Why does $\langle \hat{A} \rangle = \mathrm{tr}(\hat{\rho} \hat{A})$, where $\hat{\rho}$ is the density operator, $\hat{\rho} = |\psi\rangle \langle \psi|$?
More importantly, how does trace manifest itself in a general operator, that is not a ma... |
I don't know much about this topic so I am sorry if my question is silly. As far as I understand if neutrinos are Majorana particles, one consequence is that neutrinos are their own antiparticles. This can be observed, for example, in neutrinoless double beta decay. However, if we take the following reaction: $$\nu+p\t... |
Light creates gravity, and the greater the light's frequency, the greater this gravitational effect is. It stands to reason then that light of different colors would react slightly differently to gravitational fields. Namely, bluer light would bend more than red light, causing gravitational lenses to act like prisms.
|
The LC circuit has a Hamiltonian:
$$\hat{H}={E_L\over2} \hat{\varphi}^2 + 4E_C \hat{n}^2$$
where $\hat{\varphi}$ is the magnetic flux and $\hat{n}$ is the number of charge.
What is the Hamiltonian for the following circuit?
|
A body free to rotate about a given axis can make angular oscillation. This angular oscillation are called Angular simple harmonic motion,
In derivation,
Ohm = theta ✖ w ✖ cos(wt+ phi)
Where omega is angular velocity, w is angular frequency and theta is maximum angular displacement . I am really confused bewteen two!
... |
The case $\lambda=1$ is well known free field kernel. What about $\lambda$ in between 0 and 1 ??
... for $\lambda>1$ I have a proof that the kernel is not reflection positive ,
but for $\lambda<1$ there is the so called fractional Brownian motion representation of the corresponding semigr... |
Arc discharge and dielectric breakdown - are these the same phenomena?
With the subtle distinction, arc discharge generally occurs in the gaseous state and dielectric breakdown in condensed matter.
|
So the radius $R$ of the nucleus is directly proportional to $A^{1/3}$ (the nucleon number).
As $$V = \frac 43 \pi r^3,$$ this makes $V$ directly proportional to $R^2$. Also, as the nucleon number increases, the mass also increases and as the masses of protons and neutrons are similar you could say that the mass of the... |
First of all, I don't really believe that humans are special. So I know the answer must be that they are not.
But the way quantum mechanics is described is that all particles exist as clouds when humans are not looking but exist as particles when humans look at them. How is this consistent with the fact that humans are... |
Can anyone explain the principle that results in a distant object being perceived as larger when viewed from an elevated position? eg: I notice when viewing a Shipping Vessel from the shoreline it appears significantly smaller than when viewed from an elevated position of approx 30 meters & 1/2 mile inland from the sho... |
This is related to my previous question:
Hamiltonian of a quantum circuit including a diode?
The current most promising candidate for quantum computing are superconducting circuits, Transmon for example. One problem with Transmon, an anharmonic oscillator, is the leakage to higher energy levels when trying to drive ... |
If we are dealing in one dimension, what will happen if a hypothetical particle Tachyon (pure imaginary rest mass, $v>c$ and real momentum & total relativistic energy)? Will it interact with the normal particle, and is it legal to apply the relativistic momentum and energy conservation in dealing with such a problem?
|
I am going to explain what I think I know and how that leads up to my question - please correct any false claims I make or conclusions I draw.
I initially thought that $G$s were defined purely by acceleration. This confused me though, because when a body is at the surface of the Earth, even without change in velocity, ... |
Proof:
Suppose there are two forces, F1 and F2, acting on two ends of the rope, in directions parallel to the rope. Obviously the net force F equals F1 - F2 (in the same direction as F1)
We know F=ma.
Since m=0, we have F = 0. Hence, F1 - F2 = F = 0. F1 = F2.
Q.E.D.
In other words, as long as there are two forces acti... |
I am just confusing myself with binding energy and the binding energy curve.
I want to know whether I have interpreted the graph right.
So when both nuclei have a nucleon number over 56 and are fused together, the product nucleus must have a binding energy which is less than the binding energy of the two lighter nuclei... |
The wikipedia page for atomic radius shows two periodic tables for the atomic radius https://en.wikipedia.org/wiki/Atomic_radius
One was published by slater in 1964, the other by Clementi in 1967. I understand why those tables are different, but I am asking myself if these radii are still somewhat correct. I found that... |
I'm given the following problem:
At what times is the particle found at $x= 20m$?
I know this is a very fundamental problem, but still I cannot see how the answer ends up being $4$ and $12$. Note that I'm asked to use "motion diagrams" and/or vector arithmetic, not any formulae here.
|
A box of mass $m (kg)$ is on a slope and is attached to a wall via a light, in-extensible rod, which prevents the box from sliding down the slope. There are a few more details in the diagram above. The box is in equilibrium.
My aim is to find the value of the thrust, $T$ in the rod in terms of $m$, and the friction fo... |
What is the most efficient way to simulate steady state configurations of the Ising model? I am just interested in having a large set of random steady state configurations of the 1D Ising model (with homogeneous coupling constants). A few ideas came to mind:
Brute force sampling. Since the Ising model is exactly solva... |
It is theorized that till about 380,000 years after the Big Bang, the universe was opaque. Why did the particles present before the formation of atoms make the universe opaque? Why did the universe suddenly became transparent once the atoms started forming? And how do we know that it was opaque since the stars hadn't s... |
The structure functions $F_2^{\rm ep}$ and $F_2^{\rm en}$ for electron-proton and electron-neutron deep inelastic scattering deduced from the model of valence quarks and sea quarks of proton and neutron have the expressions$$
\frac{1}{x}F_2^{\rm ep}(x)=\Big(\frac{2}{3}\Big)^2[u_p(x)+\bar{u}_p(x)]
+\Big(\frac{1}{3}\Big)... |
The phenomenon of all photons being detected at only one detector seems quite reasonable to me, classically. If a photon gets deflected at the first beam splitter for whatever reason, it gets deflected at the second BS as well for the same reason. Similarly, if a photon passes through the first BS and it does the same ... |
Both in classical (non-relativistic) electromagnetism and in relativity the equation of motion of an electron in electromagnetic field is
$$ \frac{d\mathbb{p}}{dt}= e(\mathbb{E}+\frac{\mathbb{v}}{c}\times \mathbb{B}).$$
The momentum $\mathbb{p}$ in the non-relativistic situation is $m\mathbb{v}$, while in the relativis... |
Is it possible to make an atom which is half matter and half antimatter (mostly meaning that it's particles are equaled) ? And if it would be possible, how this atom would behave comparably with its normal counterpart?
|
I am currently reading Sean M. Carroll’s book about General Relativity. He claims that, in order to convert a tensor density of weight $w$ into a true tensor, one should multiply by $\sqrt{|{g}|}^w$, where $g=\det g_{\mu v}$ is the determinant of the metric. Knowing that $g’=\left(\det\frac{\partial x^{\mu’}}{\partial ... |
If $h=h(T, P)$.
Does $ dh = c_pdT + \left[v - T\left(\frac{\partial v}{\partial T}\right)_P \right]dP \Rightarrow h_2 - h_1 = \int_{T_1}^{T_2} c_pdT + \int_{P_1}^{P_2}\left[v - T\left(\frac{\partial v}{\partial T} \right)_P\right]dP $ ?
If so, how?
I apologize for this, but I just haven't been able to find an appropiat... |
A typical mammal cell has a double lipid layer membrane that is hydrophobic on the inside. This is the way cells separate their internal milieu from the external milieu, allowing differences in ion and other solutes concentrations. So even in non-aquatic animals, cells have water inside and outside most of their cells,... |
In "Our Mathematical Universe" Tegmark claims that inflation theory implies the existence of an infinite set of universes.
My simple question is: what kind of infinity, and why that kind ?
I am not sure whether the amount of universes at any point in time is infinite in this model, but supposing that that amount is inf... |
I have a question about a specific step in this problem that comes from 'University of Chicago Graduate Problems in Physics', Cronin, Greenberg, and Telegdi.
A long hollow cylindrical conductor of radius $a$ is divided into two parts by a plane through the axis, and the parts are separated by a small interval. If the ... |
Physically, what would it look like if we lived in a universe with a boundary at finite distance?
|
In the Ising model when $T<T_C$ with $T_C$ being the Curie temperature, there is a finite jump of the mean magnetization per spin, $m$, as the external field crosses $0$ (goes from negative values to positive or vice versa). What is the physical explanation of this non-analyticity?
|
When a body is rotated with a constant angular velocity $\omega$ and is dropped to ground, the friction should act as in the picture below
Now, because of the friction, the center of mass must accelerate forward and the body should continue moving forward until the friction stops acting when the velocity of the point o... |
I am reading the paper by Fradkin and Susskin on the lattice gauge theory (Order and disorder in gauge systems and magnets). In section III. C, where they were trying to introduce the duality transformation of the ($3D$) Hamiltonian form of $Z_2$ gauge theory, they define the so-called axial gauge, which is to require:... |
When a charged disc is rotated about it's axis does it exert torque on itself?
It seemed logical enough as there is magnetic feild associated with the spin of disc has force on it but I didn't find any way to calculate that feild at parts other than the center of the disc. Is there any logical way of approaching it.
If... |
I always see the form of the field operators derived by, in the case of a scalar spin 0 particle, imposing the field commutation relations on the classical field solutions of the Klein Gordon equation and interpreting te Fourier coefficients of the field, Fourier expanded in momentum space, as operators which will then... |
I've read that x-rays and gamma rays penetrate deeper whereas greater wavelengths like infrared don't go deep. Moreover, out of the two of radiations (alpha, beta) beta travels more in air on account of their small size. How and why does size/wavelength affects penetrating power?
|
In David Tong's lecture notes on Gauge Theory, in the section on 'Quantising the Colour Degree of Freedom', the following statement is confusing me,
Since we already have the constraint (2.16), this means that the vectors parameterise the projective space $
\mathbf{S}^{2 N-1} / U(1) \cong \mathbf{C} \mathbf{P}^{N-1}
$... |
I have a bunch of solid balls, each ball has a different diameter, a different mass and made from different material.
I can compare if one ball is heavier than another ball or if one ball is bigger than another ball, but I have no way of measuring it's mass or diameter.
What can I do to order them by their density ?
|
Instead of using the wire's magnetic field for deriving using Newton's third law can't we do the opposite using the magnetic field produced by magnet ?
I mean why doesn't the wire simply move in the direction of magnetic field produced by the magnet if magnet moves in the direction of magnetic field produced by wire ?
... |
In my problem I showed that $F^{\mu\nu}j_\nu$ is a contravariant 4-vector. Now the question is what is its 0-component's physical meaning, i.e. the meaning of $F^{0\nu}j_\nu$ if $F^{\mu\nu}$ is the electromagnetic tensor and $j$ the 4-current $(\rho,\vec{j})$. From the definition of $F^{\mu\nu}$ I know that $$F^{0\nu}j... |
Ok, I will try my best to ask my question without going too far into philosophy.
I am more or less aware of quantum physics and as far as I know it defies hard-determinism by saying that sub-atomic particles are completely random. Haven't all things in this universe a formula, but hard to determine by science and maths... |
How to choose the primary mirror focal length of a cassegrain telescope if your focal ratio is known.
|
Does cathodic protection work for cars if we attach a block of zinc to iron car chassis and connect car body to earth while parked in a garage?
|
The least-action principle is a statement in classical physics saying that all bodies in a system follow a trajectory that minimize the following functional (ignoring explicit time dependence for now):
$$
S[L] = \int dt L(x(t), \dot{x}(t)) \qquad\rightarrow\qquad
\frac{d}{dt}\Big(\frac{\partial L}{\partial \dot{x}}\Bi... |
About the diagram:
A tennis ball is attached to a string which is attached to the jar.
The string is mass less.
The density of the ball is less than that of water.
The F.B.D of the tennis ball:
Thus the ball is balanced by all this forces...
Experiment:
If we move the jar towards right then due to pseudo force,the ba... |
The second Newton's law of motion is : $\vec{a} = \frac{\vec{F}net}{m}$
I wanted to ask what was the need to define first law when we can easily derive from second law that when $\vec{F}net=0$ then ${\vec{a}=0}$.
|
Where does time function of wave on string go when expressed in the Fourier series?
A Standing wave on string of length $L,$ fixed at its ends $x=0$ and $x=L$ is: $\quad y(x, t)=A \sin (k x) \cos \left(\omega t+\phi_{0}\right) \quad$
Where: $k=\frac{n \pi}{L}$
A periodic function $f(x)$ with period $P$ is represented b... |
As matter inside a neutron star or black hole can vanish through collisions could be possible that antimatter did so more than matter in the very beginning of the universe through a high energetic process so a less quantity of antimetter remained and the result of getting anihilated with matter had as consequence predo... |
I got this Archimedes' principles from a website named smithplanets.com
Can you explain why we cut the volume of water equivalent to the weight of an object when the object is floating in the water and why we cut out volume of water equivalent to the volume of the object, if the object is submerged.
If you can give an... |
I am modifying light bulbs trying to use unique bottles and jars for the envelope. I was thinking I could prevent the filament from oxidizing by removing all $O_2$ before sealing it, and an easy way to do this is just fill the bottle with water and place the negative terminal inside the jar, completely filling it with ... |
I want to draw the "orbits" of a spherical pendulum under small oscillations. In this case its equations are given by $\ddot{x}_{1}=-x_{1}$ and $\ddot{x}_{2}=-x_{2}$. Of course the potential energy is given by $U=\frac{1}{2}(x_{1}^2+x_{2}^2)$, and the level sets of it will be concentric circles in the $x_{1}x_{2}$ plan... |
I will begin by stating the question and then I will explain my doubt. The relation between time-derivatives of a vector $\vec{u}$ observed from fixed and rotating frames (with a common origin) is
$$ \left[\frac{d\vec{u}}{dt}\right]_f = \left[\frac{d\vec{u}}{dt}\right]_r + \vec{w} \times \vec{u}$$
Question: I don't un... |
Consider an object which has been given a speed $v$ on a rough horizontal surface. As time passes, the object covers a distance $l$ until it stops because of friction. Now,
Initial kinetic energy = $\frac{1}2mv^2$
And final kinetic energy is zero. Therefore, work done by friction on the object is equal in magnitude to... |
I'm trying to get some intuition behind the spherical harmonics being the angular momentum eigenstates in quantum mechanics.
Firstly, am I correct in saying that we can imagine the angular momentum ($|L|^2$ and $L_z$ values) at every point in this angular momentum eigenstate wavefunction as being identical (and equal t... |
I was reading through applications of Lagrangian mechanics and the case of coupled oscillators. The example provided is the famous two pendula length $l$ mass $m$ hanging from the ceiling connected by a spring with spring constant $k$. We call their angles $\theta_1$ and $\theta_2$ as measured from the vertical. The to... |
I have a question.
Suppose we have a quantum mechanical system, of which we can measure 3 different observables.
Each of the observables has an eigenvector spectrum and we can express a state as a linear combination of the eigenvectors (we assume that they form a basis).
My question is the following.
The system is in p... |
When mergers involving neutron stars and / or black holes are simulated (e.g. when predicting gravitational wave signatures for these mergers), obviously complicated numerical relativity calculations are entailed.
My question is whether any matter terms are involved in these simulations (whether it be the interior of t... |
I am trying to use optical theorem* ( given in box 24.2 in Quantum Field Theory and the Standard Model, M. Schwartz ). I am trying to calculate the imaginary part of this diagram for the scalar field:
But I am getting extra factor of 2 in the calculation. I have calculated the imaginary part using complex analysis, an... |
If electric current is the movement of electrons, to what do the electrons in a wire get attracted to get a circular magnetic field?
|
When finding the slope of a position vs time graph, do you use sig figs?
For example, if the slope is 150m/10s, would the answer be 20m/s (because the least amount of significant figures in this is 1), or would it just be 15m/s?
|
How could I state in simple terms the differences between the literature of Complex Networks (after Albert-barabasi and Watts-Strogatz - Physics Literature) and the literature of Social Networks (older literature)?
I know that there are clear differences:
The amount of data;
The use of statistical physics to model ne... |
From my understanding, the magnetic field inside a solenoid is constant, so at points C and D, the magnetic field strength is the same. Magnetic field strength outside solenoid is minimal and is regarded as zero, so point B display this. But what about point A, it is just outside the solenoid, would the magnetic field... |
Then, it was pointed out by Thomson and Searle that this
electromagnetic mass also increases with velocity. This was further
elaborated by Hendrik Lorentz (1899, 1904) in the framework of Lorentz
ether theory. He defined mass as the ratio of force to acceleration,
not as the ratio of momentum to velocity, so he needed... |
We are asked to show that
$$\not A\not B = A\cdot B - i\sigma_{\mu\nu}A^\mu B^\nu $$
I know that
$$\not A = A_\mu \gamma^\nu $$by definition, and:
$$\sigma_{\mu \nu}=\frac{i}{2} [\gamma_\mu, \gamma_\nu]$$
Thus,
$$A_\mu \gamma^\mu B_\nu \gamma^\nu = A_\mu B^\mu - i\sigma_{\mu\nu}A^\mu B^\nu$$
$$A_\mu \gamma^\mu B_\nu \... |
How many degrees of freedom does a bead on a parabolic wire have? I think it must be two degrees of freedom since the bead is constrained to move on the wire (up, down motion and left/right motion). Is this correct, or does it only have one degree of freedom?
|
When do I use significant figure rules in physics for arithmetic.
I already know that I have to use it for unit conversions.
Where else would I have to use it?
|
I was revising some of the concepts from my old copies and I noticed something really weird (might not be weird for others). The texts with black pen when seen from behind the page had some yellowish and somewhat purplish appearance (as shown in figure)
1 :
2 :
3 :
(the texts might not be clearly visible in the ... |
$
\newcommand{\ket}[1]{|{#1}\rangle}
\newcommand{\bra}[1]{\langle{#1}|}
\newcommand{\braket}[2]{\langle{#1}|{#2}\rangle}
\newcommand{\acomm}[2]{\left\{#1,#2\right\}}
$Let $\{ \ket{1} \ket{1} \ket{2} ... \}$ be a complete set of orthonormal basis states for an infinite dimensional state space. Let $\hat{A} \ket{n} = n\... |
I am trying to make an educational echelle spectrograph using easily available materials, basically in a cardboard box. An echelle grating (36 lines/mm) needs another prism to do a cross dispersion and generate a two dimensional spectrum like the following (taken from a astro website).
The design I have is a very "cru... |
When a block of mass m is suspended by vertical spring system,it for sure perform SHM in the absence of damping force,only force which act on the system is internal which is -kx, where k is spring constant,so well so good but there is external force on the system which is gravitational force, which is mg (where g is ac... |
In introductory physics we are taught about position and velocity vectors. Though the representation of those vectors is identical (i.e. $x\hat{x}+y\hat{y}+z\hat{z}$) they must belong to separate vector spaces, as it would be nonsensical to add a position vector to a velocity vector. Now, when we multiply a velocity ve... |
Moving your weight back is equivalent to moving the pivot forward, like having a ball on a string and moving your hand forward, then, when it moves forward, moving your hand back.
What I don't understand is how you can propel it forward by only moving your legs forward, which should propel it back.
|
I saw this video on levitating a denser liquid on less dense air by vertical shaking. But I couldn't understand some points in the video. Particularly:
How did the liquid levitate?
I think it's because of vibrating the air in the vertical direction, which causes it to apply a force on the liquid in the upward directio... |
In sec.50 of this book, Landau discussed penetration through a barrier, and in the note he mentioned
In a passage from right to left through the lower half-plane, the function $\psi(x)$ at first increases and then decreases in modulus, becoming an exponentially small quantity on the left-hand axis ($\phi\to-\pi$), whi... |
Does viscosity depend on pressure? If depends, is there any equation by which I can calculate viscosity at a specific pressure?
|
According to Bohr's theory, electrons move around the atom in orbits having specific energy. When it absorbs energy, it gets excited to higher energy states. In H2 atom, ground state is -13.6 eV while other states have energy values: -3.4 eV, -1.51 eV and so on. But the modulus of these values are 13.6, 3.4, 1.51 etc, ... |
Consider the 2D Ising model on the finite lattice $\Lambda$ with $+$ boundary conditions, i.e., all spins outside of $\Lambda$ are $=+1$. Let $\mathscr{E}_\Lambda^b$ denote the edges in $\Lambda$ and the edges connecting $\Lambda,\Lambda^c$ so that the Hamiltonian is given by
$$
H = H_{\Lambda;\beta,0}^+ (\sigma) = -\b... |
A sphere of radius $a$ is in the vacuum and it's evenly charged with charge quantity $Q$.
Does an electric field has maximum exactly at the surface ($r = a$) or slightly above the surface ($r = a+0$) of this sphere?
$$E=\begin{cases}
0 &(r < a) \\
\frac{Q}{4\pi\epsilon_0 r^2} &(r \ge a)
\end{cases}$$
In my book it s... |
My university suspended all labs in the physics department and there is no virtual option, but for me to understand E&M I need to see some live experiments and do them myself. What lab kit on the market can help me understand concepts like Gauss' Law, electric potential and the mathematical justifications for the elect... |
Is there any generic way to calculate magnetic field in the moving inertial and noninertial reference frame?
For example, there is the Earth magnetic field, we can assume it is uniform permanent field. Let say approximately $50\mu T$ (microTesla). If I am driving the car with 100km/h and have magnetic sensor what it wi... |
Lets say we have a frictionless and massless pulley with a massless string over it. There are two masses attached to it $m_1$ and $m_2$ where $m_2>m_1$.
So $m_2$ would an experience an acceleration down while $m_1$ experiences an acceleration up and massless string would also move accordingly.
However, if the net force... |
I am comfortable with the argument that in order for the wavefunction to be single valued/2$\pi$ invariant this means that $L_z$ must be an integer value of $\hbar$.
$$U(2\pi e_z)=e^{-(2\pi i/\hbar)\hat L_z}=1$$
However I don't know how it follows from this that $|L|^2 = \beta \hbar^2$ where $\beta$ in an integer. $L_x... |
Let's say $t_1$ is the moment the radioactivity is gone:
$A(t_1) = A_0 e^{-kt}$
$A(t_1) = 0$ since it's gone
But then what? How do I find $t_1$?
Since $A_0 e^{-kt} = 0$ then I can't "$\ln$" both of sides because there is no such thing as "$\ln(0)$"
So what do I do?
|
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