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How to calculate the charge and the potential across a charged capacitor charging an uncharged capacitor?

Initially, there is a single capacitor $A$ attached to a power source that charges it to a certain voltage $V$. Once it is charged, it is instantaneously removed and placed in a circuit with an ...
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1answer
228 views

Lenz' law versus $-\frac{d\Omega}{dt}$

I am preparing for an exam, on one problem my answer differ from the solution. The current $i(t)=I_0e^{-\alpha t}$ runs in a long straight conductor along $\hat z$. Point A,B,C,D forms a triangle. ...
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3answers
94 views

Image formation (lenses) [closed]

I have a question regarding image formation by lenses. It is the following: A lense with a focal length of $-48.0cm$ forms an image $17.0cm$ to the right of the lense. Where is the object positioned? ...
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68 views

The position of a particle at any time $t$ is given by $S = V0/a [1-e^{-at}]$. What are the dimensions of $a$ and $V_0$?

To find the dimensions of and V0, I must know the dimension of S and e. So I want to know it.
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88 views

Klein-Gordon, gauge transformation [closed]

It must be really simple, but I cannot get why can we add an $i e \frac{\partial \Lambda}{\partial x}$ in the second row below. The propagation of a charged scalar particle, along the x-axis and in ...
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90 views

Escape velocity problem

I was given a problem at school: How much Energy do we need to make a rocket of mass $m$ faster than the escape velocity so that it can travel in outer space? Here's how I worked: I know that ...
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3answers
131 views

Time dilation in special relativity

Suppose a star ship is moving with some velocity. Two light pulses one in direction similar to star ship another opposite to it is shot towards the space ship. Then how time inside space ship adjust ...
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2answers
41 views

Calculating the Probability Current of a Travelling Wave

Calculate the probability current density vector $\vec{j}$ for the wave function : $$\psi = Ae^{-i(wt-kx)}.$$ From my very poor and beginner's understanding of probability density current it is : ...
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63 views

Integrating for speed [closed]

Trying to determine the speed of a falling body with respect to traveled distance and initial speed. I've been provided with the following equation for acceleration as a function of distance and the ...
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2answers
72 views

Ice throw from industrial wind turbine

I was watching a documentary where the residents didn't want to have a wind turbine erected nearby. One of the comments from the company was that an ice throw would have very little importance since ...
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1answer
100 views

Magnetic Shielding?

Can magnetic fields be "blocked"? For example, in the game, TitanFall, a robot stop bullets with ( presumably ) a magnetic shield. I wish to calculate the magnetic force required to stop a bullet ...
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74 views

Density Matrix Characterization

I am working a two dimensional Hilbert space with basis {$|0\rangle, |1\rangle$} and I am trying to show that the density matrix is characterized by 3 real numbers and show that these three numbers ...
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2answers
54 views

Homework Question involving Momentum [closed]

I'm trying to solve a homework problem as review for an exam I have tomorrow and I was wondering if someone could help explain it to me. It is as follows: You are at Lowe’s shopping for bricks ...
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2answers
108 views

Maximum range for projectile thrown from a mountain [closed]

I have doubts with the following problem: A projectile is fired from the top of a mountain that has a downward slope with angle $\phi$ from the horizontal. The initial velocity of the projectile is ...
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0answers
42 views

Determining impact velocity over long distances [duplicate]

Everything I have found concerning impact velocity from a given height deals with constant acceleration due to gravity. I would like to know how to work in varying acceleration into the equation. So, ...
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2answers
164 views

2 bodies separated by a rope [closed]

Say you have two bodies connected by a "weightless" rope, one hanging from a ledge on a pulley (classic pulley problem). If the body that is on the surface and being pulled by the object hanging ...
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2answers
232 views

Understanding field representation of force [duplicate]

I am reading the book The Evolution of Physics. I have a doubt in the topic "The field as representation". In this topic authors give the example of gravitational force represented as a field. In the ...
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2answers
130 views

Is my free diagram of a spring stretched on one end and attached to the wall on the other end correct? [closed]

Consider the following figures. The top one shows the construction of a spring where its left end is attached to the wall and its right end is stretched by a force. The bottom one is supposed to be ...
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1answer
210 views

Centrifugal force acting on ring [closed]

Take for example the case of a rod rotating about an axis passing through its centre of mass and perpendicular to it. It has a ring hung from one of its sides. The rotation of the rod causes the ring ...
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1answer
366 views

Inverse Square Law in Beta Radiation

Setup: A radioactive source is placed at alternating distances from a Geiger Counter. Counts per second for 10 different distances (each spaced 1 cm apart) were taken for preset times ranging from 200 ...
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2answers
370 views

Reflection formula for spherical surface from Fermat's principle (Query)

The snip shows a part of the method shown by my teacher, to describe the reflection formula for spherical surface. However I do not understand how the relation of AB and BI (which I have ...
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1answer
223 views

Working with a Routhian for a specific system

I asked a more general question earlier about the Routhian, but I'm still having trouble working with it. Here's my specific case. Given the following Lagrangian: ...
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1answer
602 views

Expectation value of total energy for the quantum harmonic oscillator [closed]

A particles unnormalized wavefunction is given as $$\psi(x)=2\psi_1+\psi_2+2\psi_3.$$ How can I find $\langle E\rangle $ without calculating $\langle T\rangle$ or $\langle V\rangle $ ...
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151 views

EM vector potential

We can write the electromagnetic field tensor as $$\begin{bmatrix} 0 & -E_x/c & -E_y/c & -E_z/c \\ E_x/c & 0 & -B_z & B_y \\ E_y/c & B_z & 0 & ...
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1answer
103 views

Pauli matrices identities

There are some definitions and properties for Pauli matrices and their combinations: $$ \varepsilon^{\alpha \beta } = \varepsilon^{\dot {\alpha} \dot {\beta} } = \begin{pmatrix} 0 & 1 \\ -1 & ...
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3answers
1k views

Work, Energy & Power - Body slides down a hemisphere

A small body of mass $m$ slides down from the top of a hemisphere of radius $r$. There is no friction between the surface of the block and the hemisphere. The height at which the body loses contact ...
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339 views

How does symmetry allow a rapid determination of the current between $A$ and $B$?

The following was originally given to me as a homework question at my physics 2 course: Consider the following circuit The difference of potentials between the point $V_{1}$and the ...
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2answers
116 views

Hamiltonian equations: can I divide a solution of motion for a constant?

I'm solving an exercise about Hamiltonian equations. I have followed the proceeding below. The results given by the book are different to mine because its first result is the half of mine (and the ...
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2answers
125 views

Computing $\Delta m$ in $\beta^-$ decay

$\require{mhchem}$What is the energy $Q$ released when $\ce{^131_53I}$ decays and $\ce{^131_54 Xe}$ is formed? The atomic mass of $\ce{I}$ is $130.906118~u$ and the atomic mass of $\ce{Xe}$ is ...
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3answers
2k views

Solve for Initial Velocity of a projectile given Angle, Gravity, and Initial and Final positions?

I've found equations http://www.physicsclassroom.com/Class/1DKin/U1L6a.cfm for solving everything (and rearranged to solve everything) to do with projectile motion EXCEPT this, even though it should ...
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0answers
159 views

Wave equations for two intervals at Potential step

Lets say we have a potential step as in the picture: In the region I there is a free particle with a wavefunction $\psi_I$ while in the region II the wave function will be $\psi_{II}$. Let me ...
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4answers
3k views

Product of exponential of operators

in the context of non-relativistic quantum mechanics I want to show that, for any $A$ and $B$ operators $$e^{A}e^{B}=e^{A+B} $$ if and only if $$[A,B]=0$$ I remember my professor told use about ...
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1answer
2k views

Electric field due to nonconducting sphere

For calculating electric field outside a nonconducting sphere with a hollow spherical cavity. When I use the rule (Charge density= $dQ/dV$), I don't know exactly what is $dV$, is the volume here ...
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3answers
6k views

How to derive the period of spring pendulum?

So I wanted to find out how to (simply, if that's possible) derive the formula for a period of spring pendulum: $T=2\pi \sqrt{\frac{m}{k}}$. However, Google doesn't help me here as all I see is the ...
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1answer
546 views

Can I use Newton's second law to solve what seems to be a torque problem?

The Problem: An 8-m-long beam, weighing 14,700 N, is hinged to a wall and supported by a light rope that is attached 2.0 m from the free end of the beam. If the beam is supported at an angle ...
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1answer
786 views

Ball rolling down an inclined plane going in to a loop

I apologize if this question is not up to par. When I was doing exercises in basic mechanics I checked the answers and I can't seem to find what I'm doing wrong. Suppose we have a ball with mass $m$ ...
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1answer
263 views

Transmission of Gaussian Beam Through Graded-Index Slab

The $ABCD$ matrix of a glass graded-index slab with refractive index $n(y)=n_0(1-\frac{1}{2}\alpha^{2}y^{2})$ and length $d$ is $A=\cos(\alpha d)$, $B=\frac{1}{\alpha}\sin(\alpha d)$, $C=-\alpha ...
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2answers
2k views

Acceleration/tension of object. 1 on horizontal surface one hanging

A 5.00-kg object placed on a frictionless, horizontal table is connected to a cable that passes over a pulley and then is fastened to a hanging 9.00-kg object, as in Figure. Find the ...
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2answers
651 views

Calculating two particle position and velocity with each other?

I've calculated the displacements and average velocities of both particles. $A$ average velocity $= 1.1180m/s$ displacement is $11.1803m$. $B$ average velocity $= 0m/s$ displacement is $0m$. ...
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1answer
375 views

Condition for circular orbit

I am a little confused about the condition for circular orbit. Goldstein's Classical Mechanics has the condition for circular orbit as $$f'=0\tag1$$ where $f'$ is the effective force. I understand ...
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3answers
1k views

Parallel or series connection?

Are C1, C2 and C3 connected in parallel, or C2, C3 in parallel and C1 in series with C23? Btw it appeared as a question in the basic physics Albanian A-levels yesterday. You had to find the ...
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2answers
193 views

Aerodynamic drag on a cannonball?

I'm trying to build a ballistics simulation where I shoot a cannonball. I want to allow for drag and am trying to work out the math to do so. I can work the drag out using $F = C_d\times S\times ...
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3answers
1k views

Finding Distance an Object Travels Up an Incline After Launch

I've been doing a review for an introductory physics course final. I have a question on one problem though. Here is the problem: A mass (M=2kg) is placed in front of a spring with k=900N/m, ...
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3answers
2k views

Centripetal/Gravitational Force

Suppose a satellite is orbiting the Earth. The gravitational and centripetal force supposedly point towards the Earth. Therefore, the net force is towards the Earth. Since the satellite doesn't fall ...
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2answers
6k views

Work done by spring over distance

I'm working through a problem involving energy conservation. Unfortunately, I cannot calculate the work done by a spring. ...
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1answer
633 views

Plotting Hydrogen's $2P_{x,y,z}$ Probability Densities in MATLAB [closed]

I have spent an unreasonable amount of time trying to plot $F(r,\theta,\phi)$ plane slices in MATLAB. I want to look at $x-y,y-z,x-z$ planes. Here's the function, specifically: ...
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1answer
345 views

Two-state system problem

Given a 2-state system with (complete set) orthonormal eigenstates $u_1, u_2$ with eigenvalues $E_1, E_2$ respectively, where $E_2>E_1$, and there exists a linear operator $\hat{L}$ with ...
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1answer
394 views

Functional Derivative of Convolution

How to carry out the following functional derivative? $$\frac{\delta F}{\delta n(r)}$$ where $$F=\int dr n(r) \int C(|r-r'|) n(r') dr'$$ is it simply: $$2 \int dr' C(|r-r'|) ...
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1answer
638 views

D'Alembert's Principle and the term containing the reversed effective force

For our Classical Mechanics class, I'm reading Chapter 1 of Goldstein, et al. Now I come across Eq. (1.50). To put it in context: $$\begin{align*} \sum_i{\dot{\mathbf{p}_i} \cdot ...
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2answers
2k views

Projectile motion without air resistance [closed]

Does the mass of projectile affect its trajectory when it is projected in no air resistance environment and why?