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Questions tagged [homework-and-exercises]

Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright. Please READ THE GUIDANCE IN META before asking homework-like questions.

2
votes
1answer
103 views

Are all solutions of Maxwell's equation related by a gauge transformation?

Consider Maxwell's equation (without source): $$ \partial_\mu F^{\mu \nu} = 0 \implies \partial_\mu \partial^\mu A^\nu = \partial_\mu \partial^\nu A^\mu.$$ Can we find a pair of classical field ...
-3
votes
0answers
18 views

In the given circuit find Voltage across capacitor in Volts [closed]

[ in the given circuit find Voltage across capacitor in Volts]
1
vote
1answer
27 views

Calculating Noether Current for Electromagnetic Current interacting with a Dirac Fermion

I'm trying to confirm that the conserved current of the Lagrangian $$ {L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu} -j^{\mu}A_{\mu}+\bar\psi(i\gamma^{\mu}\partial_{\mu}-m)\psi $$ associated with the ...
1
vote
2answers
34 views

Concerning Constraint Equations for Lagrangian Formalism

I was working on a problem studying for a classical mechanics class and came across an idea I'm not sure about concerning the formalism of Lagrangian mechanics concerning constraint problems. https://...
-2
votes
1answer
52 views

Energy conserved or not? [closed]

Here is the question : Two identical buggies 1 and 2 with one man in each move without friction due to inertia along the parallel rails towards each other. When the buggies get opposite each ...
1
vote
0answers
19 views

Sequential Stern Gerlach Experiment

If a beam of silver atoms were sent through multiple magnetic fields, for example, one oriented in the z direction, and then all go through one oriented in the x direction before hitting a screen, ...
0
votes
1answer
52 views

Human Body Upward Acceleration on Scale [closed]

I am reviewing for a Physics exam, and have come across the following example question: If I weigh 200 pounds, but a scale I'm standing on reads 400 pounds, then I am accelerating upward at 1g 2g 3g ...
0
votes
0answers
44 views

Finding time of acceleration with given time and distance in space [closed]

I have an issue with a problem I've been trying to solve for a few days now. So we begin with a ship in space, so no friction nor gravity. The ship needs to travel one Astronomical Unit (AU, ...
0
votes
0answers
17 views

Standing wave and fundamental frequency [closed]

The following is a problem I am working on. "Astronauts visiting Planet X have a 2.5 m-long string whose mass is 5.0 g. They tie the string to a support, stretch it horizontally over a pulley 1.8 m ...
-1
votes
0answers
20 views

Calculating viscosity of more than two oils [closed]

I would like to calculate the viscosity of mixture for more than two oils, right now I am able to calculate the viscosity of two oils from this website. I please request to provide me the calculator ...
0
votes
1answer
36 views

Non-gauge-invariance of EM angular momentum

In 16.7 b) of Zangwill we're asked to show that the expression $$ {\bf L}=\epsilon_o\int d^3r E_k ({\bf r}\times\nabla)A_k + \epsilon_o\int d^3r {\bf E} \times {\bf A} $$ is not gauge invariant. ...
-1
votes
4answers
60 views

How much energy is in a 75 kg human being? Including atomic and electrical (charge) [closed]

To calculate the energy in 75 kg of mass is easy with E = mc2. But, how to calculate how much charge are in all our atoms? It is, too, a gargantuan amount of energy.
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votes
0answers
12 views

Overall thermal efficiency, elastic limit and the relative efficiency [closed]

A heat exchanger receives hot fluid gas at 1600K and cold air at 298K.the hot fluid gas leaves the exchanger at 900K and cold air is heated to 1373K.it is given that CP of hot fluid gas divided by the ...
1
vote
2answers
65 views

How to calculate the electric field using Gauss' s Law in this example? [closed]

Suppose we have an infinite cylinder (infinite in the z-direction) with radius $a$. Inside it, there is free charge density given by $\rho = \rho_o \cos (kz - \omega t)$ and current density given by $\...
0
votes
0answers
17 views

Internal energy of paramagnetic obeying m = function of H/T independent of magnetization?

I'm stumped. In this exercise, I've got a paramagnetic obeying a $m = \psi\left(\frac{H}{T}\right)$ law, where $m$ is the average magnetization (with the volume $V = 1$, so it's equivalent to the full ...
0
votes
1answer
23 views

Moment of inertia of solid sphere [closed]

Why isn't the moment of inertia of a solid sphere (9/64)piMR², but (2/5)MR²?
0
votes
0answers
24 views

Magnetism and magnetic field [closed]

A current carrying ring, carrying constant current 2/π A, radius is 1m and mass is 2/3 kg having 10 windings is free to rotate about its tangential vertical axis. A uniform magnetic field of 1 tesla ...
1
vote
1answer
17 views

The relation between decay width and vacuum polarization

Recently I have found this problem: My question: Does the relation $\mathrm{Im}\,\Pi(M^2)=-M\Gamma$ work for arbitrary theory or it should be modified?
-2
votes
0answers
17 views

Velocity of sound of a inert Gas [closed]

Need your advise to solve below problem correctly; Q 5 Moles of He is inside a closed bulb, if Ne gas is added to the following bulb what would be the ratio of the speeds of sound in the system ...
0
votes
0answers
44 views

Commutator of Lie Group Generators

This is from Maggiore's "A Modern Introduction to Field Theory", Page 15. I have a Lie group with matrix generators $$ T^{a}_{R}$$ Where $a$ takes values from 1 to the dimension of the Lie group. ...
0
votes
0answers
23 views

How can I test if an elastic pendulum with a hacksaw blade as the spring follow hooke's law? [closed]

The setup is shown above. I'm not sure how I should tackle this problem; the hacksaw blade acts differently from a regular spring and curves when you bend it.
1
vote
2answers
89 views

Half Witt algebra

I have the following Lie algebra which is generated by $\{L_n|n\geq 0\}.$ It satisfies the following commutation rule $$ \Big[ L_i ,L_j \Big]=\frac18 \frac{(2i+2j-1)(2j-2i)}{(2j+1)(2i+1)}L_{i+j-1}-\...
0
votes
0answers
38 views

Invariance of measure under Lorentz transformations without the four dimensional expression

Ticciati's book Quantum Field Theory for Mathematicians states that the invariance of the measure $$\int\frac{\text{d}^3\vec{k}}{2\sqrt{\left\|\vec{k}\right\|^2+\mu^2}}$$ can be shown by direct ...
0
votes
0answers
37 views

Joules exerted by asteroid falling on Earth [closed]

The gravitational pull of the earth on an object is inversely proportional to the square of the distance of the object from the center of the earth. At the earth's surface this force is equal to the ...
0
votes
2answers
42 views

Equipotential lines around two parallel charged wires

I'm studying electric potential, and I'm trying to follow the derivation of equipotential lines surrounding two parallel, oppositely charged wires, found here. But I feel like the source is skipping a ...
2
votes
0answers
41 views

Why can't I use the equation for centripetal acceleration to solve for acceleration in this problem? [closed]

A small car with mass 0.800 kg travels at constant speed on the inside of a track that is a vertical circle with radius 5.00 m. If the normal force exerted by the track on the car when it is at the ...
-2
votes
0answers
68 views

How to get multiple surface friction in diametral engine? [closed]

i assume the inicial velocity equals to acceleration and then calculate braking (v²/250u) with the weight and applied force. And i tried, on sample 2, 5 and 8, to calculate friction as an avarage ...
0
votes
0answers
20 views

Qualitative Statements about two students measurement with Vernier Caliper [closed]

Suppose two students measure the length of a piece of wire three times each. Student A obtains results of 8.0, 8.1, and 8.2 centimeters. Student B obtains determines a length of 8.1 centimeters ...
0
votes
1answer
37 views

Reduced wave vector using Bloch's theorem

In every solid state physics book it says that the wave vectors appearing in Bloch's theorem can be confined to the first Brillouin zone and provide a hint on how to show this. Most of the times this ...
0
votes
1answer
36 views

Is there a simplification to the triple product of levi-civita symbols

IS there any way to simplify: $\epsilon_{ijk}\epsilon_{klm}\epsilon_{mni}$ I know how to simplify the product of just two into summations of delta functions but not sure how to do it with three
0
votes
0answers
20 views

2D deSitter conserved charges

For $1+1$-dimensional dS spacetime, the metric takes the form (in comoving coordinates) $$\mathrm{d}s^2=\left(\mathrm{d}x^0\right)^2-e^{2Hx^0}\left(\mathrm{d}x^1\right)^2.$$ I want to find the ...
0
votes
1answer
36 views

Problem with finding the density of states of an $N$-body system

I am having problems solving a particular problem in my Statistical Mechanics course. We have a system that is composed of $N$ non-interacting particles each of mass $m$. The particles are bound to ...
0
votes
0answers
23 views

How can I determine, in what extent the fit to experimental data is good in Matlab?

I have experimental spectrum in which y-axis is intensity values, and x-axis is frequency values. Int - array of experimental intensities (y-axis). w - array of frequencies (x-axis). I know the view ...
-1
votes
1answer
46 views

Need some help with a question involving the Levi-Civita symbol

Been struggling with this question: Given: $c_{ij}=\epsilon_{ijk}a_k$ I have to show that $a_k=\frac{1}{2}\epsilon_{kij}c_{ij}.$ I was thinking of multiplying both sides by some epsilon, but not ...
0
votes
1answer
55 views

To consider or not to consider potential energy of a mass attached to a spring in oscillation? [closed]

For the above system I have the following expressions for kinetic and potential energy: $$ V = \frac{1}{2}\,k\,x^{2}+m\,g\,l\,(1-cos\,\theta)-m\,g\,x\\ T = \frac{1}{2}\,m\,\dot{x}^{2}+\frac{1}{2}\,m\,...
0
votes
0answers
19 views

Applying torque on static structure [closed]

Hi all, Please consider the attached picture, which shows a mass-less rigid body. This body is pinned/screwed on points A and B, and a torque with intensity "M" is applied with an axis on point C. ...
0
votes
1answer
45 views

Parity of Harmonic oscillator in 2 and 3 dimensions: the case of $l_z$

From doing exercises and trying to understand their solutions, i figured in two dimensions, not all values of $l_z$ can be taken by the particles (this is to conserve parity). For example, for n=0, ...
2
votes
2answers
59 views

Computation of $e^{i \hbar \omega a^{\dagger} a} a e^{-i \hbar \omega a^{\dagger} a}$

I need to compute terms like : $$e^{i \omega t a^{\dagger} a} a e^{-i \omega t a^{\dagger} a}$$ Where $[a,a^{\dagger}]=1$ (they are the bosonic annihilation/creation operators). I wonder if there ...
0
votes
0answers
26 views

Conformal symmetry and the Weyl Tensor [closed]

I need help for a problem concerning a work. I'm studying general relativity in case of Conformal symmetry and I met this problem: Let's consider a conformal symmetry such as : $\cal{L}_X \ g_{\...
-3
votes
0answers
25 views

Airoplane landing [closed]

A plane leaves the airport in Nadi and flies 170 km at 68° East of North and then changes direction to fly 230 km at 48° South of East, after which it makes an immediate emergency landing in a pasture....
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votes
0answers
22 views

How to get those specific values of mass and velocity? [closed]

I'm confused as to how the solution values for mass and velocity is given by 9600, 2, 5400 and 1. If someone could make me understand how, that would be great.
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votes
0answers
24 views

Pendulum oscillatory motion [closed]

For small angular displacement (i.e $\sin\theta \approx \theta$), a simple pendulum oscillates harmonically. For larger displacement the motion: A-- becomes periodic B-- remains periodic with the ...
0
votes
0answers
21 views

Momentum Perturbation SHO [closed]

H=H0+H' where H' is λP^2. I need to find the first/second energy shifts of the nth energy level of harmonic oscillator (which is fine with ladder operators) Part b- Now consider the full Hamiltonian ...
0
votes
0answers
23 views

1D Potential Barrier Boundary Conditions (tunneling)

I'm trying to solve the boundary conditions of a 1D potential barrier for a free particle. The boundary conditions on the continuity of the wave function and its first derivatives leads to four ...
1
vote
0answers
38 views

Particles colliding at greatest height [closed]

Could I please ask for advice on the following question? It's the very last part. Surely it is wrongly printed because $(\sqrt3-1)(\sqrt3+1)=2$ And coefficient of restitution (e = separation ...
-1
votes
3answers
78 views

Why am I getting two answers from the same question? [closed]

In this problem, if I use the formula for power as $\frac{F\cdot s}{t}$, then the answer is 37.5 W. But if I use the formula $F\cdot v$, then the answer is 75 W. How is it possible that the man has ...
1
vote
0answers
25 views

How many dimensions has a Majorana Fermion state space?

For an exercise question, I'm wondering on how I can determine the dimensionality of a state space spanned by Majorana fermions. A (Dirac) fermionic excitation ($f , f^\dagger$) has a state space of ...
0
votes
0answers
29 views

Relation between spin degrees of freedom and the dimensions of Hilbert space

I came across a question which reads "Suppose the spin degree of freedom of two particles (nonzero rest mass and nonzero spin) is described completely by a Hilbert space of dimension twenty one. ...
2
votes
1answer
91 views

Beta function in the Standard Model

In Srednicki's textbook "Quantum Field Theory", Problem 89.4 asks us to compute the leading terms in the beta function for each of the three gauge couplings of the Standard Model. These gauge ...