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.

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1answer
58 views

How to “transfer” indices from dot product to metric?

In this source, the author (Andrzej Pokraka, Solutions to problems from Peskin & Schroeder) is computing an integral related to scalar QED. In the step where the equation is labelled (29), the ...
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2answers
77 views

Why is $\theta=\beta/2?$ - Kinematics [on hold]

An aircraft is flying horizontally in a circle of radius $b$ with constant speed $u$ at an altitude $h$. A radar tracking unit is located at $C$. Write expressions for the components of the ...
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1answer
56 views

How to calculate $\langle0|S(b) S(b) |0\rangle $ where $S(b)$ is the squeeze operator? [on hold]

How to calculate $\langle0|S(b) S(b) |0\rangle $ where $S(b)$ is the squeeze operator
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2answers
55 views

Question related to maximum static friction and minimum $\mu_s$

I think I have the right formulas the answer the following question, but there is something conceptual that is throwing me off (see end of question). A body with mass $m$ is located on a slope with ...
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1answer
41 views

Interaction between various forces, by which one is to calculate an angle?

I am new to Newtonian mechanics, and was wondering about the following question. I basically have the ingredients for the answer, but I cannot seem to find the way to put this together into one ...
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1answer
40 views

Fictitious forces in relation to normal force

I am new to Newtonian mechanics, and was wondering regarding the following: The system pictured below is moving at acceleration $a$ towards the left. The mass of the ball is $m$, and there is no ...
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1answer
34 views

How to solve this boundary-value problem in electrostatics? [on hold]

I was reading The Feynman Lectures on Physics, Vol. 2 and came across the following on page 7-1. There are a few problems for which Eq. (7.1) can be solved directly. For example, the problem of a ...
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Work Done to Separate two contact bodies [on hold]

can anyone solve for the case when sphere is with a cavity , can we do it by COM method to find potential , then energy ?? So as to find work done ?I want to know by equating self energies , r we able ...
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1answer
56 views

A Question About $4$-Spinor Contractions

Let $f_{abc}$ be a constant which is totally anti-symmetric with respect to indices $a$, $b$ and $c$. Let $\psi^{a}$, $\psi^{b}$, $\psi^{c}$ and $\epsilon$ be Grassmann-valued Majorana fermions. How ...
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0answers
12 views

Calculate the power supplied by voltage source [closed]

Hi for this question (sorry about the picture), if the current source ($2A$) receives $20 W$ of Power, determine the $R$ of the resistor and the power of the voltage source. I sort of know I have to ...
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1answer
59 views

Juggling a ball

I have the following exercise: Explain the progress of the force you need to juggle a $5\ \rm{kg}$ ball as a function of time. Now since the question is kind of imprecise to me, I have problems ...
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34 views

Magnetic field earth, effect on bar magnet [on hold]

The magnetic moment of small magnet is 4.8 Am$^2$. It is kept in eanhs magnetic field in magnetic meridian with its north pole pointing towards geographical soudm. The neutral points are ...
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2answers
49 views

Rate of change of area of a circular loop exiting a uniform magnetic field

The question is to find the variation in induced electromotive force w.r.t to time or put simply $\varepsilon(t)$ for a circular loop being removed from the region of the magnetic field at a constant ...
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3answers
42 views

Inclined plane with friction and a spring

I am given a body with a mass of 1 kg that slides at a constant speed down an inclined plane with an angle of 30 degrees. At the end of the incline there is a spring with a spring constant of 500 N/m. ...
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27 views

Reciprocity Between $X$ and $K$ operators [on hold]

Ref.: Shankar 2nd edition page 69. Regarding the reciprocity Between the $X$ and $K$ operators, goes on to compute the matrix elements of $X$ in the $K$ basis : $$\langle k|X|k'\rangle=\frac{1}{2\pi}\...
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3answers
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Why Didn't the Energy-Momentum Relation Work?

I am currently studying for the GRE Physics subject test by working through published past tests. My question is about problem 20 from the test GR8677: A positive kaon ($K^{{}+{}}$) has a rest ...
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1answer
75 views

Probability distribution of the overlap between two random quantum states in an $n$-dimensional Hilbert space? [on hold]

Let two pure states $|\Psi\rangle$ and $|\Phi\rangle$ be drawn uniformly and independently from an n-dimensional Hilbert space $\mathbb{H}^n$. (see Note). What is the probability distribution of ...
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7 views

Hall coefficient '$R_H$' for intrinsic semiconductor [on hold]

The Hall coefficient of an intrinsic semiconductor is: A) Positive B) Negative C) Zero D) Infinite ? What will be the best answer for this question? According to me It should be very ...
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1answer
72 views

Perturbation expansion with path integrals

This is from Hugh Osborn's 'Advanced Quantum Field Theory' notes, Lent 2013, page 15. I want to evaluate the expression $$ Z = \exp\Big(\frac{1}{2} \frac{\partial}{\partial \underline{x}} . A^{-1} \...
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1answer
36 views

PDE from Hamiltonian density

For the wave equation Hamiltonian density is $2H=\phi_t^2+\phi_x^2$ while the Lagrangian density is $2L=\phi_t^2-\phi_x^2$. I can easily compute the pde from the Lagrangian density but how does one do ...
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1answer
40 views

Objects Rolling Downhill - Ratio of Rotational and Translational Kinetic Energies [on hold]

Let's say I roll a uniform disk down a ramp (without slipping), and the disk rolls 10 meters down the ramp which is angled at 30 degrees to the horizontal. At the bottom of the ramp, what is the ratio ...
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75 views

Two equations of motion yield different results [closed]

I have the following question: A ball is thrown upwards with an velocity of $30\space m/s$. What is the displacement of the ball after $2\space s$? I can use two equations: $$s = \frac{1}{2}(v+u)\...
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How are the two Stacking Faults namely intrinsic(formed by vacancy agglomeration) and extrinsic(formed by interstitial agglomeration) different?

Stacking Faults and its association with partial dislocations seem to bother me day in and day out.With regard to this I do not understand how Partial dislocations lead to stacking faults and not the ...
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1answer
59 views

What is the speed of air molecule?

Given the minimal temperature measured in the Earth's atmosphere is not $0\space K$, air molecules are moving. I see no reason for air molecule to move all at the same speed. The question is ...
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2answers
43 views

Minimum and Maximum values of Effective Resistance [closed]

Assume we have resistors of resistances $R_1$, $R_2$, $\ldots$ , $R_n$. Let these resistances be connected in a network. Are the following statements true? $(i)$ Effective Resistance is maximum when ...
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0answers
122 views

Derivation of $U=e^{-iHt/\hbar}$ [closed]

When trying to derive the time evolution operator, I arrive to this differential equation: $$\frac{\partial}{\partial t}{\hat U(t,t_{o}})=\frac{-i}{\frac{h}{2\pi}}{\hat{H}}{\hat U(t,t_{o}})$$ How ...
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0answers
25 views

Current associated with the orbital angular momentum

Problem: For a 3d electron in an external magnetic field of 2.50×10−3 T, find (a) the current associated with the orbital angular momentum, and (b) the maximum torque. Attempt: because ...
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26 views

Newtonian gravity for cylinder [duplicate]

Given a cylinder of uniform mass density $ \rho $ . It has a unit length and radius. For any point situated at a distance $ r $ radially away from the central axis is the gravitational field strength ...
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1answer
73 views

An exploding projectile [on hold]

A mass $3m$ is thrown with a velocity of $20\sqrt3$ m/s at an angle of $30^{\circ}$ to the horizontal from a point, say $A$, on level ground. After reaching a certain height, $h$, it explodes into two ...
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0answers
38 views

Calculating electric fields from charge density [closed]

Above I have a calculation of the electric field due to a sheet of nonzero thickness with constant charge density, d. First, I know there are far easier ways to determine the result. I want to do it ...
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0answers
28 views

MCS Lagrangian and Euler-Lagrange

I'm trying to solve the Euler-Lagrange equation for the MCS Lagrangian density as given by Kharzeev in this article (Eqn. 7): $$ \mathcal{L}_{\textrm{MCS}} = -\frac{1}{4}F^{\mu\nu}F_{\mu\nu}-A_\mu J^{...
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Static friction in a slope and two boxes problem

The context: Calculate the string tension in the situation where two boxes are stacked on a slope and moving with uniform velocity, given that the kinetic friction coefficient between the heavier (...
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0answers
15 views

A rigid rod movement in a Cartesian coordinate system [closed]

I'm struggling with this problem. I've never approached something like this. A straight, uniform, rigid rod of lenght $a$ and mass $m$, subject to its own weight (consider $g$ as the grav. ...
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0answers
25 views

Surface tension [closed]

A thin metal ring of internal radius 8 CM and external radius 9cm is supported horizontally from the pan of A balance so that it comes in contact with a glass vessel. It is found that ans extra weigh ...
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0answers
38 views

Differential equation of Serial RL which are connected to parallel C [on hold]

I have a serial RL which are connected to a capacitor in parallel I'm trying to find the governing differential equation of the circuit. So far, I have tried using Kirchhoff's laws for current ...
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2answers
80 views

Chain slipping off a sphere - Mechanics problem

A uniform flexible chain of length l rests on a fixed smooth sphere of radius R such that one end A of the chain is at top of the sphere while the other end B is hanging freely. The chain is held ...
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0answers
34 views

Derivative of Planck's law [closed]

I am trying to get the derivative of Planck's law: $$B\lambda(\lambda,T) = \frac{2\pi hc^2}{\lambda^5} \frac{1}{e^{hc/\lambda k_BT}-1} .$$ I can't seem to the answer as below: $\frac{dB\lambda}{d\...
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0answers
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Help Finding angular velocity ω [on hold]

Two wheels A and B of a machine rotate about a common axis in the same direction with angular velocity $ω1 & ω2$ respectively.Moment of inertia of A about the axis of rotation is $I1$ and that of ...
2
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2answers
81 views

Quantization of angular momentum of system of particles

Suppose there is a system of particles interacting with each other. Is it the angular momentum of each particles which would be quantized as $\sqrt{n(n+1)} \hbar$ or is the angular momentum of the ...
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0answers
48 views

Unequal forces acting on two blocks connected by a string [closed]

Two blocks A and B are separated by some distance and tied by a string as shown in the figure. Find the tension in the string. I can see that maximum value $f_1$ can attain is $7 N$ and the maximum ...
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Homework and exercises [closed]

The question goes: A particle is moving with a velocity v = k(yi + xj), where k is a constant The general equation for its path is? (a) $y = x² +$ constant (b) $y² = x +$ constant (...
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22 views

Variable acceleration kinematics [closed]

Two massive planets originally separated at displacement x away from each other. The plants have the same mass m. By considering the non-changing acceleration, calculate the time taken by the two ...
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1answer
36 views

Tension in a ring rotating about its own axis

A ring of mass m and radius R is placed on a smooth horizontal table and is set rotating about its own axis in such a way that each part of the ring moves with a speed v. What is the tension in the ...
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0answers
21 views

Reasons for only providing solutions to either even or odd number questions [closed]

I have read several books such as Principles of Physics by Walker Halliday and Resnick and University physics by Sears and Zemansky's and I found that the exercise problems only had solutions for ...
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1answer
34 views

Schrodinger equation: If $V(x)=V(-x)$ then prove that $\psi(x)=\psi(-x) $ or $\psi(x)=-\psi(-x)$ [duplicate]

The title explains itself. If the potential is an even function then prove that wave function is either odd or even. I set $-x$ in Schrodinger equation and find out that $\psi(-x)$ is also a solution ...
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3answers
43 views

Why tap water doesn' instantly form crystals when you shake it after cooling it?

For the science fair I am doing the experiment about nucleation in which I put a bottle of water in the freezer and after one hour and a half I take it out and it is supposed to instantly freeze when ...
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1answer
54 views

Motion of Particle Described by Given Equation

I encountered a problem wherein I was given that the electric lines of force in a region varies as $$x^2+y^2=1$$ A charged particle was initially at rest at $(1,0)$. I had to answer whether the ...