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How did Jackson get the exact solution to potential in polar coordinates

On page 45 of Jackson's Classical Electrodynamics (3ed), He solved a polar potential problem with known source distribution. $$ \frac{1}{\rho}\frac{\partial}{\partial \rho}\left( \rho\frac{\partial ...
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2answers
546 views

Electric field. Linear charge density [closed]

I was wondering if anyone could help me out in this exercise I've been struggling to solve. A straight, nonconducting plastic wire $ 8.50 cm $ long carries a charge density of 175 $ nC/m$ ...
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2answers
424 views

Equilibrium of Force Systems including Torque

please help me to solve this problem.. this is only the #3 on my homework and the only thing i didn't know here is how to calculate the tension T. please teach me how to solve the tension here ...
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1answer
122 views

If the velocity of particle $A$ exceeds that of $B$, is the acceleration of $A$ greater than $B$?

Two particles $A, B$ are travelling along parallel straight paths. At some point, the velocity of $A$ exceeds that of $B$. Does this necessarily mean that the acceleration of $A$ is greater than the ...
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1answer
318 views

Equation of progressive wave [closed]

A progressive wave traveling in positive x-direction given by $y=a\cos(kx-\omega t)$ meets a denser surface at $x=0,t=0$. The reflected wave is then given by: I know that since the wave changes its ...
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1answer
86 views

Lunar and solar tides [closed]

I just read the following statement in a book: If the diameter of the earth increased by 20%, both lunar and solar tides would be weakened with lunar tides weakening more than solar tides. What ...
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0answers
58 views

Setting Lagrangian [closed]

Can you help me to set Lagrangian? I found that $$\vec r_A=b\sin\theta\vec i+b\cos\theta\vec j$$ $$\dot{\vec r_A}=b\dot\theta\cos\theta\vec i-b\dot\theta\sin\theta\vec j$$ For point $G$ I've got ...
5
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1answer
279 views

Do mutual eigenkets imply commutation of two operators?

I have been working on this question. I have solved it, and I would like to check whether my line of reasoning is right or wrong Question: Prove that if there exists a mutual complete set of ...
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2answers
232 views

accelerated charged particles and interaction with magnetic field

In high school we are taught that magnetic field perpendicular to velocity of an charged particle experience perpendicular force that causes it to move in circular path by relation ...
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1answer
232 views

Speed of a falling pencil [closed]

If you balance a pencil of length $d$ on its tip, and let it fall, how do you compute the final velocity of its other end just before it touches the ground? (Assume the pencil is a uniform one ...
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1answer
54 views

Where does a sparkly (CO$_2$) water bottle have more presure [closed]

Where does a sparkly (CO$_2$) water bottle have more pressure? At a higher altitude (7000 feet) or under sea level (-8 feet)?
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1answer
231 views

Double slit paradox

This is a relativity-paradox which I can't resolve: The distance between interference lines in the double-slit experiment is: $$\ w = z \lambda/d$$ Where: w: Distance between fringes z: Distance ...
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1answer
763 views

How to find the total current supplied to the circuit?

Recently, I came across a question based on finding electric current of a circuit. Here's the image... I know, by using the formula $I=V/R$, we can easily calculate the current as $V$ is given and ...
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2answers
271 views

What are the forces used in this weightlifting example? [closed]

You have a person doing a bench press. Their hands are equidistant apart and they are centered on the bar - each hand about 1.5 feet from center of the bar. The bar weighs 45 pounds. In example 1 ...
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1answer
208 views

Centripetal acceleration for particle that moves in a circle at non-constant speed

How is $a_{R}=v_T^{2}/r$ derived for changing tangential speed? ($a_R$-centripetal component $r$-distance from axis $v_T$- tangential speed)
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0answers
248 views

Scalar field lagrangian in curved spacetime

I am studying inflation theory for a scalar field $\phi$ in curved spacetime. I want to obtain Euler-Lagrange equations for the action: $$ I\left[\phi\right] = \int ...
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1answer
651 views

Equations of motion for a spherical pendulum in a non-inertial reference frame

Take a spherical pendulum with bob mass $m$, rod length $\ell$ and physical coordinates $\theta$, $\phi$ (spherical angles) and $h$ (the hinge height with respect to the coordinate origin). The rod is ...
3
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2answers
1k views

Using the image charges method to find the electric field

The following is a question from a tutorial in my Physics 2 course about conductors and the Method of image charges. We are given two infinite perpendicular and grounded plains. The first ...
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0answers
79 views

Angular momentum contained in E&M fields

I am trying to do this question as a prep for my quals and find my solution too simplistic. I fear I am missing something important. "Iron atoms (atomic mass 56) contain two free electron spins that ...
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0answers
95 views

How to understand the transmission coefficient from the following question?

I want to understand the transmission coefficient and construct a time-independent Schrodinger equation where $$ V(x)=\left\{ \begin{array}{c c} \delta(x), & |x| < 1 \\ + \infty, & ...
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0answers
47 views

path planning with invasive measurements

My background is not science, and I hope the question I am about to ask doesn't look like a homework kind of a thing! Anyway, I will try my best to make the point clear. imagine there is a lake, and ...
0
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1answer
541 views

Electric field outside a hollow cylindrical conducting shell [closed]

Imagine that a point charge $+Q$ is located at radius $R$ and height $z=0$ inside of an infinitely long conducting cylinder shell of inner radius $a>R$ and outer radius $b$. From what we know of ...
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2answers
114 views

Can you justify force calculations using more than one of Newton's laws?

If an object is at rest on a flat surface I remember my school teacher would say, "By Newton's 1st law the normal reaction, R, is mg (mass x g)". Ok, sure this is fine because the object is at ...
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2answers
69 views

Stability of equilibrium points

For a spinning top, the linearised equation in the angle $\theta$ when the top is spinning about its axis of symmetry, which is vertical, is of the form ...
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1answer
64 views

A question of BRST symmetry of bosonic string theory

This question relates to this post I tried to verify Eq. (4.2.7) in Polchinski's string theory book vol I p. 127 but I miserably miss a sign $$ \delta_B (b_A F^A) = i \epsilon (S_2 + S_3) ...
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3answers
734 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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1answer
200 views

Walking along a moving train, we make 18 steps. Opposite: 11. How long is the train?

A man walks in the same direction as a slowly moving train ($v_{man} > v_{train}$). He counts the train to be 18 steps long. Then he turns around and counts the train to be 11 steps long. ...
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1answer
112 views

Does a 27 hp engine output the same amount of energy as lifting a 1 ton stone block almost 3 meters per second?

I’m trying to get a sense of how much energy a 27 horsepower engine outputs. 27 hp $=$ 20 133 watts (joules/second). Potential energy can be calculated as $E = mgh$ where $g = ~9.8\ m/s^2$ on earth. ...
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3answers
275 views

Problem on apparent height of postage stamp underneath paperweight

A postage stamp is placed on a surface and a glass cube of refractive index $1.5$ is placed over it. When observed through the cube, the stamp appears at a height of $1.5cm$ from the bottom of the ...
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1answer
71 views

Find the distance from the initial location [closed]

Sing Huat drives a car with initial speed 30 km/h and acceleration 2 km/h2 toward Tee, whose displacement is 200 m away from him. At the same time, Tee drives another car toward Sing Huat with ...
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1answer
250 views

Variable Tension in the string [closed]

A body of mass $m$ is hanging with a string having linear mass density $\lambda$. What is the tension at point $A$ as shown in the figure. I am aware of the scenarios in which string is ...
0
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3answers
781 views

Calculating acceleration function for given time, distance, initial velocity [closed]

An object has an initial velocity of v and should stop in d meters, in t seconds where v*t >= d. I can predict that this acceleration won't be constant but it is a function of time and this problem ...
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1answer
123 views

Circular motion [closed]

A small block slides down from the top of a hemisphere of radius $r$. It is assumed that there is no friction between the block and the hemisphere. At what height $h$ will be the block lose contact ...
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1answer
129 views

Relative acceleration with pullys

I have tried this question every way I can think but in the equation for particle $L$ $g$ cancels every time. Could someone show me how to do it correctly or tell me what I am doing wrong. Thanks, ...
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1answer
165 views

Free body diagram of rod in sphere

I was finding the free body diagram part of dynamics quite easy until I found this question , Here's how it goes : A rod AB is placed inside a spherical shell, whose inside surface is rough. Draw ...
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2answers
53 views

Does a 27 hp engine output the same amount of energy as lifting a 1 ton stoneblock almost 3 meters per second? [duplicate]

I'm trying to get a sense of how much energy a $27$ horsepower engine outputs. $$27 \mathrm{hp} = 20133\mathrm{W}$$ Potential energy can be calculated as $$E = mgh$$ where $g ...
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votes
1answer
101 views

Some complex-number manipulation when calculating coefficients

I am going through Sakurai's quantum mechanics, and at one point the solution to a problem says: $(\sin(\beta)\cos(\alpha)-i\sin(\beta)\sin(\alpha))b+\cos(\beta)a=a$ ...
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1answer
104 views

Derivation of Pressure/Kinetic Therory problem involving hole in box

A box of volume $V_0$ has a small hole of area $A_0$. The box initially has one mole of an ideal gas at $t = 0$, which is at an initial temperature $T (t = 0)$. Find the rate of energy flow through ...
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1answer
368 views

Rigid bar suspended by two ropes, tension of first rope after second rope is cut?

This is from a practice exam, I've been sitting here thinking about it for over an hour and can't convince myself of an answer, or write down any relevant exact equations. A bar of uniform density ...
0
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1answer
306 views

Equation for the equipotential lines? [closed]

What is the equation for the equipotential lines in $x$-$y$ plane for a dipole oriented along the $x$ axis?
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1answer
164 views

Beads sliding on a hoop

Two particles, $P_1$ and $P_2$, of equal masses $m$ are linked by a spring of stiffness $k$ and natural length $a$. They are sliding freely without friction along a horizontal fixed hoop of radius ...
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1answer
250 views

General Solution of Mechanics Problem

I had a homework problem that Given velocity, $v^2(t)=\frac{K}{x(t)}$, where $x(t)$ is distance, find $v$ as a function of $t$. Of course if we assume a positive root, it is easy but what if ...
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0answers
872 views

Equations of motion for a pendulum and spring system

The question is available here: I've modeled the building as a rod on a torsional spring (with a pendulum hanging from the top). $\phi$ is the angle from the centre for the pendulum and $\theta$ ...
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0answers
26 views

How to calculate independent componets of tensor for crystal symmetry?

I have a question as title says. For a formula $j_i = \beta_{ijl} e_j e_l^*$, where $i$, $j$, $k$ are coordinate and $\beta_{ijk}$ is the tensor, if I know the tensor should be satisfied for crystal ...
2
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1answer
169 views

Distinction between Larmor frequency and Rabi frequency

Wikipedia said "In the context of a nuclear magnetic resonance experiment, the Rabi frequency is the nutation frequency of a sample's net nuclear magnetization vector about a radiofrequency field. ...
3
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1answer
134 views

Equations of motion of displacement field

We have an action: $$S[\boldsymbol{u}] = \frac{1}{2} \int dt \int d^3x \left\{ \mu (\frac{\partial u_{i}}{\partial t})^{2} - \nu (u_{ii})^{2} - \rho(u_{ij})^{2}\right\} $$ Where $u_{ij} = ...
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1answer
187 views

X-ray and neutron powder diffraction: peak broadening due to crystal size

When analysing powder diffraction patterns, the broadening of peaks can be used to estimate crystal sizes. Smaller crystal size gives larger broadening according to the Scherrer equation: $$ \beta = ...
3
votes
1answer
121 views

Rocket propelled by a giant monochromatic laser

I am preparing for my quals and stumbled across the following problem, and although it only requires undergraduate-level physics, I feel I can't piece everything together. "A rocket of mass $m_0$ is ...
2
votes
2answers
876 views

Angular Velocity expressed via Euler Angles

On the top of the fourth page from here, the author trivially derives the components of angular velocity, expressed via Euler angles of the system. I fail to understand how the components of angular ...
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1answer
84 views

3D billiard with no gravity nor air drag

If I have a projectile shot in a vacuum-box that has no gravity or wind resistance inside it (lets say the box is 1000 units tall and 1000 units wide), with the only rule being that the projectile ...