Sphere Definition and 1000 Threads

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Why the area of the thin rings are ##2πasin\theta \, ds##? (a is the radius of the hollow sphere) If we look from a little bit different way, the ring can be viewed as a thin trapezoid that has the same base length ( ##2πa sin\theta##), and the legs are ## ds##. The angle between the leg and...

According to my current understanding rolling friction rolling friction is the static friction (parallel to the surface on which the object is moving) applied by the frictional surface (rough surface) on the contact point or contact area of the object whose v≠Rw(v is translational velocity and...

I'm trying to draw a 2D globe

How will the friction work on a sphere which is purely rolling on a horizontal surface such that both the sphere and surface does not deform. The sphere at any time t will only have one point of contact, which would continuously changing as the sphere rolls. Will The friction be applied to the...

Hi A sphere with radius r is buried in an elastic ideal medium at pressure P1. Inside the sphere I use energy E to create a variation of pressure of dP. What variation dPx I would measure if the sphere was buried in a medium at pressure P2 using the same energy E? Is it possible to solve...

##\iiint 3 dr d\rho d\phi## The volume of a sphere is ##4\pi /3 r^3## so naturally the answer is ##4 \pi R^3## But when I integrate I do: ##3 \iint r |_0^R d\rho d\phi## ##3R \int \rho |_0^{2\pi} d\phi## ##6R\pi * \phi |_0^\pi = 6R\pi^2## What am I doing wrong?

I know that (a) is right, and (b) is wrong. The problem is with (c)... It seems correct to me! I can't see how this is not true. The electric charge o the sphere by itself will create an electric field, which will move the particle.

Back here again.. but I am sorry guys, only the parameters are on my paper so wouldn't be of much help to show. I basically have no clue on how to start solving this problem at all. I stopped yesterday and let it sit overnight but still have no clue on how to approach the problem basically...

I presume that the sphere is pointing at the declination of -90, and that the descriptions "torrid" & "temperate" correspond to tropic & non-tropic, respectively; as such, it seems that these descriptions are on the wrong sides...

I tried to solve it for some time and then looked at the solution manual, which got me completely lost. Those are the first lines of the solution : I'm not so sure how equation 4.39: makes him conclude that the same relation holds for dipole moments. My second concern is that I'm not sure how...

My attempt was to consider spherical shells of radius ##r## (##r\leq R##))and thickness ##dr## and then the potential energy of this shell would be in the field only of the "residual" sphere of radius ##r## (a result also known as shell theorem) $$U_{dr}=G\frac{\rho\frac{4}{3}\pi r^3 \rho 4\pi...

My attempt: We have 3 charges inside 2 +ve and 1 -ve so i just added them up. 4 + 5 +(-7) = 2q Then there is a -5q charge outside the sphere. I did 2q + (-5q)= -3q . The electric field flux formula is Flux= q/ E0 . So i got -3q/E0 which is obviously wrong : ) . After quick googling , I...

Is the electric field inside a sphere always 0? Even if we have charges on the surface?

The Hamiltonian of a particle of mass ##m## on the surface of a sphere of radius ##R## is ##H=\frac{L^2}{2mR^2}## where ##L## is the angular momentum operator. I want to solve the TISE ##\hat{H}\psi=E\psi## and in order to do that I rewrite ##L^2## in Schroedinger's representation in spherical...

I have a problem with this Hamiltonian: two identical particles of mass ##m## and spin half are constrained to move on the surface of a sphere of radius ##R##. Their Hamiltonian is ##H=\frac{1}{2}mR^2(L_1^2+L_2^2+\frac{1}{2}L_1L_2+\frac{1}{2}S_1S_2)##. By introducing the two operators...

I am not very good at proofs. The only thing I have come up with is the following regularity. However, I am not sure how this can be related to the above problem. Given a sphere ##S_a## with a center ##C## and a diameter of ##a##. I can now construct a line segment ##b## with the endpoints...

i don´t understand the question

if a sphere rotates, it's like multiple currents going around in a circle. I can find the magnetic field of each of those currents at the center point of the circle and add them together. We can integrate with respect to y and R. y ranges from 0 to 5 cm away from the center of the loop and the...

a) We know that ##Q_1=1,2\, \textrm{nC}## and ##Q_2=6\, \textrm{nC}##. By the TOTAL influence theorem: $$-Q_1=Q_{2i}=-1,2\, \textrm{nC}$$ $$Q_2=Q_{2i}+Q_{2e}\rightarrow Q_{2e}=7,2\, \textrm{nC}$$ b) Electric potential difference crust: $$V_A-V_\infty=$$ How was this potential difference thing...

Hi PF! Given three random numbers between 0 and 1, how to evenly populate a sphere of radius ##R## (assuming we use every point). I think it's similar to the 2D circle equivalent described here. Does this imply the PDF is ##4 x^2##, where the remaining analysis holds? Then one point is the...

Below is an image to calculate the surface area of a sphere using dA. I can see how ##rcos\theta d\phi## works, but I don't understand how that side can't just be ##rd\phi## with a slanted circle representing the arc length. The second part I don't understand is why it is integrated from...

The solution says that the tension in the string in the negative x direction is balanced by the force of the plate on the ball (red). Why is the repulsive force of the ball on the plate (in blue) not included in this calculation?

Hi , I'd like a little bit of clarification about Section 2.6 from Jackson's classic book on E & M. Section 2.6 starts out with the problem of a "conducting sphere" near a point charge, but then it confusingly veers away to a problem where potential is prescribed to vary with azimuth and polar...

Hi! I've been trying to attempt this problem over here but the solutions state that the solution is this below? However, from integrating the density and then plugging it into Gauss's law, I get the exact same thing, except a 15 instead of a 5. Could any please help point out if there is an...

In a quantum mechanical exercise, I found the following Hamiltonian: Consider a particle of spin 1 constrained to move on the surface of a sphere of radius R with Hamiltonian ##H=\frac{\omega}{\hbar}L^2##. I knew that the Hamiltonian of a particle bound to move on the surface of a sphere was...

Dear Forum, My goal is to rotate several points on a sphere by a theta and phi. For example, I have a sphere where the elevation is theta (90 to -90) and the azimuthal is phi (-180 to 180). I have the following points on the sphere: theta = [45 45 45 45] phi = [-180 90 90 180] This generate...

To solve a particle on a sphere problem in quantum mechanics we get the below equation :##\left[\frac{1}{\sin \theta} \frac{d}{d \theta}\left(\sin \theta \frac{d}{d \theta}\right)-\frac{m^{2}}{\sin ^{2} \theta}\right] \Theta(\theta)=-A \Theta(\theta) ## To solve this differential equation, we...

$$I = \int{r^2dm}$$ $$dm = \sigma dV$$ $$dV = 4\pi r^2dr$$ $$\sigma = \frac{M}{\frac{4}{3}\pi*R^3}$$ $$I = \sigma 4 \pi \int_0^R{r^4 dr} = \frac{3*MR^2}{5},$$ which is not the correct moment of inertia of a sphere

I am currently reading Griffiths book for electrodynamics and having trouble making a jump in one of the problems. I have attached the problem (3.6) in question. In the part that is highlighted, I don't see how we go from (1-cosθ) to (P0cosθ-P1cosθ)? I can see that from the Legendre...

Picture : My answer : I guess net electric flux is 0. so electric flux passing through surface 1 = -(electric flux passing through surface 2) and electric flux passing through surface 1 is EA = E(pi)(r^2) Is it correct? Thank you ...

Sorry i don't understand English very well , if someone want to explain to me this problem?

I solved this problem on my own using the Energy formula. When I compared my answer to online answers (attached) as well as the griffiths solution manual, I noticed they also include the Electric field outside the sphere into their calculations. I did not and only use the Electric Field inside...

If I draw the fbd then some force will accelerate the car in horizontal direction which I think does not effect the string in vertical direction. So same tension regardless of acceleration. But we know it will increase. So what will be the correct physics behind it?

Hello, I would like to ask one question. What is the equation for the lift force of a rotating sphere when flying through the air: m = 0.25 g v = 130 m/s angular velocity = 105 rad/s radius = 3 mm air density = 1.2292 kg/m^3 air pressure = 101200 Pa air temperature = 15 °C = 288.15 K If anyone...

a) From impulse-momentum theorem I have: ##J=mv## so ##v=\frac{J}{m}## and since the ball doesn't slip ##v=\Omega b## so ##\Omega=\frac{J}{mb}## and ##\dot{\theta}=\frac{v}{a+b}=\frac{\Omega b}{a+b}##. b) I considered the angular impulse: ##-J(a+b)=I_0 \Omega_0 \Rightarrow...

Since there is no free charge ##\int_S \vec{D} \cdot d\vec{a} = 0## and ##\rho_f = 0## ##\sigma_f = 0## ##\vec{nabla} \cdot \vec{P} = 0## since P is a constant ##\rho_b = - \vec{nabla} \cdot \vec{P} = 0## For a simple surface we can find the boundary conditions for ##\vec{E}## using a Gauss'...

The problem says I have a spherically symmetric spinning constant charge distribution of charge Q and angular momentum w; I saw two possible explanations but none of them has made me realize why it is zero, one mentions thata constant w somehow implies a constant E which would mean there is no B...

In this question it is given that the sphere which is conducting is initially given a charge q then due to nonuniform mechanical strength and due to electrostatic force it creates a Small hemispherical bulge on its surface? okay my doubt is Let me define a term σ where σ is surface density...

I used the equation for the refraction on a spherical surface: ##\frac{n_1}{p}+\frac{n_2}{q}=\frac{n_2-n_1}{R}##, where ##n_1=1## is the index of refraction of air, ##n_2## the index of refraction of the sphere, ##R## is the radius of the glass sphere, ##p## is the object distance which, since...

Trying to calculate a circumference of a sphere from a radius of 3.09 inches. Is 19.4 a correct answer? Just ran numbers in the first circumference calculator I found http://calcurator.org/circumference-calculator/. Can I use the same formula for a sphere? What can I say ...Geometry is not my...

I am not sure how to solve for E(r) for R1<r<R2.

So, to obtain the motion equations I initially plotted the free-body diagram (see picture). Then I’ve tried to get equations, but I’m not sure, do I have done it rightl. I will be gratefull if someone could help me.

A thin shell in reality doesn't have zero thickness. Consider the image below, showing a cross-section of a small portion of the shell: Here we are considering a more general case in which we have electric fields of magnitude ##E_1## and ##E_2## on each side of the shell. Gauss's Law...

I am not sure what form of mass conservation to use to solve the above problem from An Introduction to Combustion by Stephen Turns. Can anyone explain what form of mass conservation applies to a sphere in this context?

Let ##m_s = 0.05, m_{s_1} = 0.02, m_r = 0.12, L = 0.8.## be the masses of the two spheres, mass of the rod, and length of the rod. Then the work done by gravity when the rod reaches the vertical position is ##(m_s(L/2) - m_{s_2}(L/2))g## and the kinetic energy equals ##\frac{1}2 (\frac{1}{12}...

Does the central projection of the position of a star to the firmamentum (celestial sphere) has a special name?

Hi, I'm new here, so I don't know how to write mathematical equations, and I may not be fully aware of the rules here, so I'm sorry if I made a mistake. I know how to calculate the electrostatic potential energy of a countable number of charged particles, but I don't know how to calculate the...

Specifically a monolithic Dyson Sphere; also, how would a Dyson Swarm work / be a better option?

I know I must have done something wrong somewhere here, but I cannot figure out exactly which one Answer is supposed to be (2/5)MR2 Whatever disaster I have in the last image does not evaluate closely to that at all. I'm not looking for another way to find the MOI of solid sphere, I would...