Sphere Definition and 1000 Threads

I need to calculate the magnetic field generated by a static sphere at its center. On the surface of the sphere flows a constant current ##K \hat \phi##. Now, my guess was that the field produced would be equal to the field produced by a lot of rings, that is, i will split the sphere in a lot...

The answer given states that: The entire x-y plane is obviously at the same potential since all the fields are strictly perpendicular to it (draw a diagram if youre confused). Since we choose the sphere to be at potential zero, the point on the sphere which cuts the x-y plane is also at zero...

Caution: This video has music. Turn sound off before watching if this bothers you!

I'm not quite sure where to start. If someone could help me I would very much appreciate it.

Help please - okay so I have a question and struggling here. I need to know the radius of the sphere and how much water it displaces. One sphere inside an inverted cone One sphere for which the maximum possible amount of water is displaced. The problem is I’m only given the height of the...

I'm re-watching Star Trek TNG and I just started the episode where they encounter Scotty aboard a ship that's crashed into a Dyson sphere. That got me thinking. What would the mass and external surface gravity of a Dyson Sphere be? I've done the math myself, but I'd appreciate someone double...

I tried to find the charge distribution using the given potential but couldn't produce the correct result. Also, Gauss's Law doesn't help, as the electric flux is 0 but we don't have any symmetry. Can someone please shine a light on this? Thanks in advance..

I = 2/5M R^2 + Md^2 This is analagous to Earth's movement about the Sun. Is the moment of inertia of Earth about the centre of mass of the Earth Sun system = 2/5MR^2 + Md^2, where: M = Mass of earth, R = Radius of Earth, d = distance from Earth to centre of mass of earth-sun system.

in my head this is just a silly problem in which i need to determine the ↓ force (weight) and the ↑force (archimedes bouyant force) and then the difference must be the drag force ↑ (the force that involves velocity) but i can't get any sense out of this answer how is possible for the sphere to...

Given a certain manifold in ##R^3## I've been told that at every location ##p## it is possible to encounter a reference frame from which the metric is the euclidean at zero order from that point and its first correction is of second order. This, nevertheless does not match with the following...

<mentor - Epistemology (how do we know or perceive) is not subject PF supports in the science forums - moved to General Discussion> Since my previous topic The arrangement of our visual system and the objective truth was closed I will open a new one, less philosophical. So, just imagine that...

I'm not sure this a strictly Astronomy question; perhaps it should go in Aerospace Engineering. I have always thought that Dyson's work was more of an Astronomy topic, although admittedly, from the POV of observing some other system's sphere. In any case, I was thinking about future...

The surface area of the sphere is 4πr^2. dr/dt is given as 3cm^-1. dS/dt=dS/dr*dr/dt Differentiating 4πr^2 is dS/dr= 8πr dS/dt=8πr*3 dS/dt=24πr Given that r=5 dS/dt=24π*5=120 π The volume of the sphere is 4/3πr^3, differentiating which is dV/dr=4πr^2 dV/dt=dV/dr*dr/dt dV/dt= 4πr^2*3...

So using the above equation, e=dQ/dt / (A*5.67E-8*303.8^4) The surface area of a sphere is 4(pi)r^2 and I get 136.8478 m^2. dQ/dt would be the net radiation (I think? Its in the correct units), 1074W. Plugging everything in I get 0.01625, but the answer is 0.0524. Now as I was writing this I...

I did the question as attached, so I think A and D are correct but the given answer is E. Where am I wrong? Thanks.

Let us attempt part C first, which is to find the total energy of the entire system. I can definitely find an expression for the force, as given by Coulomb's Law. However, why should I integrate this force from infinity to d, where d is the distance of the external charge to the centre of the...

The force per unit area (Pressure) on a part of the sphere is given by F = (E outside + E inside)/2 * Q = 0.5 (kQ/R^2) * (Q/ 4piR^2) = (Q^2/ 32pi^2 e0 R^4). I understand the above line. The solution then says this pressure is exerted on the contact area between the 2 spheres, as given by...

My question is this: - Friction exists (for no slipping/pure rolling to occur) - Why is the work done against friction not accounted for in the conservation of energy equation? Thank you!

Could anyone tell me the capacitance of a one food diameter metal sphere. I know that this is a one terminal component but it still should have a capacitance. If a charge of Q is small and a 6 inch radius is drawn about the point then that 6 inch radius ( 12 in diameter ) should have a...

I traced a spherical X-ray Gaussian (green) where the negative charges were diametrically opposite. My question is this: I can transform the entire charge of the Gaussian sphere into a point charge placed in the center. So, can I analyze only the electrical forces of the two negative charges...

I can use integral as attached to obtain the answer. However, I wonder why I can not use " V = KQ / r " the get the correct answer. Thanks.

Summary:: Describe what the intersection of the following surfaces - one on one - would look like? Cone, sphere and plane. My answers : (1) A cone intersects a sphere forming a circle. (2) A sphere intersects a plane forming a circle. (3) A plane intersects a cone forming (a pair of?)...

Solving for the volume and surface bound charge densities was easy using equations 1) and 2). The polarization only has an r component so ##ρ_b=-\frac 1 {r^2} \frac {d} {dr} (r^2 \vec P)=-α(n+2)r^{n-1}##, and ##\hat n=\hat r## so ##σ_b=αa^n##. To find ##\vec E## I intend to use equation 3)...

The Sub Photon Sphere Escape (SPSE) Game Game Board: Vast Empty Space Game Pieces: ##\space## 1) A large perfect Schwarzschild black hole ##\space## 2) A Carrier/Trigger. This is a massless device that sets the Player Device into a selected position and velocity and then triggers it...

I am rather confused how to answer this (Please focus on "find the potential at the center"): I thought that would be a good idea try to answer this with the Poisson equation. $$\nabla \phi = - \frac{\rho}{\epsilon}$$ So that, since the eletric field inside a hollow spherical shell is zero, the...

Cylinders rolling down inclines are a common demo. But how do you model the movement of a sphere rolling within a rolling cylinder? I teaching a physics class and this question came up and my dynamics math is a little rusty. But I haven't found anything like this in any book or online. There's...

I've spent well over two hours searching the web for two functions of the radius of a Schwarzschild BH. One would give me the escape velocity of the BH assuming a perfectly vertical trajectory (so it isn't a normal escape velocity). The second relates to the trajectory of a photon that is...

I have worked out (and then verified against some sources) that ##R^\theta_{\phi\theta\phi} = sin^2(\theta)##. The rest of the components are either zero or the same as ##R^\theta_{\phi\theta\phi} ## some with the sign flipped. I was surprised at this, because it implies that the curvature...

I know some multivariable calculus, I just want someone to walk me through the integration deriving the mass element dM and the integration of thin rings composing the hollow sphere. It would also be nice if you could show me doing it one way using the solid angle and one way without using the...

Here's an image. O and O' are the respective centers, a is the distance between them, r is the distance from the center of the sphere to P, and r' = r - a, the distance from O' to P. The approach (which I don't understnad) given is to use Gauss' Law and superposition, so that we calculate the...

The answer with no details is given by First, I considered a spherical shell because I thought the velocities at different radius ##r## will be different and hence the four-momentum will be different, as well. Then, I writed down the linear momenta by $$\epsilon^{ijk} r_i p_j = L_k$$ with...

a) Just using the equations gives us: surface charge density = ## \rho_{\rho s} = kR^2 ## volume charge density = ## \rho_\rho = -4kR ## b) I am not sure here but the Q on the shell is the same as within. If that's the case we can use gauss law to find Q which I guess is the total charge. ##...

Consider the Hubble horizon as the proper distance over which Hubble expansion equals c, so that you are in the center of a Hubble sphere with a radius of about 13.5 billion light-years. As you approach light speed in any direction, does the Hubble horizon draw closer in that direction due to...

The integral that I have to solve is as follows: \oint_{s} \frac{1}{|r-r'|}da', \quad\text{ integrating with respect to r '}, integrating with respect to r' Then I apply the divergence theorem, resulting in: \iiint \limits _{v} \nabla \cdot \frac{1}{|r-r'|}dv' =...

Ornstein-Zernike states that ##h(r_{12}) = c(r_{12}) + \rho \int d\mathbf{r}_3 c(r_{13})h(r_{32})## which after a Fourier transform becomes ##\hat{C} (\mathbf{k}) = \frac{\hat{H}(\mathbf{k})}{1+\rho \hat{H}(\mathbf{k})}## However, I don't see how to simplify this to the second equation he has...

I'm assuming the way to go about it is to integrate in spherical coordinates, but I have no idea what the bounds would be since the bottom edges of the square pyramid are some function of r, theta, and phi.

Well, in this problem, I try to use $$d \tau '= \mu ^2 \sin {\theta} {d\mu} {d\theta} {d\phi}$$ With these domain integration: $$0<\mu<r$$ $$0<\theta<\pi$$ $$0<\phi<2\pi$$ , I get $$V=\frac{1}{4\pi \epsilon_0} \frac{3Qr^2}{2R^3}$$ This result is wrong because doesn't match with Prob 2.21, which...

I used the potential at the surface of the sphere for my reference point for computing the potential at a point r < R in the sphere. The potential at the surface of the sphere is ## V(R) = k \frac {Q} {R} ##. To find the potential inside the sphere, I used the Electric field inside of an...

i tried a force balance around the sphere but the weight of the displaced fluid is greater than the weight of the sphere which gives a net acceleration upwards and no terminal velocity but the book says that the terminal velocity has a certain value from there the exercise is meaningless to me...

Here is what the solution says: As usual, quote the general potential formula: $$V(r,\theta)=\sum_{l=0}^{\infty}(A_lr^l+\frac{B_l}{r^{l+1}})P_l(cos\theta)$$ The potential outside the sphere is: $$V(r,{\theta})=\sum_{l=0}^{\infty}\frac{B_l}{r^{l+1}}P_l(cos\theta)$$, which makes sense to me...

So I already have a solution available to this problem and the link for the solution is: I have understood everything in the video except the part where they are equating the force dF=GM/r²*dm According to my reasoning the inner part of the sphere (the part below the dm element we have taken)...

Let's say I place a positive point charge inside a hollow conducting sphere. If we take a Gaussian surface through the material of the conductor, we know the field inside the material of the conductor is 0, which implies that there is a -ve charge on the inner wall to make the net enclosed...

I draw a sketch of the diagram to the right. The body has a radius of ##r_B = 0.2## m. The volume of the body is given by ##V_B = \frac{4}{3}\times \pi \times 0.2^3 = 0.034\;\text{m}^3##. The mass of the body : ##w_B = \rho_B V_B = 400\times 0.034 = 13.37\,\text{kg}##. Hence the mass of the...

I've tried a few ways of solving this, both directly and by using Stokes' Theorem. I may be messing up what the surface is in the first place F= r x (i + j+ k) = (y-z, z-x, x-y) Idea 1: Solve directly. So ∇ x F = (-2,-2,-2). I was unsure on which surface I could use for the normal vector...

I am trying to integrate ##\sigma=\chi\int\frac{dA}{A}## for a sphere. The answer is supposed to be ##\sigma(R)=\chi(R^2/R_0^2-1)##. The answer I keep getting is ##\sigma(R)=2\chi ln\frac{R}{R_0}##. I also tried doing it in spherical coordinates, and all I get for the integration of...

The volume of the sphere = \frac{32{\pi}r^{3}}{3} The answer given at the back of the book is (\frac {32}{3} - 4\sqrt{3}){\pi}r^3 To drill a hole completely through the sphere, the hole would have to have a length of 4r. To get the answer in the back of the book, it requires setting the...

Least count of the screw gauge = Pitch÷No. of divisions on circular scale=1.5÷100 mm =0.015mm According to me,in this case the main scale reading should be taken as 2 mm because it is the one which is visible and circular scale reading should be 76. So, Diameter=2 mm + 0.015×76 mm = 2 mm + 1.14...

I don't know if i can use V=E · d. I've read about gradient but i never used it so i was asking if there is another way to get tje electric field equation

A homogeneous sphere of mass M and radius R is at rest on a rough horizontal plane with coefficient of static friction μ . A spring of elastic constant k, is connected to the rotation axis of the sphere illustrated in the figure. The center of mass of the sphere is positioned at rest so that...