Sphere Definition and 1000 Threads

Homework Statement A) Use Gauss's Law to derive the electric field in all space for a non-conducting sphere with volumetric charge distribution ρ=ρ0r3 and radius, R. B) Repeat when there is a concentric spherical cavity within the non conducting sphere with radius, A. Homework Equations...

UPDATE: the first 2 assignments are done (i think). I'm stuck on 3. and I have explained in attempted solution what I have tried thus far. I have an important homework assignment due in Electromagnetism, and I have no idea where to start. It has many sub-assignments, but I cannot even figure...

Homework Statement You have a conducting sphere that is in equilibrium, it has a cavity in it with positive charge +q. If you bring another charge +q2 near the outer edge of the conductor does the total surface charge on the wall of the cavity, q(int) change? There is an image attached that...

Homework Statement A spherical cavity is hollowed out of the interior of a neutral conducting sphere. At the center of the cavity is a point charge, of positive charge q. (picture attached) a)What is the total surface charge q(int) on the interior surface of the conductor (i.e., on the wall of...

Homework Statement Consider three identical metal spheres: Sphere A carries a charge of -9q, Sphere B carries a charge of +3q, and Sphere C is neutral. Spheres A and B are touched together and then separated. Next, Sphere C is touched to Sphere A and then separated from it. Finally, Sphere C...

Homework Statement This is a problem from Boas, Mathematical Methods of the Physical Sciences chapter 5, section 5, number 6. Find the area of the cylinder x^2+y^2-y=0 inside the sphere x^2+y^2+z^2=1. Homework Equations This section deals with projecting curved areas onto a coordinate plane...

That 2D analogy part is fantastic!Just trying to share great videos.

Homework Statement Homework Equations The Attempt at a Solution The textbook says that the electric field on a surface of a conductor is: . So, I guess since the sphere is metallic I can assume that what I have written there is true?

Homework Statement Derive the volume of sphere using Calculus. i saw videos on this topic on youtube, but i want to do it by the method of integrating a circle at angle θ (Theta) . i am posting a photo where i explained every thing i did but i couldn't know what i am doing wrong. Homework...

Homework Statement Homework Equations The Attempt at a Solution for part ii) a<r<b E=0 I am not sure what will be the difference between the formulas for the electric field for a<r and a>b I think the formulas will look the same: The only difference that I can think of is that when r<a...

Lets say I have a conducting neutral sphere containing a spherical hollow space. The hollow space contains a point charge at its center. This setup will result in a charge equal in magnitude with opposite sign of the point charge spreading evenly over the boundary of the hollow space and a...

Have cylinder made from semipermeable material .There is positive pressure inside cylinder and negative pressure outside cylinder .How gradient of pressure will be changed if we convert from cylinder t o sphere? Thank you

If I consider a tetrahedron of four densely packed spheres of unit radius, what it the radius of the largest sized sphere that can fit in the space in between?

Hello, I was recently given the task to find experimentally the moment inertia of a sphere. I thought of rolling the sphere down an inclined plane and applying conservation of energy to the sphere. The equations i came up with are: mgh = 1/2mv2 + 1/2Iω2 solving for v^2 we come up with the...

So I have been having a bit of trouble trying to derive the moment of inertia of a solid sphere through its center of mass. Here is my working as shown in the attached file. The problem is, I end up getting a solution of I = (3/5)MR^2, whereas, in any textbook, it says that the inertia should...

Homework Statement Bildschirmfoto 2018-06-19 um 18.50.50.png In the y-z plane there is an infinite long surface with charge density ##\sigma## that slices through a sphere with radius R. Determine the Flux.The Attempt at a Solution I have solved the problem but am stuck at the last part. I used...

Homework Statement Hollow iron sphere is half submerged in water.Sphere has outer diameter of 10 cm. Calculate thickness of the wall , when the iron density is 7.9 g / m3. I get answer 0.11cm, book says that it is 0.22cm. Homework Equations [/B]The Attempt at a Solution First i found buoyant...

Homework Statement Homework Equations Stokes theorem $$\int_C \textbf{F} . \textbf{dr} = \int_S \nabla \times \textbf{F} . \textbf{ds}$$ The Attempt at a Solution I have the answer to the problem but mine is missing a factor of$$\sqrt 2 $$ I can't seem to find my error

Homework Statement A solid insulating sphere of radius a = 3.6 cm is fixed at the origin of a co-ordinate system as shown. The sphere is uniformly charged with a charge density ρ = -215 μC/m3. Concentric with the sphere is an uncharged spherical conducting shell of inner radius b = 11 cm, and...

Homework Statement Assume a conducting sphere has a radius of 3400km with an electric field of 100 V/m at it's surface. a) Calculate total charge of sphere. b)Calculate potential at the surface using infinity at reference point c) Calculate capacitance of the sphere using the result of a or b...

Homework Statement A hollow conducting sphere with an inner radius of 5 cm and an outer radius of 6 cm contains a smaller sphere of radius 3 cm, located symmetrically inside the hollow sphere. The electric field strength at 4 cm from the center is measured to be 2400 N/C pointing inward. The...

Hi everyone! Sorry for the bad English! Please, I'm trying to understand Dirac' s notation and the Bloch sphere, but I'm stuck here: I've read that, thinking about the Bloch Sphere as a compass, the North pole would be 1 and the South pole would be 0. And in the classical bits the bit could be...

Hello, I'm trying to calculate Christoffel symbols on 2D surface of 3D sphere, the metric tensor is gij = diag {1/(1 − k*r2), r2}, where k is the curvature. I derived it using the formula for symbols of second kind, but I think I've made mistake somewhere. Then I would like to know which of the...

While studying Relativity I decided to take over a concrete case. So I thought of (what I think is) the simplest case which is the Sphere ##S^2##. So I want to construct the tangent space to the sphere. I think for this I need to embbed it in ##R^3##. I worked out similar problems in the early...

Homework Statement Homework Equations gauss law q=charge on sphere Q=total charge enclosed by gaussian surface Q=alpha/r x (4/3 pi r^3-4/3 pi R^3) + q The Attempt at a Solution EA=Q/ε[/B] E=Q/(Aε) now for E to be independent of r, alpha/r x 4/3 pi r^3 + q = 1/(4)(pi)(r^2) alpha x 4/3...

Homework Statement Two spheres are placed side by side on an inclined plane and released at the same time. Both spheres roll down the inclined plane without slipping. (a) Using FBD, explain what force provides the torque allowing the sphere to roll down the inclined plane. (b) Which sphere...

Homework Statement Homework EquationsThe Attempt at a Solution There can be two cases 1) The sphere might be a shell such that it floats on the water .When the temperature increases , even though density of water decreases , the force of buoyancy should remain same . Because force of...

Homework Statement [/B] An uncharged nonconductive hollow sphere of radius 10.0 cm surrounds a 20.0 µC charge located at the origin of a cartesian coordinate system. A drill with a radius of 1.00 mm is aligned along the z axis, and a hole is drilled in the sphere. Calculate the electric flux...

Homework Statement Calculate the volume of a sphere of radius ##r## in the Schwarzschild metric. Homework Equations I know that \begin{align} dV&=\sqrt{g_\text{11}g_\text{22}g_\text{33}}dx^1dx^2dx^3 \nonumber \\ &= \sqrt{(1-r_s/r)^{-1}(r^2)(r^2\sin^2\theta)} \nonumber \end{align} in the...

Homework Statement If we have a hollow ball completely filled with water which is rolling without slipping on a horizontal ground. If the water freezes which of the parameter will remain unchanged- angular speed, angular momentum, linear momentum, kinetic energy, total energy Homework...

I got into a little debate about the nature of a problem where you put a giant solenoid around the equator of Mars to give it a magnetic field (not my idea, I like futuristic things but... there are probably better things to worry about). Anyways, I got into a debate about the effect of the...

A sphere of radius a carries a total charge q which is uniformly distributed over the volume of the sphere. I'm trying to find the electric field distribution both inside and outside the sphere using Gauss Law. We know that on the closed gaussian surface with spherically symmetric charge...

Homework Statement Find the acceleration of a uniform solid sphere (of mass ##m## and radius ##R##) rolling without slipping down an incline at angle ##\alpha## using the Lagrangian method. Homework Equations Euler-Lagrange equation which says, $$\frac{\partial\mathcal{L}}{\partial...

would a gravity well resemble a angle food cake pan well traveling through a sphere? being you start outside the well. travel inward towards the core then outwards to the edge of the well again. wouldn't this also mean gravity wells would be replaced with pressure wells at the core?

in case of rolling without slipping of a solid sphere having uniform mass density the condition is Vcm (velocity of center of mass ) = Rω or [a][/cm] = Rα ,which comes from the fact that if an object that rolls without slipping the geometric center of the body travels 1 circumference along...

Homework Statement Homework Equations Volue of a sphere: ##~\displaystyle V=\frac{4}{3}\pi r^3## Area of a sphere: ##~\displaystyle A=4\pi r^2## Minimum/Maximum occurs when the first derivative=0 The Attempt at a Solution The fixed area is k, the edge is a: $$6a+4\pi...

I am to use this formula: https://d2vlcm61l7u1fs.cloudfront.net/media/fee/fee798ea-5480-47af-9904-35c76ac35e25/phpSzecLa.png I tried using intergral of (E*dr) as in the equation to integrate over the distance of V(2A)-V(0) But when i am to plug in zero into my integrate it would give a math...

In my introduction to quantum mechanics, I learned about the particle in a box, followed by the quantum harmonic oscillator. In both instances, zero energy was not possible; the ground states had non-zero energy. However, in deriving the solutions to the Schrödinger equation for a particle on a...

I worked problem 2.28 of Nayfeh and Brussel's Electricity and Magnetism. The problem asks for the potential near the center of a charged hollow sphere, based on the near-field expansion given by equation 2.62, which is: ##\Phi=\frac{1}{4\pi\epsilon_0}[\frac{dq}{r^\prime}+ \vec r \cdot \int...

I have a non conducting sphere with a charge ρ=A/r per uni vollume A is constant. suppose there is a cavity in the centre and within a particle of charge q. i want to find the E inside the sphere in respect with r. Homework EquationsThe Attempt at a Solution for radius equal of the cavity i get...

Homework Statement Homework EquationsThe Attempt at a Solution When a sphere of charge Q is touched to A and removed , A acquires charge Q/2 . When B is earthed , potential of B becomes zero . B acquires some charge q . V( B's center ) = 0 kQ/[2(d+2a)] + kq/a = 0 q = -aQ/[2(d+2a)] Now...

<<Moved from a technical forum, no template>> Why the answer is A?

$\textsf{Find the volume of the given solid region bounded by the cone}$ $$\displaystyle z=\sqrt{x^2+y^2}$$ $\textsf{and bounded above by the sphere}$ $$\displaystyle x^2+y^2+z^2=128$$ $\textsf{ using triple integrals}$ \begin{align*}\displaystyle V&=\iiint\limits_{R}p(x,y,z) \, dV...

Homework Statement A spherical shell with radius R and surface charge density σ is sandwiched between two infinite sheets with surface charge den- sities −σ and σ , as shown in Fig. 2.46. If the potential far to the right at x = +∞ is taken to be zero, what is the potential at the center of...

If the force acting between two point charges were proportional to \frac{1}{r^ 3}, instead of \frac{1}{r^ 2}, what would be the electric field intensity and charge density inside a charged solid metallic sphere?

I'm trying to model a sphere having force applied at position P in the following diagram: I know that this applied force will have an x and y component; the y component will propel it upwards, but what I am confused about is the x component of the force. I know that the x component will propel...

i don't know to using limit of r ?

Homework Statement [/B] The International Space Station (ISS) has a mass of 400,000 kg and orbits 408 km above the Earth’s surface. The ISS is 109 m across. Homework Equations : [/B] R=a(semimajoraxis) cubedroot(m2/3M1)The Attempt at a Solution : [/B] ive tried multiple ways with multiple...

I am pretty sure that I would be comparing apples and oranges in this question, but as I usually learn something from the responses telling me in detail that my question is silly, here goes: Does the phase used as a weight in Feynman's path integral formulation (i.e., the quantum action S in...

I want to calculate the volume of a sphere cut by two arbitrary plane. There is a intersection angle between these two planes, which is not 90 degrees. One of these two planes is fixed and located on plane "x-o-y", and the other is perpendicular to plane "x-o-z" and moves the distance "a" from...