Surface Definition and 1000 Threads

Homework Statement a) 21.4-nC of charge is placed on a 4.8-m long steel tube with a d = 5.9-cm diameter. What is the magnitude of the electric field as a radial distance of r = d / 3? b) What is the magnitude of the electric field as a radial distance of r = 20 d? I was able to determine the...

What effect (if any) would changing the surface area of electrodes in a lithium ion battery have? Would it allow for faster battery charging? Faster discharge rate? Thanks in advance

When deriving the conserved currents from continuous symmetries, my book states that we can also add a 4-divergence to the lagrangian density which does not change the action under variation. The four divergence can be transformed into a boundary integral by stokes theorem. However, my book...

[Moderator's note: Spin-off from another thread.] I'm sorry, does black hole have surface area? Did you mean the sphere defined by Schwarzschild Radius?

Homework Statement Water is sprayed at an angle of 90° from the slope at 20m/s. Determine the range R. PLEASE SEE ATTACHMENTHomework Equations [/B] Kinematic Equations: acceleration: A = 0i +g(-j) + 0k; velocity: dV/dt = A; position: dR/dt = V; Origin set at the point spout...

Homework Statement A rope is pulled off with a force F from a combined cylinder. the smaller cylinder's radius is r and the big one's is R. the cylinder rotates on a rough surface without sliding. the force makes an angle θ with the horizon. What's the acceleration's "a" magnitude and...

Hello, I have data for optimization that contains different values of 4 different parameters, and the respective function value based on them. I want to find the maximum of this function, while making sure it's a "stable" maximum, i.e., for nearby parameters, the value of the function shouldn't...

I'm beyond multi-variable calculus, where this is taught, but I still don't know what the hell a surface integral is. I understand that d\sigma is the surface element, and | \frac{\partial \vec{r}}{\partial u}du \times \frac{\partial \vec{r}}{\partial v}dv | = d\sigma = |\frac{\partial...

A heavy board is fixed to another flat surface along its entire upper edge and not moving. How can I find the tension force that is acting on the board? Is it the same as if the board would be fixed to a string in the middle of the upper edge and hung and then the tension would be T=mg?

This stems from considering rigid body transformations, but is a general question about total derivatives. Something is probably missing in my understanding here. I had posted this to math.stackexchange, but did not receive any answers and someone suggested this forum might be more suitable. A...

This is no homework; but I cannot work it out so I assume one of my assumption is off... no matter how much I looked at it I can't get to the textbook answer. I tried searching (Google is my friend); I got to Prof. Burge's wonderful lectures slides (Arizona.edu) but he follows a different path...

What exactly are surface bound charge and body bound charge? Is there any difference between: 1) surface bound charge and surface charge 2) body bound charge and body charge How do we know if surface and body bound charge exist? Does polarized material always have surface and/or body bound...

Homework Statement Calculate the surface density (planar density) of the Silicon diamond structure in the [1 0 0],[1 1 0],[1 1 1] planes. Given a = 5.431 A (latice constant) Hint: For the (111) plane, it should help you to think of the diamond lattice as two interpenetrating FCC lattices.2...

I am trying to use the Israel junction conditions for a null surface, but I am running into complications with defining a normal vector for a null surface. As I understand it the normal vector is defined to be perpendicular to the surfaces tangent vectors n\cdot e_i=0, as well as satisfying...

Assume that we have a conductor of any shape, say a ball of copper. At electrostatic equilibrium, it is well known that the potential inside this conductor is constant, for otherwise free charges would move from points of highest potential to points of lowest potential (this includes the surface...

A disk with a uniform positive surface charge density lies in the x-y plane, centered on the origin. The disk contains 2.5 x 10-6 C/m2 of charge, and is 7.5 cm in radius. What is the electric field at z = 15 cm? I have used the formula...

Homework Statement Find parametric equations for the portion of the cylinder x2 + y2 = 5 that extends between the planes z = 0 and z=1. Homework Equations I can't really find any connection but I do have x=a*sinv*cosu y=a*sinv*sinu z=a*cosv The Attempt at a Solution I...

I was looking at a problem: http://gyazo.com/c872ea999197823a42568809f9d97d3f and I understood that the reason that the force would have to be greater on a surface with friction because the equation for the force of friction is dependent on mass (μk * mg) and with two masses it essentially...

I understand mild steel is very bad at out gassing so is never usually considered for hard vacuum applications. But if the decision was constrained by other factors would it be possible to apply a surface treatment or coating to the internal walls of the vessel - am I correct in assuming that as...

Normal density of Earth is 5,5 tons/m3 and surface gravity is 9,8 m/s and. But if we would compress mass of Earth to 50 km diameter, we would get density 1,4 mil tons/m3 and surface gravity would be 158 860 m/s. I know the math, in basic gravity equotation F=Gm1m2/r2 with decreasing r you get...

Rather a short question, but what kind of design can be used for a narrow potential surface curvature in molecules?

Could a particle(proton, gold ion, electron) beam reach the surface of the moon, given current technology? Would the beam diffuse too much too scenter the regolith? Or would the beam have to be focused or continually refocused in order to achieve that? If so why can they do it with laser...

Hello. Let's say we build the Faraday cage which surround strong radiation such that no radiation can escape to outside world for safety. What happens on external surface of the Faraday cage in voltage during shielding? Is it fluctuated?

Hi, I am making a faraday cage to be used in reactive ion etching of silicon. I was wondering if the size of the cage, or the surface area has any impact on it's effectiveness or how it works? I know the size of the mesh and the material I use, as well as whether or not it is grounded all...

Surface current density, K is defined as: K = σv where σ is surface charge density and v is velocity. Given a uniformly charged spherical shell with radius R, spinning at constant angular velocity ω, find the current. So, I start with this formula: dI = K dl dI = σ Rω dl and I placed the...

Homework Statement I want to know if I got the answer correct and if my reasoning is sound. The text answers and solutions manual only gives answers/solutions for odd numbered problems. Here is the problem: And a direct link to the imgur page: http://i.imgur.com/Tko1xFh.png Homework...

I would like to obtain the conformal map from a uniform rectilinear fluid flowing in the x-direction, where the field is bounded below by the x-axis, to the flow in the w-plane. In the w-plane the flow is correspondingly bounded from below by a trochoid. (A trochoid is a continuous waveform...

Homework Statement Given a 2.0 kg mass at rest on a horizontal surface at point zero. For 30.0 m, a constant horizontal force of 6 N is applied to the mass. For the first 15 m, the surface is frictionless. For the second 15 m, there is friction between the surface and the mass. The 6 N force...

I'm trying to find the resulting location of a point on a sphere in spherical coordinates or Cartesian. Based on velocities from the perspective of an object on the sphere. So given the: location on the sphere (in spherical or Cartesian) zy - plane rotation of the point up direction of the...

A straight line in 3 space can be described as A + Bt, where A is a position, B a direction, and t a scalar parameter. CAD surfaces can be represented in terms of polynomial functions of two variables (u and v) with the highest degree term being u^nv^n. The intersections can then be obtained as...

Homework Statement A cylindrical diving bell with open bottom and closed top 12.0m high is lowered into a lake until water within the bell rises 8.0m from the bottom end. Determine the distance from the top of the bell to the surface of the lake. Homework Equations I actually solved this...

1. Calculate the gravitational field strength at 500km above Mars' surface. Mass of Mars: 6.39 x 1023 kg Radius of Mars: 3.39 x 103 km Constant G: 6.67 x 10-11 2. I used the equation g = GM / r23. To begin with I added the 500km height above ground to the radius, giving 3.89 x 103 km. I then...

The equation. Q(x, y,z) = -5/2:X2 - y2 + 4z2 + 7xy - 2xz - 2yz. Find its axis and draw its intersection with the plane x + y + z = 0 .

Homework Statement Let g_{\mu\nu} be a static metric, \partial_t g_{\mu\nu}=0 where t is coordinate time. Show that the metric induced on a spacelike hypersurface t=\textrm{const} is given by \gamma_{ij} = g_{ij} - \frac{g_{ti} g_{tj}}{g_{tt}} . Homework Equations Let y^i be the coordinates...

Homework Statement An infinitely long cylindrical surface of circular cross-section is uniformly charged lengthwise with the surface density σ = A cosΦ where Φ is the polar angle of the cylindrical coordinate system whose z axis coincides with the axis of the the given surface. Find the...

Homework Statement Considering the vector Field F(x,y,z))(zx, zy, z2), and the domain whose boundary is provided by S=S1∪S2 with exterior orientation and S1={(x,y,z)∈ℝ3 : z=6-2(x2+y2), 0≤z≤6}, S2={(x,y,z)∈ℝ3 : z=-6+2(x2+y2, -6≤z≤0}. Compute the total flux of F across S. Homework Equations...

Hi, What's the surface joining two points in a family of concentric spheres? Shown below is the general idea; it's actually optical. Two rays meet at P from P1 and P2, respectively, where each point comes from a different sphere. How do I find surface S if I know the coordinates of P1 and P2...

Question: Evaluate the surface integral $$J = 2xzdy \land dz+2yzdz \land dx-{z}^{2}dx \land dy$$ where S \subset {\Bbb{R}}^{3} is the rectangle parametrised by: $$x(u,v) = 1-u,\ y(u,v) = u,\ z(u,v) = v,\ \ 0\le u, v \le 1$$ so far I have: \begin{array}{}x = u\cos v, &dx = \cos v\, du -...

Am I correct in thinking that the force of gravity between 2 test objects at rest on a planet's surface is less than it would be for the same objects at rest in deep space? I understand that this occurs because in GR gravitational potential has a mass value which is lost on the surface, while...

Suppose I have already found the surface normal vectors to a set of points (x,y), how do I compute the surface height z(x,y)? Basically what I have are the normal vectors at each point (x,y) on a square grid. Then I calculate the vectors u = (x+1,y,z(x+1,y)) - (x,y,z(x,y)) and v =...

I recently read that the charge density is less on surfaces with greater radius of curvature on the surface of a charged irregular conducting body . if anyone can provide a proof or explanation , please help!

I have been told by my teacher that the surface of a fluid is always perpendicular to the net force acting on it. The reason being a fluid can not withstand tangential stress and if a shear stress is applied to it, it will slip until the surface becomes perendicular to the net force. So my...

Homework Statement Two identical metal blocks, H and A, are placed at equal heights on frictionless ramps as shown above. The blocks are released at the same time, travel down the ramp, and then slide off their respective ends of the table. Block H leaves the table from a horizontal surface...

Is there something in General Relativity whose value is 9.8 m/s2 at the surface of the Earth?

I have two images below. This is a single piston with pressure inside, the variables are as listed. P_in = 2700 Pa. P_out = 0 Pa. R1 = Radius 1 = 10 cm. R2 = Radius 2 = 5 mm. P_contact = ? My solution to P_contact is as follows. Area A1 of piston at R1 = .0314m^2 and area A2 at R2 =...

During a physics lecture, the professor demonstrated how to find the period of an object that was dropped through a hole drilled straight from one end of our planet to the other. He finished by saying "an object orbiting the Earth near the surface will have a period of the same length as that of...

Homework Statement Air flows at a mass flow rate(m) of 0.05kg/s in a thin pipe with a diameter of 0.15m. The air enters the pipe at (Ti)103 deg celc and cools to(To) 77 deg celc after traveling 5 m in the pipe. The heat transfer coefficient between the duct outer surface and the ambient...

Member warned about posting without showing an effort 1. Homework Statement 'Using the graphing function on your Graphics Calculator, or otherwise, determine the radius for a minimum Surface Area.' I HAVE NO IDEA WHAT TO DO? Homework EquationsThe Attempt at a Solution

Homework Statement The electric field has been measured to be horizontal and to the right everywhere on the closed box shown in the figure. All over the left side of the box E1 = 80 V/m, and all over the right, slanting, side of the box E2 = 400 V/m. On the top the average field is E3 = 260...

Homework Statement Find the surface temperature of a small planet having circular orbit around the sun with time period T,assuming sun and planet to be black bodies. Take radius of sun = R, its mass = M and its surface temperature as ##\theta_0##. Homework Equations ##P=eA\sigma T^4## Total...