Surface Definition and 1000 Threads

Why is this way of thinking wrong?. can't I assume that when Δx tends to zero is a sufficient approximation of what I want to get? It confuses me with the basic idea of integrating a function to get the area beneath a curve of a function (which isn't also as perfect) . PD: I put Δx tends to...

Hi PF! I'm trying to compute $$ \frac{1}{\sqrt g}\frac{\partial}{\partial u^\mu}\left( \sqrt g g^{\mu v} \frac{\partial \eta(s,\phi))}{\partial u^v} \right) $$ where I found $$ \sqrt g = \csc^2\alpha \sin s\\ g = \begin{bmatrix} \csc^2\alpha &0\\ 0 & \csc^2\alpha\sin^2 s \end{bmatrix}...

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...

Homework Statement I am doing a report on the effect of the surface roughness of a wing on the wing's performance. This was done by testing a a wing design in a wind tunnel using a smooth, intermediate and then rough surface. The test involved varying the pitch angle and tunnel power setting...

Homework Statement Given $$\phi = x^{2} +y^{2}-z^{2}-1 $$ Calculate the unit normal to level surface φ = 0 at the point r = (0,1,0) Homework Equations $$ \hat{\mathbf n} = \frac{∇\phi}{|\phi|}$$ $$ z = \sqrt{x^{2}+y^{2} -1} $$ $$ \mathbf n = (1,0,(\frac{\partial z}{\partial x})_{P})...

1. A uniform linear charge density of 4.0 nC/m is distributed along the entire x axis. Consider a spherical (radius = 5.0 cm) surface centered on the origin. Determine the electric flux through this surface. Homework Equations L=2rπ φ=Q/ε λ=Q/L The Attempt at a Solution I found the charge by...

Hi there. I wanted to plot a surface, given implicitly by a function ##f(x,y,z)=c##, with ##c## a constant. My ##f(x,y,z)## is obtained numerically, so I don't know the expression explicitly, I have the values of ##f(x_i,y_j,z_k)## for given integer numbers ##(i,j,k)##, ##i=1,2,3...## same for...

I attempted the question but it was wrong... I don't understand where i went wrong my working seems logical, can someone please help. When a needle is gently placed on the surface of still water (γ = 0.0730 N.m-1) it can be supported by surface tension if the mass of the needle is small enough...

Homework Statement Homework EquationsThe Attempt at a Solution I know the relation between electric field and electric potential . I can also find Electric field if expression for potential is given and vica versa . But I do not know how to work with electric field and equipotential...

Homework Statement Homework EquationsThe Attempt at a Solution When air is evacuated , atmospheric pressure pushing down the cork is eliminated , cork should rise a little i.e option b) . This is incorrect . What am I missing ?

Homework Statement Homework Equations ##E=\frac{kQ}{r^2}## The Attempt at a Solution The answer is "A".Right ?

Homework Statement Homework Equations ##Q_{net}=Q_1+Q2## The Attempt at a Solution ##Q_{net}=Q_1+Q2## ##-15 = +5 + Q_2## ##Q_2=-15-5 = -20nC##

Homework Statement (a) Explain how heat is lost from a hot surface to the surrounding air. The Attempt at a Solution We will assume as there has been no other stipulation that the effect of radiation is negligible and thus we are taking purely about conduction. We will also assume as there...

I placed a hot metal lid on a cool surface. When i tried to pull it up, it had a lot of resistance, i had to really try to pull it up. I could hear sounds under the lid, I'm guessing it was boiling water. What do you think could have caused this resistance?

Homework Statement A meter stick is held 60 degrees to the horizontal on a flat frictionless surface. If it is let go what is the distance the back the stick will reach with respect to the length of the meter stick (l). Homework Equations I = 1/3 mL^2 Don't know what to use. This seems more...

Homework Statement Homework Equations n1/n2 = (sinθ2)/(sinθ1) = v2/v1 The Attempt at a Solution Moving from a lower refractive index to a higher refractive index. ( Lower density to higher density means faster speed to slower speed) The answer is answer B, I don't understand why.

Hi All, Due to the differences in their conductivities, but considering that both the metallic and the glass plane surfaces produce mirror images of objects, is there any difference in the explanation of the mechanism of reflection of light in these materials?

There's something I need to confirm about Gauss' law. If I have to determine the electric field at point P due to charge +q, I take a Gaussian sphere enclosing the charge with the point on the surface of the sphere. So Gauss law doesn't care about the charge +Q because the flux do to this charge...

Homework Statement Homework Equations ΦE = ∑Q enclosed / ε ∑Q enclosed = λh The Attempt at a Solution ΦE = ∑Q enclosed / ε ∑Q enclosed = λh ΦE = λh / ε

Hello, Many Researchers talked about the following parameters: 1. Propagation length of the surface plasma wave(spw). 2. penetration depth of surface plasma wave(spw). 3. concentration of the (spw). 4. the equation of the interface in vacuum - plasma interface. I feel confused regarding such...

Hello, For a project I am working on, I am trying to design a 2D with parallel sinusoidal patterns. Imagine a 2D section of a pipe (two parallel surfaces with distance in between). Each surface is basically a sine function. Peak points meet with each other, as well as troughs. Liquid is...

Do we know roughly what the surface of a protein channel looks like? In most of the diagrams they are depicted as a sort of cylindrical tube with a smooth surface, but I'm curious if there are some more detailed documentations somewhere? For example I know they aren't rigid objects and may be...

How do i calculate percentage of changes in radius, when the surface which cause the radius, will be compressed by a certain percentage? To illustrate better, i have drawn the picture of the question. How to calculate radius ?? if radius A Is known. Changes in the surface is also known. Thank...

A solid sphere has surface charge density, Rho (r) Rho(r) = k 1 ( 0 < r < a) k2 x ( a < r < R) 2) Find the electric field in all region i.e 1) r < a and 2) a < r < R and 3 ) R < The attempted solution and the question with the diagram is attached below Could the answer be verified...

Homework Statement (Problem 2.38 From Griffth's Electrodynamics): A metal sphere of radius R, carrying charge q, is surrounded by a thick concentric metal shell (inner radius a, outer radius b). The shell carries no net charge. Find the surface charge density ##\sigma## at R, a, and b...

Homework Statement First I will say, I know I post here alot, but that is because I have exams coming up soon and I am a beginner, and It's crunch time, I'm self taught with only the help of friends and the internet. I'm currently doing a past examination as practice, but this one is much...

My question is basically similar to a thread that was posted 12 years ago: https://www.physicsforums.com/threads/electrons-flying-off-a-conductor.119269/ I was glad to see that there was already a thread which asked my question in the forum. But when I read through all of the discussion, I don't...

Fluid comes in at ##T_1## and comes out at ##T_2## and I know that heat is exchanged with steam at constant ##T_{steam}##. If I want to know the Surface of the exchanger then ##US(T_{steam}-T_{fluid}) = \dot m_{fluid} cp_{fluid} (T_2-T_1)## My question is, since ##T_{fluid}## changes, which...

Homework Statement The tension in the skin of the left ventricle of heart is 4.90 N/m. A cut is made on the left ventricle during surgery. How many stitches must be used to repair the cut? Each stitch will safely support a tension of 0.4 N. Homework Equations Surface tension = force/length...

What is the value of electric field at the surface of a spherical shell?

Homework Statement The surface area, A, of a cylinder with height, h, and radius, r, is given by the equation ##A=2πrh+2πr^2##. A company makes soup cans by using 32π square inches of aluminum sheet for each can. If the height of the can is 6 inches, find the radius of the can. Homework...

Homework Statement Show that the surface and volume element on a deformed sphere are \sigma = \frac{\rho^2 \sin \theta}{\cos \gamma} d\phi d\theta, dV = \rho^3 \sin \theta d\phi d\theta, if \gamma is the angle between normal vector and radius vector. Homework Equations n\cdot r = \cos...

Does the event horizon of a black hole really represents the surface of the "star" (or mass) itself? What I mean to say is: That the event horizon is the (let's say it this way) sphere surface where the scape velocity is => than the speed of light. So it is not necessary for event horizon to be...

When studying Fresnel equations in EM, I very often came across the following type of picture for a s-polarized incident wave on a dielectric interface (http://iqst.ca/quantech/pubs/2013/fresnel-eoe.pdf) : Many similar diagrams can be found on the internet, for instance...

I have a surface defined by the quadratic relation:$$0=\phi^2t^4-x^2-y^2-z^2$$Where ##\phi## is a constant with units of ##km## ##s^{-2}##, ##t## is units of ##s## (time) and x, y and z are units of ##km## (space). The surface looks like this: Since the formula depends on the absolute value of...

What will be the area of common surface of two identical bubbles of radius R , i know there common surface will be flat as the radius of curvature of comman surface will tends to Infinity , but how do i relate with area of flat surface I tried to use Energy = Surface tension * area And then...

Hi .how can i calculate the molar volume and surface tension of nanoparticles ? shoud i have to calculate? or these parameters is available in tables or sth?

Well, my physics teacher taught us about rotation the other day and I came across a scenario where a sphere and a ring roll down a friction-less inclined plane from a point of absolute rest. I found it counter-intuitive as I started to think about why would they start rolling in the first place...

Homework Statement Homework EquationsThe Attempt at a Solution ## v = \frac { \omega } k ## ## \omega = \sqrt{ kg \tanh (k) } ##I have no idea to guess the graph. I put g = 9.8 and tried to calculate ## \omega ## for different values of k. ## \omega (0 ) = 0, \omega (30) =...

Homework Statement Everything that can be used is in the picture. μ is the coefficient of friction between both B and A and A and the surface. A is moving upwards the surface with a certain acceleration. B doesn't move in relative to the surface. 1. Why the direction of A's motion must be...

Homework Statement Homework Equations I consider four directions from the point of throwing the balls, east, west, up, down. At any given time, the balls will be at different distance from this point, (the upward ball will travel less distance than the downward ball). So, it could not be a...

Homework Statement A body that is on a horizontal surface begins to move under the action of horizontal force equal to 60% of its weight. Force acts for a while, then stops acting. Determine the total time of movement if the body has traveled a distance of 24m. Homework Equations [/B] I'm...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] The thing to remember is that inside the Earth surface, the gravitational field does not remain inversely proportional to ##r^2##. The equation of motion is ## \ddot r = \frac { -gr} R## ....(1) This means that the...

Hi, I am quite confused about followed question, I think scientist think the last scattering surface was dense plasma at the temperature of 3000K. If the today's universe much cooler and less dense then "the last scattering surface" how can anyone says entropy increased by time? Isn't universe...

I need help understanding what kind of problem this is at all, since I'm really lost. I'm missing the specific topic name (I called the topic "circular motion" because it's got something to do with it, but maybe it has a more specific sub-topic name), probably missing key formulas, and generally...

I am using a Micromeretics ASAP2020 machine. The sample is ~25mg of reduced graphene oxide based film. The problem is I am getting adsorption isotherms showing negative volumes of adsorbate (N2) entering the tube as P/P0 increases. The sample was degassed prior to testing at 250°C for 3...

Let's imagine a situation where we have a wheel of mass ##M## and radius ##R## on a frictionless surface, and we apply a force ##\vec{F}## as shown in the diagram. The force will produce both linear acceleration of centre of mass ##a## and angular acceleration ##\alpha##. The wheel starts to...

Homework Statement The surface tension of a layer of water obeys ## \sigma = a- bT##, where ##T## is the temperature. Find the change in temperaure, ##\Delta T## when the area is increased isentropically. Homework Equations ## dU = dQ -dW## , ##dW = \sigma dA##, ##dU = C_A dT + [\sigma...

Homework Statement Consider a cyclinder made of linear dielectric material with uniform dipole distribution. An externally applied field ##E_{ext}## is applied in the direction parallel to the axis of the cyclinder. What are the values of the bound chrages at the surface. Homework Equations...

It will be very helpful if someone suggest any articles or reading materials on this topic for detailed study.