Relation Definition and 1000 Threads

1-If we had a spherical capacitor and the voltage across it is 1000 V, I need to know the charge on every plate, I know 2 ways to solve this either using C=Q/V or V=Q/r * 1/4ε0∏. So, which one should I use, and why? 2-Another thing, according to hyperphysics the formula for the capacitance of...

Homework Statement This is not a homework problem, but a topic in a microeconomics book that I am unclear about. My book argues that the set X = {a, b, c, d} of preferences can be (i) transitive but (ii) incomplete. Is it possible for a similar set of preferences to be (i) complete but (ii)...

Problem: Define $a_n=(1^2+2^2+ . . . +n^2)^n$ and $b_n=n^n(n!)^2$. Recall $n!$ is the product of the first n natural numbers. Then, (A)$a_n < b_n$ for all $n > 1$ (B)$a_n > b_n$ for all $n > 1$ (C)$a_n = b_n$ for infinitely many n (D)None of the above Attempt: The given sequence $a_n$ can be...

Hello. Sorry for being annoying, I've posted like three questions today. But I'm studying nuclear chemistry and still somewhat confused regarding the binding energy and mass defect and their relation with the strong nuclear force.. 1) in this Hank Green video... He says that the mass defect...

I need to know the relation of wave function and vertex function of mesons. Any one give me an explanation of them. Are they same? in some journals their expressions are the same and in other papers the wave function expresses as a function of the vertex function of meson. Which one is the...

Homework Statement Let ##\mathbb{R}^2 = \{Q = (a,b) | a,b\in \mathbb{R}\}##. Prove that if ##q_1 = (a_1,b_1)## and ##q_2=(a_2,b_2)## are equivalent, meaning ##a_1^2+b_1^2 = a_2^2 +b_2^2##, then this gives an equivalence relation on ##\mathbb{R}^2##. What is ##[(1,0)]...

i know the relation between these two. with increase in pressure, the viscosity of liquids (expect water] increases while that of gases is practically independent of pressure. The viscosity of water decreases with increase in pressure. i want to know the reason behind this.

The question assumes that there really exists an objective probability such as disposition or propensity that is an extensive property of a state of affairs. Usually the dissipation of a work potential is associated with the mechanical motion of a system, and work potential is the free...

We say on-shell and off-shell mass of quarks. 1) What is the difference on-shell and off-shell mass of quarks. 2) At lab. center of mass frame for lepton particles p2= -m2. Can we apply this equation for quarks. Thank you!

i heard that aeroplanes are an application of benoulis theorem. Can you please explain it to me.

Homework Statement I don't seem to understand the proper intuition behind the electric field intensity potential difference relation? please can anyone explain it with solid intuition and maybe a good analogy...and can anyone give a short analogy about the concept of electric field...

Homework Statement By considering small changes in enthalpy, and using the central equation, derive the Maxwell relation \left (\frac{\partial S}{\partial V} \right )_{T}= \left (\frac{\partial p}{\partial T} \right )_{V} Homework Equations H=U+pV dU=TdS-pdV The Attempt at a...

Hello! I was playing around with a problem and while I was doing it I noticed a similarity between Cv*T=h by using Celcius and not Kelvin. So if I have a compressed liquid at say 50°C, looking up at a property table I find the hf to be 209.34 kJ/kg (the pressure is considered to be...

I boxed the portion of the solution that I am questioning. How come the number of invalid strings is only 3n-1 - an-1 and not 3(3n-1 - an-1) ? As you can see there are three cases (Which are to the right of the black box) In all the three cases, the portion boxed in red is a string...

I am having difficulty knowing which "cases" include in the recurrence equation. My solution to problem in paint document. Cases 1 - 6: All cases contain strings of length n Let ak represent number of bit string of length k with a pair of consecutive 0s. For cases 1 and 2. an-1, k = n-1...

I'm trying to solve a third order recurrence relation but not sure how. I wrote the characterisitc polynomial and factored it into (x-1)^3. Now what?

Hello everyone. I'm am looking for some literature (articles or books) containing information about how is the relation between the liquid water pressure (macroscopic thermodynamic quantity) and it's quantum molecular dynamics (collisions, vibrations, etc.). Like: The pressure increase...

We know that the mass of anybody turns to zero as it gains the velocity of light. From Einstein's Mass-Energy relation, E=mc2 so that, m=E/c2 It is clear that mass is directly proportional to energy. For a body to gain light's speed, we have to apply...

A circuit has n switches, all initially off. In order to be able to flip the ith switch, the (i-1)th switch must be on and all earlier switches off. The first switch can always be flipped. Find a recurrence relation for the total number of times the n switches must be flipped to get the nth...

Find the number of ways to arrange three types of flags on an n foot flag pole: red flags (1 foot high), white flags (1 foot high), blue flags (3 feet high) Find a recurrence relation for this number with one condition that there cannot be three 1 foot flags in a row (regardless of their...

hey guys, I am building an electric go kart for a final project, and I'm just trying to get my initial justifications correct, with respect to the classical physics involved. SPECS: i was the car to be able to reach 15km/h, The total weight of the car will be approx 200kgs. the size of...

As far as I know, F_ {ext} = d (\hbar k)/dt = d p_{electron} / dt + d P_{crystal} /dt. could one say that \hbar k = P_{electron} + P_{crystal}?

Say we have two vector fields X and Y and we form the projection of Y, Y' orthogonal to X. Since every vector field is associated with a curve with a corresponding parameter, is there a relation between the parameters of Y and Y'?

One of the most popular mass loss equations of a star, developed by D. Reimers, is given by: dM/dt = -(4x10^-13) * η(L/(gR)) solar masses per year Where η is a free parameter close to unity and L, g, and R are the luminosity of the star, surface gravity of the star, and the radius of the star...

If there is a formula relating the exponential with sine and cosine normal and hyperbolic (exp(ix) = cos(x) + i sin(x), exp(x) = cosh(x) + sinh(x)), there is also a formula relating the logarithm with arcsin, arccos, and arcsinh arccosh?

In transitions in the crystals we always use conservation of wave vector of electron, not electron momentum conservation. For example in an indirect transition from top of valence band to bottom of conduction band, the group velocity of electron and hence its momentum would not change (it is...

relation between r ,ω and θ for rotation around fixed axis. \frac{d\textbf {r}}{dt} = \textbf {ω} \frac{dθ}{dt} = ω \lvert\frac{d\textbf {r}}{dt}\rvert = \frac{dθ}{dt} bold means vector. Is this right?

I'm having trouble wrapping my head around what should be a trivial detail, but it is important, so hopefully someone else putting it in explicit words might help me understand it. What I am having trouble grasping is why do row operations preserve linear dependence relations for the columns...

Hello, I have an issue with the problem below. I have a series connection of two variable capacitances C_{1}(t) and C_{2}(t). I want to establish the differential equation between the current i and voltage V on the ports of the series connection. The capacitance of the series connection of...

Homework Statement The density of a sample of air is 1.211 kg/m3, and the bulk modulus is 1.42 · 105 N/m2. a) Find the speed of sound in the air sample. b)Find the temperature of the air sample. Give answer in °C. Homework Equations The Attempt at a Solution I found...

How can I prove the following relation T(∂p/∂T)v,N +(∂T/∂V)u,N =p(∂T/∂U)v,N where p= pressure, V= volume, U=internal energy, T= Temperature. I tried by fundamental relation and Maxwell's relation but couldn't able to prove it. I would appreciate if anybody helps me out.

I believe many users here are teachers now or they were in the past and some might be working as professors at universities. I think if you teach a certain subject you understand it well day after day and you realize that you are learning new things and the concept is becoming fundamental as...

hi, in quantum physics completeness relation is often use it equals to one - what is its significance in multiplying with state vector . thanks wasi

Homework Statement For main sequence stars, the mass–luminosity relation can be approximated by L\proptoM^{3.5} f) If luminosity and mass are both measured in solar units, what is the constant of proportionality? {2} I know that the luminosity value of the sun is 4x10^{26}W and M =...

On the set of Z of integers define a relation by writing m \triangleright n for m, n \in Z. m\trianglerightn if m-n is divisble by k, where k is a fixed integer. Show that the quotient set under this equivalence relation is: Z/\triangleright = {[0], [1], ... [k-1]} I'm a bit new the subject...

Homework Statement The displacement due to a wave moving in the positive x-direction is given by ##y=\frac{1}{1+x^2}## at time t=0 s and by ##y=\frac{1}{1+(x-1)^2}## at t=2 s, where x and y are in meters. Find the velocity of the wave in m/s.Homework Equations ##...

Hello, I have recently been reading some texts focusing on modern physics. Both include sections on Planck and how he arrived at the conclusion that energy is not continuous. However I am confused as to what conditions inspired him to make this leap. I am aware of the Ultraviolet Catastrophe...

Hi. I'm working through one of my first problems on sets and relations, and I need some help understanding if I'm getting this right. Any help/suggestions on my through process is greatly appreciated. The question is: Determine whether the relation R on the set of all real numbers is...

Hey guys, I have recently performed a lab where we are to find the equation relating the magnetic field strength to a distance from a dipole in both the transverse and longitudinal direction. We did this using a Hall Effect Probe and a magnetic dipole. What I found after plotting a Log...

I just read that the definition of work is not related whatsoever to the notion of time, whereas the relation between time and work is expressed by the explicit notion of power. However, W=Fs, and F is proportional to the acceleration a, which is the change of rate of the velocity wrt time...

Homework Statement . Calculate by a line integral the following double integral: ##\iint\limits_D (y^{2}e^{xy}-x^{2}e^{xy})dxdy##, D being the unit disk. The attempt at a solution. Well, if we consider C to be the curve that encloses the region D (C is the unit circle), then C is a...

Homework Statement A man of mass m is applying a horizontal force to slide a box of mass m' on a rough horizontal surface. It is known that the man does not slide. The coefficient of friction between the shoes of the man and the floor is ##\mu## and between the box and the floor is ##\mu'##...

Homework Statement It is customary to express fibre loss in units of dB/km: \alpha(dB/km) = \frac{10log(P_{in}/P_{out})}{L(km)} where P_{in} is the power entering the fibre and P_{out} is the power leaving the fibre. Show that \alpha(dB/km) = 4343\alpha(m^{-1}) The Attempt at a Solution...

Hey, Ive a question in my textbook and I don't really know what to do! The question is: I know I need to prove that the relation is 1)Symmetric 2)Reflexive 3)Transitive But how do I prove this

I have a metric g on spacetime and a spatial metric ##\gamma## such that the components of g can be written in matrix form as $$ g_ {\alpha, \beta} = \begin{pmatrix} g_{00} & g_{0 j} \\ g_{i 0} & \gamma_{ij} \end{pmatrix} $$ where ##i,j = 1,2,3## and ##\alpha = 0,1,2,3##. Now I want to find a...

Hi all, i have a doubt. How much teeth in relationship to his radius need to have a gear to be optimal? And, if i have 2 gears with same radius and same #of teeth, to have low friction and low negative effect from weight how much teeth they need to have and with which radius? I know it's too...

Hi, Say y=x2: the solution set is equal to the relation, which is also a set. What's the difference between saying "plot the relation y=x2" and "plot the solution set of y=x2"? Thanks for help.

Please help me in in proving the relation between H2n(x) and Ln(-1/2)(x2) where Hn(x) is the Hermite polynomial and Ln(-1/2)(x) is associated Laguerre polynomial.

Hey! Maybe this is a "piece of cake" question, but here is the thing, i have the Maxwell equations in the Lorenz gauge are \begin{array}{c} \partial_{\mu}\partial^{\mu}A^{\nu}=\mu_{0}j^{\nu} \end{array} In vacuum this gets reduced into \begin{array}{c} \partial_{\mu}\partial^{\mu}A^{\nu}=0...

hi guys, i have a question about the orbit-spin relationship of the celestial objects. for example in our solar system i understand the orbital period becomes lengthy for the planets more distant than the sun, it's logical, but what happens with their spinning motion..? i don't understand why...