Form Definition and 1000 Threads

http://www.physicspages.com/2014/08/22/electromagnetic-waves-in-vacuum/ Sorry i have no idea how to get the last step in the vector form how to convert and mix it?thank you

Homework Statement Reduce ##xy+zy## to diagonal form. Homework Equations The desired diagonal form is ##Q(\vec{x})=(\alpha_1(\vec{x}))^2+...+(\alpha_k(\vec{x}))^2-(\alpha_{k+1}(\vec{x}))^2-...-(\alpha_{k+l}(\vec{x}))^2,## where ##\alpha_i## are linearly independent linear functions. Also known...

Homework Statement Express the complex number (−3 +4i)3 in the form a + bi Homework Equations z = r(cos(θ) + isin(θ)) The Attempt at a Solution z = -3 + 4i z3 = r3(cos(3θ) + isin(3θ)) r = sqrt ((-3)2 + 42) = 5 θ = arcsin(4/5) = 0.9273 ∴ z3 = 53(cos(3⋅0.9273) + isin(3⋅0.9273)) a = -117 b...

Homework Statement Prove that ##[L_i,x_j]=i\hbar \epsilon_{ijk}x_k \quad (i, j, k = 1, 2, 3)## where ##L_1=L_x##, ##L_2=L_y## and ##L_3=L_z## and ##x_1=x##, ##x_2=y## and ##x_3=z##. Homework Equations There aren't any given except those in the problem, however I assume we use...

Mod note: Based on an attachment in a later post in this thread, the actual expression is ##(9 - 16\cos^2(\theta))^{3/2}## Homework Statement : https://www.physicsforums.com/posts/5610105/ Homework EquationsThe Attempt at a Solution my working is (9^1.5) - (16^1.5)[ (cos theta)^1.5 ] =...

sorry I have use the image I made. Since I don't know how to perform the formula on forum :( This is the problem I am having.

In particular how does matter "clump" together to form stars and planets, and how do Galaxy/star systems form? For the latter question is the answer simply that near massive enough bodies, the spacetime curvature is significant enough that the geodesics within its vicinity are closed curves...

Homework Statement in this question , solving equation 1 and 2 , how to get the F1 = (A1E1 P ) / ( 2A1E1 + A2E2) ? and also F2 ? Homework EquationsThe Attempt at a Solution we know that F2 = P -2F1 ) I have tried to sub (F2 / A2E2 ) in F1 = (A1E1 P ) / ( 2A1E1 + A2E2) , but i ended up...

Homework Statement I have the second order diff eq: Solving by Laplace transform gets me to: I could use the inverse laplace transform that takes me back to e^{at}cos(bt) with b=0, but that only solves for the homogeneous (complementary) part of the equation, it won't reproduce the dirac...

The material I am studying express the Ricci form as ##R = i{R_{\mu \bar \nu }}d{z^\mu } \wedge d{{\bar z}^\nu } = i\partial \partial \log G## where ##G## is the determinant of metric tensor, but I am not sure what does ##\log G## here, can anybody help?

Hi. Is the Maxwell equation $$\nabla\cdot\vec{E}=\frac{\rho}{\varepsilon_0}$$ even true in the stronger form $$\frac{\partial E_i}{\partial x_i}=\frac{\rho}{3\cdot\varepsilon_0}\enspace ?$$ I guess not, since I haven't found a source suggesting this. But shouldn't the isotropic electric field...

Okay, I'm following a series of video lectures on applications of finite element method to engineering, and the tutor started by demonstrating the mathematical background of FEM using a simple heat transfer problem. He derived the governing equation (in just one dimension): (1)...

$-x^2+4x-1$ should be converted to the vertex form of $y=k-(x-h)^2$ How can this be solved by factoring or any other method ? My attempt to solve this problem , I will be using the completing the square method, $\left(-x^2+4x+\frac{-b}{2a}\right)=1+\frac{-b}{2a}$ Here $\frac{-4}{-2}=2$...

Hi, I'm a high school science teacher. Most textbooks classify EM radiation as kinetic energy. But this doesn't seem right to me. As a photon is massless it's hard to see how it can have kinetic energy which is 1/2 mv^2. It could be said that it has energy hf and therefore mass hf/c^2. Then its...

If equation of motion(K-G Eqn.,) follows, ∂μ∂μΦ+m2Φ=ρ where 'ρ' is point source at origin. How time independent form of above will become, (∇2-m2)Φ(x)=gδ3(x) where g is the coupling constant, δ3(x) is three dimensional dirac delta function.

I was looking for a derivation of E=(2kλ)/r for an infinite line of charge. I understood that you need to use Gauss's Law and a cylinder around the line. When looked it up, I found this: http://www.vizitsolutions.com/portfolio/gausslaw/lineCharge.html He starts out with ∫E⋅dA=4πq. I have never...

Hello all, I am trying to bring this: (p \iff q ) \implies r into a CNF form. I have started with the logical equivalences: (p \implies q) = \lnot p\lor q (p \iff q) = (p \land q)\lor (\lnot p \land \lnot q) and then I have applied De Morgan's rules and the distribution rules, but...

Homework Statement Homework Equations Cartesian to Cylindrial The Attempt at a Solution What I was doing is that, I changed the limits of z, and the function.

Homework Statement Show that the Lorentz Force Law, \frac{dp^{\nu}}{d \tau} = -q U_{\mu} F^{\mu \nu}, is consistent with P^\mu P_\mu= -m^2. Here U is the 4-velocity, F is the Electromagnetic Tensor, and p is the 4-momentum. (Minkowski Space) Homework Equations As stated above. The Attempt at...

I have been around Sailboats all my life. For the last 25 years I have built and raced r/c model sailboats. My current question, I hope, can be more of a discussion than just a simple question and answer. Since I am into the design of all aspects of boat and sails. I have a question about...

Simplify the function f(x)= (x-(1+i))(x-(1-i)) . Is the function you wrote in factored form [ f(x)= (x-(1+i))(x-(1-i)) ] , the same as the original function in standard form [ f(x) = x^2 - 2x +2) ] ?

Homework Statement Express F1 and F2 in cartesian vector form Homework EquationsThe Attempt at a Solution I feel fairly confident in my work for F2 but F1 not so much. Especially the j component of F1. I assume my F(1x) component runs from the z axis to the tip of F1 and my F(1k) component...

Hi PF! I was reading my book and I understand the following $$\sum \vec{F} = \frac{\partial}{\partial t} \iiint_{CV} \rho \vec{u} dV +\iint_{CS} \rho \vec{u} ( \vec{u_{rel}} \cdot \hat{n}) dS$$ ##CV## is a control volume, ##CS## is control surface, ##u## is velocity, ##u_{rel}## is velocity...

Hi For brevity one usually writes Fredholm integral equation of the 2nd kind $\psi(x)=f(x)+\int_{a}^{b} \,k(x,s)\psi(s) ds$ into the form $\psi=f+K \psi$ where $K$ is the operator kernel My question can one write an integro differential equation $\d{\psi(x)}{x}=f(x)+\int_{a}^{b}...

Homework Statement Suppose that a surface has an equation in cylindrical coordinates of the form ##z=f(r)##. Explain why it must be a surface of revolution. Homework EquationsThe Attempt at a Solution I consider ##z=f(r)## in terms of spherical coordinates. ## p cosφ = f \sqrt{(p sinφcosθ)^2...

Hello, I have a maybe unusual question. In a paper, I recently found the equation $$\mathcal{L}_v(v_i dx^i) = (v^j \partial_j v_i + v_j \partial_i v^j) dx^i$$ Where v denotes velocity, x spatial coordinates and \mathcal{L}_v the Lie derivative with respect to v. Now I'm an undergraduate who...

Homework Statement Given x(t)=8cos(70\pi t)+4sin(132\pi t)+8cos(24\pi t), find the Fourier transform X(f) in the form of \delta function. Homework Equations X(f)=\int ^{\infty}_{-\infty}x(t)e^{-j\omega _0t}dt cos(\omega t)=\frac{e^{j\omega t}+e^{-j\omega t}}{2} sin(\omega t)=\frac{e^{j\omega...

I am trying to establish a Rationalist approach to Physics as a side project, and have taken Hamilton's Principle as one of the few postulates in my work. I've developed the concept enough to arrive at the usual stuff, like the Euler-Lagrange equations, Newton's First Law and Nöther's Theorem...

http://arxiv.org/pdf/1609.00716.pdf Date: September 2, 2016 Source: European Space Agency (ESA) Summary: ESA's Planck satellite has revealed that the first stars in the Universe started forming later than previous observations of the Cosmic Microwave Background indicated. This new analysis also...

Homework Statement Write this complex number in the form "a+bi" a) cos(-pi/3) + i*sin(-pi/3) b) 2√2(cos(-5pi/6)+i*sin(-5pi/6)) Homework Equations my only problem is that I am getting + instead of - on the cosinus side.(real number) The Attempt at a Solution a) pi/3 in the unit circle is 1/2...

Homework Statement Homework Equations Theta = arctan (y/x) The Attempt at a Solution Hopefully this is the right section to post in, but I am a bit confused with complex numbers. I am working on the problems above and I just wanted to make sure I am doing each part correctly. I think A...

Homework Statement Write the given numbers in the polar form ##re^{i\theta}##. ## \frac {2i} {(3e^{4+i})} ## Homework Equations ## z = re^(i\theta) ## ## \theta = Arg(z) ## ## r = |z| = \sqrt { x^2 + y^2 } ## The Attempt at a Solution I'm not really sure how to go about the exponential...

Hey all, I need the complex version of the sigmoid function in standard form, that is to say $$f(\alpha) =\frac{1}{1+e^{-\alpha}} , \hspace{2mm}\alpha = a+bi , \hspace{2mm} \mathbb{C} \to \mathbb{C}$$ in the simplified form: $$f = m+ni$$ but found this challenging, for some reason i assumed...

Hello! (Wave) I want to write the language of the automaton with the following transition function in regular form with $A$ as an initial state and $B,D$ as final states. $$\delta:\begin{matrix} & & 0 & 1\\ & A & B & C\\ & B & C & D\\ & C & D & B\\ & D & D & C \end{matrix}$$ I have...

When the temperature in a city is lower and one has a bath in the bathroom then why does more vapour get created? More vapour than it would be created when the temperature is higher?

There is no difference in electronegativity, so how do bonds form? Take for example C-C, they both want 4 electrons for a full valence shell to become more stable - they meet each other, but how come they share 4 electrons? There is no difference in electronegativity for them to attract each...

Is it correct that, from the perspective of an observer, time slows down and ultimately stops at the event horizon of a black hole, implying that no black holes have had time to form in the universe ?

Homework Statement can someone explain about the formula of the circled part? Why dA will become r(dr)(dθ)? Homework EquationsThe Attempt at a Solution A = pi(r^2) dA will become 2(pi)(r)(dr) ? why did 2(pi) didnt appear in the equation ?

Does anyone know whether the following integral has a closed-form solution? If not, is anything known about the asymptotic behavior? f(x) = \int_{-\infty}^{+\infty} \frac{e^{iux}}{\sqrt{u^2 + 1}} du

Hello guys! can i get the derivation for this equation ?

Homework Statement in the third picture , we know that π2 can be written as function of π1 , where π2 is inverse of reynold number , how if i want to change it to π1 = function of π2 , can i write it as (Reynold number ) = F / ρ (D^2)(v^2) ? p/s : π1 is actually inverse of reynold number...

The Navier-Stokes equation may be written as: If we have a fixed volume (a so-called control volume) then the integral of throughout V yields, with the help of Gauss' theorem: (from 'Turbulence' by Davidson). The definition of Gauss' theorem: Could someone show me how to go from the...

Homework Statement http://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/fprops/dimension/node9.html in the link above , the author stated that F / (rho)(D^2)(v^2) = f( (rho)(v)(D) / (μ) ) , Homework EquationsThe Attempt at a Solution can i rewrite in in anotgher way ...

Homework Statement How would I go about solving 1/z=(-4+4i) The answer that I keep on getting is wrong The Attempt at a Solution [/B] What I did z=1/(-4+4i)x(-4-4i)/(-4-4i) z=(-4-4i)/(16+16i-16i-16i^2) z=(-4-4i)/32 z=-1/8-i/8 This is the answer that I got however it says that it is...

Hey! :o I want to find all the matrices in Jordan form with characteristic polynomial the $(x+2)^2(x-5)^3$. Let $\mathcal{X} (x)=(x+2)^2(x-5)^3$. The possible minimal polynomials $m(x)$ are the ones that $m(x)\mid \mathcal{X} (x)$, so $(x+2)^2(x-5)^3$ $(x+2)(x-5)^3$ $(x+2)(x-5)^2$...

Homework Statement 2. Homework Equations The Attempt at a Solution a) [/B]f(x) = -5x2 + 20x + 2 y = -5x2 + 20x + 2 Factor -5 from the first two terms: y = -5x2 + 20x + 2 = -5 (x2 – 4x) +2 Complete the square in the bracket: (1/2 b)2 = [1/2 (-4)]2 = (-2)2 = 4 Group the perfect...

Some say that AC should form a closed loop circuit for electricity utilization but is there really an loop from the Power station(hot wire) to the Ground(neutral) and then from Ground to power station so that it forms a loop?

Homework Statement $$2e^z=\sqrt{2}+i\sqrt{2}\\e^z=\frac{\sqrt{2}+i\sqrt{2}}{2} $$ Then i write the right side as polar form and the abs(right hand side)=2 , and then multiplied with an angle. But in the answer there is only pi/4*i. which is the angle i get, but since the abs(right hand side)=2...

I'm looking for the general form of a symmetric 3×3 matrix (or tensor) ##\textbf{A}## with only two different eigenvalues, i.e. of a matrix with the diagonalized form ##\textbf{D}=\begin{pmatrix}a& 0 & 0\\0 & b & 0\\0 & 0 & b\end{pmatrix} = \text{diag}(a,b,b)##. In general, such a matrix can be...

i3 -? This is how I tried to solve using cramer's rule (denominator is the determinant of the matrix, while numerator is the determinant of the modified matrix) I ignored the prefix Kilo, but the method is right. So I get a different value for i3. Does anyone know what's wrong?