Scalar Definition and 777 Threads

A scalar like electric potential. Say I have a positive charge, and 4m to the right, and 3m up is a point P. If I wanted to calculate the potential at point P, I'd use V=kQ/r (r=√(4^2 + 3^2)). But I'm confused about why finding the potential at 4m to the right (the x component), and the...

Homework Statement Determine the value of k so that the line with parametric equations x = 2 + 3t, y = -2 + 5t, z = k is parallel to the plane with equation 4x + 3y – 3z -12 = 0. Homework Equations The Attempt at a Solution let k=a + bt x=2+3t y=-2+5t z=a+bt direction...

Homework Statement r=xi+yj+zk and r =\sqrt{x^2 + y^2 + z^2} Let f(r) be a C2 scalar function Prove that \nablaf = \frac{1}{2}\frac{df}{dr}r Homework Equations Vector identities? The Attempt at a Solution \nablaf = (\frac{df}{dx} , \frac{df}{dy} , \frac{df}{dz})...

My question is at the bottom of this post PREAMBLE: If a dipole is turned by an angle θ (in a uniform electric field) then the torque applied on the dipole by the electric field will be: τ = 2.q.a.E.sin(-θ) = -2.q.a.E.sin(θ) with the negative sign referring to it being a "restoring" torque...

Homework Statement Let vectorB= 5.45 m at 60°. Let C have the same magnitude as A and a direction angle greater than that of A by 25°. Let B·A = 32.4 m2 and B·C = 35.1 m2. Find the magnitude and direction of A . Homework Equations A·B=MagAxMagBcosθ The Attempt at a Solution I just...

Homework Statement I have a function F defined in a slightly strange way, and I'm not asked to test if curl(F) == 0, but I thought I would do this as part of my working out. Lo and behold, it looks like it doesn't == 0, and this means, as far as I know, that there is no scalar potential but...

Homework Statement Find the scalar equation of the plane containing the points A(-3, 1, 1) and B(-4, 0, 3) and the vector u = [1, 2, 3]. Homework Equations I am at a lost, since I can't tell how to figure out the normal vector. I am supposed to find: Ax+By+Cz+D=0, where [A,B,C] is the...

What's the algorithm for finding scalar function satisfying div f=F if I know vector F?

What is a "scalar (under rotation) 1-chain"? Hi all, I am trying to make sense of a paper involving differenital geometry and Lie algebras. Here's the part I am confused about: Now things begin with finding the cohomology of a Lie algebra. The galilean algebra is taken as an example, and...

How to prove that \nabla x (\phi\nabla\phi) = 0? (\phi is a differentiable scalar field) I'm a bit confused by this "differentiable scalar field" thing...

Okay this might be a nooby question, but it bothers me. What is the difference between the line integral of a scalar field and just a regular integral over the scalar field? For a function of one variable i certainly can't see the difference. But then I thought they might be identical in...

Special relativity predicts that electric fields transform into magnetic fields via Lorentz transformations and that the vice versa also occurs. It also has been argued, since experiments verifying the quantum mechanical phenomenon of the Aharonov–Bohm effect, that the vector potentials are more...

Homework Statement Prove: If a matrix A commutes with all matrices B \in M_{nxn}(F), then A must be scalar - i.e., A=diag.(λ,...,λ), for some λ \in F. Homework Equations If two nxn matrices A and B commute, then AB=BA. The Attempt at a Solution I understand that if A is scalar, it...

Homework Statement A x (B dot C) (A x B) dot C They are vectors. Homework Equations A x (B dot C) (A x B) dot C The Attempt at a Solution I know how to do my homework, but I am confused on these formulas. Is the first formula "A x (B dot C)" the same as the second one? I know the...

Homework Statement Look up, figure out, or make an intelligent guess at the product rule for the scalar product. That is, a rule of the form d/dt [a(t).b(t)] =?+? Verify your proposed rule on the functions a(t) = ti + sin(t)j + e^(t)k and b(t) = cos(t)i - t^(2)j - e^(t)k: Homework...

Homework Statement Consider the scalar field V = r^n , n ≠ 0 expressed in spherical coordinates. Find it's gradient \nabla V in a.) cartesian coordinates b.) spherical coordinates Homework Equations cartesian version: \nabla V = \frac{\partial V}{\partial x}\hat{x} +...

Homework Statement Let S is a (hyper)surface defined by {x|F(x)=0}. Suppose n1 and n2 are both normal to S at x=a. Then n1 and n2 are scalar multiples of each other. Homework Equations The Attempt at a Solution If S is a surface in R3, then I think it's clear geometrically that the...

Homework Statement A scalar field is given by the function: ∅ = 3x2y + 4y2 a) Find del ∅ at the point (3,5) b) Find the component of del ∅ that makes a -60o angle with the axis at the point (3,5) Homework Equations del ∅ = d∅/dx + d∅/dy The Attempt at a Solution I completed part a: del ∅ =...

Using a scalar projections how do you show that the distance from a point P(x1,y1) to line ax + by + c = 0 is \frac{|ax1 +b y1 + c|}{\sqrt{a^2 +b^2}} I do not know how to approach this, please provide some guidance.

Homework Statement show that \nabla \times (f F)= f \nabla \times F+ (\nabla f) \times F The Attempt at a Solution How will I represent the scalar function? Do I write f=\psi(x,y,z) or f=A_x+A_y+A_z I chose F=a_x \vec i +a_y \vec j +a_z \vec k Using f=\psi(x,y,z) I work out...

http://www.hyiq.org/Library/E.T.Whittaker-1904.pdf "On an Expression of the Electromagnetic Field due to Electrons by Means of Two Scalar Potential Functions" by E. T. Whittaker published in Proceedings of the London Mathematical Society, Vol. 1, 1904) In the paper Whittaker 1904...

What's the meaning of negative temperature if temperature can only be a scalar? Why the construction of negative temperature in degrees Fahrenheit?

Homework Statement The goal of the question I'm being asked is to show that the covariant derivatives, D_{\mu}, "integrate by parts" in the same manner that the ordinary partial derivatives, \partial_{\mu} do. More precisely, the covariant derivatives act on the complex scalar field...

Quick question about the EFE's. When writing the einstein tensor G_{\mu\nu}=R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}, and using the definition of the Ricci scalar R=g^{\mu\nu}R_{\mu\nu}, how does this not give you problems when you expand out R so that the second term becomes...

Homework Statement I am given an equation for a quantized, neutral scalar field expanded in creation and destruction operators, and need to find the vacuum expectation value of a defined average field operator, squared. See attached pdf. Homework Equations Everything is attached, but I...

Homework Statement I am working through Boas' Mathematical Methods in the physical sciences book and I don't understand the triple scalar product and torque example. k [dot] (r X F) = 0 0 1 = xF_y - yF_x x y z F_x F_y...

My professor asks, "Double check a formula that specifies how Riemann tensor is proportional to a curvature scalar." in our homework. The closet thing I can find is the relation between the ricci tensor and the curvature scalar in einstein's field equation for empty space.

Homework Statement For a real scalar field \phi, the propagator is \frac{i}{(k^2-m_\phi^2)}. If we instead assume a complex scalar field, \phi = \frac{1}{\sqrt{2}} (\phi_1 + i \phi_2), where \phi_1,\phi_2 are real fields with masses m_{\phi 1},m_{\phi 2}, what is the propagator...

Hallo, I was wondering what is the physical significance of scalar field \Phi (x) as an quantum operator. \Phi (x) have canonical commutation relation such as [ \Phi (x) , \pi (x) ] so it must be an opertor, thus what are his eigenstates? Thanks, Omri

I understood that curl H = J H being magnetic field intensity and magnetic flux density B = u H (u being permeability of free space) divergence of B is zero because isolated magnetic charge or pole doesn't exist. but then they define magnetic scalar and vector potentials .i can imagine H...

Hello, As I'm sure you are aware the Kretschmann scalar (formed by contracting the contravariant and covariant Riemann tensors) has some use in the identification of gravitational singularities. Specifically, because K is essentially the sum of all permutations of R's components, but is...

Homework Statement f(x,y) = \sqrt{1+9xy}, y = x^{3} for 0≤x≤1 Homework Equations The Attempt at a Solution I don't even know how to start this problem. I thought about c(t) since that's all I have been doing, but there isn't even c(t). I only recognize domain. Can anyone help me...

http://s2.ipicture.ru/uploads/20111115/BiYq94IS.jpg Here is the determinant for axb: w x y z 1 -2 3 -4 -1 2 4 -5 Then, how to proceed?? Can someone please help?

Homework Statement Find the scalar equation for the plane containing L1 and L2. Consider the lines: L1 : x = t + 1, y = 2t, z = 3t - 1 L2 : x = s - 1, y = 2s + 1, z = 3s - 1 Homework Equations Scalar equation for a plane: a(x - x0) + b(y - y0) + c(z - z0) = 0 The Attempt at a Solution These...

Can someone help me intuitively understand why if a field has zero curl then it must be the gradient of a scalar potential? Thanks!

Derivation of expansion scalar for FRW spacetime -- weird observation In a recent thread... https://www.physicsforums.com/showpost.php?p=3567386&postcount=137 ...I posted a formula for the expansion scalar for the congruence of "comoving" observers in FRW spacetime. When I posted, I...

I am trying to understand why work is a scalar, without knowing ahead of time that work is defined as: W_{ab} = \int ^{\vec{r_{b}}}_{\vec{r_{a}}} \vec{F} \cdot d{\vec{r}} Essentially, I am trying to understand how this definition was derived (based on the one-dimensional work-energy theorem...

Homework Statement Let: p = (2,k) q = (3,5) Find k such that p and q are parallel The Attempt at a Solution Well, I know that for two vectors to be parallel we need to have p = kq. I know the answer will be kind of obvious but I just can't get it lolll, any help please?? Thanks

Hi. What physical meaning does scalar made from inner product of electromagnetic four potential, gαβAαAβ, have? Regards.

Homework Statement Let T:ℝ^{2}→ℝ be defined by T\left(\begin{array}{c} x_{1} \\x_{2}\end{array}\right) = (0 if x_{2} = 0. \frac{x^{3}_{1}}{x^{2}_{2}} otherwise.) Show that T preserves scalar multiplication, i.e T(λx) = λT(x) for all λ \in ℝ and all x \in ℝ^{2} The Attempt at a Solution...

Hello I have found in some textbooks that the magnetic scalar potential is continuous across a boundary. Now, how can this be explained starting from the two boundary conditions of Maxwell's equations (continuity of normal flux density Bn and tangential field Ht)? Thanks in advance for...

Hi I know it's easy to prove that if a vectorfield is the gradien of a potential, \vec F = \nabla V, then \nabla \times F = 0. But how about the converse relation? Can I prove that if \nabla \times F = 0, then there exist a salar potential such that \vec F = \nabla V? I get as far as...

Homework Statement We wish to find, in 2+1 dimensions, the analogue of E = - \frac{1}{4\pi r} e^{-mr} found in 3+1 dimensions. Here r is the spatial distance between two stationary disturbances in the field. Homework Equations In 3+1 we start from E = - \int \frac{ d^3 k }{(2\pi)^3}...

Scalar and Vector HELP please A boat is traveling on a bearing of 25 degrees east of north at a speed of 5 knots ( a knot is 1.852km/hr). After traveling for 3 hours, the boat heading is changed to 180 degrees and it travels for a further 2 hours at 5 knots. What is the boat's bearing from its...

This is probably a dumb question, but I have a book that claims that if you have a function of the momentum squared, f(p2), that: \frac{d}{dp^2}f=\frac{1}{2d}\frac{\partial }{\partial p_\mu} \frac{\partial }{\partial p^\mu}f where the d in the denominator is the number of spacetime...

Homework Statement Let A be an n x n matrix and \alpha a scalar. Show that det(\alpha A) = \alpha^{n}det(A) Homework Equations det(A) = a_{11}A_{11} + a_{12}A_{12} + \cdots + a_{1n}A_{1n} where A_{ij} = (-1)^{i+j}det(M_{ij}) The Attempt at a Solution det(A) = a_{11}A_{11}...

Homework Statement how come pressure have directions, and yet is a scalar quantity? Homework Equations The Attempt at a Solution

I have a puzzle when I study the hybrid inflation model. Suppose we have two scalar fields, \phi_1 and \phi_2 first, let's consider the situation where they are in their independent potentials V(\phi_i)=m_i^2\phi_i^2, i = 1,2 with initial value \phi_i^{ini} We can solve the scalar...

Hi, I was looking at the lagrangian and conserved currents for the free complex scalar field and it looks like it has a striking similarity to the conserved current for probability: \frac{\partial \rho}{\partial t}=\nabla\cdot \vec{j} where j_i =-i(\psi^{\ast}\partial_i \psi -...

Hi guys, If I use the definition of the scalar complex field as the combination of two scalar real fields, I can get \phi (x) = \int \frac{d^3 p}{(2\pi )^3} \frac{1}{\sqrt{2p_0}} [ \hat a _{\vec{p}} e^{-ip.x} + \hat b _{\vec{p}}^{\dagger } e^{ip.x}] which I can rewrite in terms of...