Scalar Definition and 777 Threads

  1. S

    Can you not separate a scalar into x and y components?

    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...
  2. B

    Scalar Equation of Plane Determining the value of k

    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...
  3. P

    Grad of a generalised scalar function

    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})...
  4. J

    Translating scalar torque quantities to their vector analogues (RE: Dipoles)

    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...
  5. M

    What Is the Correct Theta to Use in Calculating the Scalar Product of Vectors?

    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...
  6. A

    Scalar potential of a function F, stuck on curl(F) = 0

    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...
  7. A

    How Do You Find the Scalar Equation of a Plane from Two Points and a Vector?

    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...
  8. R

    Scalar function satisfying div f=F

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

    What is a scalar (under rotation) 1-chain ?

    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...
  10. C

    Is \(\nabla \times (\phi \nabla \phi) = 0\) for a Differentiable Scalar Field?

    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...
  11. A

    How Does a Line Integral of a Scalar Field Differ from a Regular Integral?

    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...
  12. K

    LT of the magnetic vector potential when the scalar potential=0

    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...
  13. F

    If a matrix commutes with all nxn matrices, then A must be scalar.

    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...
  14. B

    Understanding the Triple Scalar Product in Vector Calculus

    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...
  15. D

    Product Rule for Scalar Product: Verifying the Functions

    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...
  16. H

    Is My Gradient Solution for a Scalar Field Correct?

    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} +...
  17. K

    Normals to (hyper)surface must be scalar multiples?

    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...
  18. F

    Partial Derivative: Finding the vector on a scalar field at point (3,5)

    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 ∅ =...
  19. T

    Scalar projection - finding distance between line and point

    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.
  20. B

    How will I represent the scalar function?

    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...
  21. R

    Whittaker 1904 paper on scalar potential functions

    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...
  22. G

    Temperate a scalar than why negative temperature?

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

    Variation of scalar kinetic lagrangian

    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...
  24. U

    EFE's question regarding Ricci scalar

    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...
  25. M

    Scalar Field Theory-Vacuum Expectation Value

    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...
  26. H

    Triple Scalar Product and Torque Explained?

    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...
  27. L

    How is the Riemann tensor proportinial to the curvature scalar?

    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.
  28. R

    Complex scalar field - Feynman integral

    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...
  29. O

    Scalar field as quantum operator.

    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
  30. reddvoid

    Magnetic vector and scalar potential

    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...
  31. H

    Usefulness of Kretschmann scalar

    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...
  32. D

    Computing the line integral of the scalar function over the curve

    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...
  33. DryRun

    Evaluate scalar triple products

    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?
  34. S

    Finding the scalar equation for a plane

    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...
  35. R

    Zero curl and gradient of some scalar potential

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

    Derivation of expansion scalar for FRW spacetime - weird observation

    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...
  37. F

    Why is Work a Scalar? Understanding its Definition

    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...
  38. A

    Finding a scalar such that vectors p and q are parallel

    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
  39. sweet springs

    Scalar made from electromagnetic four potential

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

    Show that T preserves scalar multiplication - Linear Transformations

    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...
  41. B

    Continuity of Magnetic Scalar Potential

    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...
  42. C

    Existence of Scalar Potential for Irrotational Fields

    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...
  43. X

    Massive Scalar Field in 2+1 Dimensions

    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}...
  44. I

    Calculating Boat's Bearing After Changing Direction: Scalar and Vector HELP

    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...
  45. R

    Derivative of a function of a lorentz scalar

    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...
  46. 3

    Proof for determinant of a scalar multiplied by a vector

    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}...
  47. A

    Is Pressure a Scalar Despite Acting in All Directions?

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

    Why Do Scalar Fields in Hybrid Inflation Model Diverge with Large Mixing Term?

    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...
  49. jfy4

    Complex Scalar Field and Probability Field

    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 -...
  50. W

    Complex scalar field and contraction

    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...
Back
Top