Cross Definition and 1000 Threads

Hi, I was just wondering if you have a cross product can you multiply out the constants and put them to one side. So ik x ik x E is equal to i^2(k x k x E) therefore is equal to -k x k x E. Is that correct?

So yeah, I understand that you can calculate torque as F*d, and you get a "number". But when you calculate a cross product of torque, r x F, what does that actually give you? It is a vector, perpendicular to F and r, but what "is" that? I mean, is it like an axis around which the object is...

Will someone explain this step to me?

Homework Statement The problem is given in the following photo: Actually I did the first proof but I couldn't get the second relation. (Divergence of E cross H). Homework Equations They are all given in the photo. (a) (b) and (c). The Attempt at a Solution What I tried is to interchange...

Homework Statement good afternoon, I am a problem with the E cross B drift velocity calculus from a charged particle. At first, an eletron is submitted a uniform magnetic field and have a circular trajetory. After, appear a uniform eletric field that create a drift velocity. The equations...

Homework Statement If ##u,v,w\in\mathbb{R}^3##, show that ## u\times(v\times w) = (u.w) v - (u.v) w ##. Homework Equations The Attempt at a Solution Since ## u\times(v\times w)##, ##v## and ##w## are orthogonal to ##v\times w##, these vectors are coplanar. Therefore, there must be reals ##...

Reading a book about 3d math, and I am confused as to what happened on this Vector Cross Product problem. I'm thinking there was just an error that wasn't caught. For the first row, instead of (3)(8)-(-4)(-5) shouldn't it have been (3)(8)-(4)(-5) and had the same displayed result of 44? And for...

Homework Statement The diagram shows a box with parallel faces. Two of the faces are trapezoids and four of the faces are rectangles. The vectors A, B, and C lie along the edges as shown, and their magnitudes are the lengths of the edges. Define the necessary additional symbols and prove...

Homework Statement [/B] Vector A lies in the yz plane 63.0 degrees from the +y axis, has a positive z component, and has a magnitude 3.20 units. Vector B lies in the xz 48.0 degrees from the +x axis, has positive z component, and has magnitude 1.40 units. a) find A dot B b) find A x B c)...

Hello, PF! I had a quick question that I hoped maybe some of you could help me answer. The question is simple: Why is the cross product of two parallel vectors equal to the zero vector? I can see this easily mathematically through completing the cross product formula with two parallel...

Given a rectangular prism that is composed of various horizontal layers made of different materials, how can one calculate the modulus of elasticity? Currently the materials used and their respective ratios have not been specified. We wish to determine this information using the results of...

Let's say we have: \vec{E}=E_x\vec{i}_x+E_y\vec{i}_y+E_z\vec{i}_z and \vec{B}=B_x\vec{i}_x+B_y\vec{i}_y+B_z\vec{i}_z and the Lorentz Force 0=q(\vec{E}+\vec{v}X\vec{B}) which due to \vec{E}X\vec{B}=\vec{B}X(\vec{v}X\vec{B})=vB^2-B(\vec{v}\cdot \vec{B}) and transverse components only...

The Lawson criterion suggests that a chain fusion reaction will only occur in a confined plasma. Since it's a product of temperature and pressure (or density) a chain reaction would be virtually impossible in a cold target at pressures attainable in a lab. Likewise, the Coulomb barrier makes it...

Homework Statement https://www.dropbox.com/s/8l90hahznjlv9d0/vector%20problem.png?dl=0 Homework Equations Dot and Cross product The Attempt at a Solution although I know the dot and cross product, I'm not sure what I'm being asked or how to proceed? any help?[/B]

How can I calculate the absorption cross section of a harmonic oscillator in an EM field?

Hello, I hope this is the right forum section. I'm having trouble understanding how calculating the cross product arrives at the final result. When I do something simpler like multiplying a vector by a scalar, I can easily visualize in my head how each component "shrinks" or "grows". With the...

Can someone point towards how to derive that the cross section is proportional to the imaginary part of the Action? Also, I thought the Action was a real number? Thanks!

Homework Statement Calculate the ratio ##R = \frac{\sigma_{had}}{\sigma_{\mu+\mu-}}## for energy around ##10~GeV##. At sufficiently high energies, the ##e^+e^- \rightarrow \mu^+ \mu^-## reaction can proceed via the ##Z^0## boson. Assuming vertex factors for EM and weak interaction are the same...

Homework Statement Vectors A and B both have magnitude M. Joined at the tails, they create a 30' angle. What is A x B in terms of M? Homework EquationsThe Attempt at a Solution 0? OR M^2? Sqrt(3)M/3?

Pre-knowledge A matrix is a linear transformation if, T(u+v)= T(u) +T(v) and T(cu)=cT(u). Theorem 8.4.2 If V is a finnite dimensional vector space, and T: V-> V is a linear operator then the following are equivalent. a) T is one to one, b) ker(T)=0, c)...

Let \mathbb{F} be an arbitrary field, and let a,b\in\mathbb{F}^3 be vectors of the three dimensional vector space. How do you prove that if a\times b=0, then a and b are linearly dependent? Consider the following attempt at a counter example: In \mathbb{R}^3 \left(\begin{array}{c} 1 \\ 4 \\ 2...

Homework Statement [/B] (a) Find the ratio of cross sections. (b) Find the cross section for electron-neutrino scattering by first writing down relevant factors. Homework EquationsThe Attempt at a Solution Part (a)[/B] These represent the neutral current scattering for the muon-neutrino and...

I am going over the optical theorem (specifically from Sakurai) and I just have a simple couple of questions. The optical theorem says \sigma_{total}=\frac{4\pi}{k}\text{Im}(f(0)) Where ##f(0)## is the scattering amplitude in the forward direction. (Which I am assuming means the direction...

Hi All, I have a question about resonance cross sections. I have been doing the design work on the reactor I want to propose for testing at Oak Ridge National Labs, and have run into a problem. It is an accelerator driven reactor transmuting thorium into uranium, then burning the uranium by...

In the text-book example of CP violation in the kaon system, the usual statement is that the KS decays much faster than the KL because the phase space is larger for a decay into two pions, compared to three pions. (See, for example, Griffiths or "Modern Particle Physics" by Thomson.) I was...

I was studying my notes and specifically for the ##e^+e^- \rightarrow \mu^+ \mu^-## process, cross section is given by \sigma = \frac{4\pi}{3} \left( \frac{\alpha \hbar c}{W} \right)^2 where ##\alpha = \frac{g_{EM}^2}{4\pi}## and ##W## is the centre of mass energy. Is this the same for...

I was reading about control rods in a nuclear reactor. The carbon rods slow down the neutrons so they can interact better and induce fission. Is the reason that they don't interact when raveling fast is this because the have a smaller de broglie wavelength?

Homework Statement (a) Explain the results. (b) Why is the cross section much higher? Suggest the dominant decay product pair.[/B] Homework EquationsThe Attempt at a Solution [/B] Part(a) For a centre of mass energy of ##170GeV##, you produce pairs of oppositely charged ##W^{\pm},W^{\mp}##...

Can anyone tell me why?

Homework Statement The following equation is presented in my textbook, with very little context and J is simply described as the "trans-membrane fluid flux, which can be modeled by using Darcy’s law." Typically in this bioseparations class, when we discuss permeate flux, it is a unit volume...

Homework Statement Given a×b=-i-j+3k and c×a=2i-3j+k, find a×(a-2b+c) Homework Equations Cross product (DONE WITHOUT MATRICES). The Attempt at a Solution a[/B]×b=c=-(b×a)is all I'm getting to at this point

In one of my classes, I should give a talk about pair production cross section in front of the class and so I'm now searching for resources. But I can't find a place where the differential cross section for pair production process is given. Anyone knows somewhere I can find it and , preferably...

Hydrogen - Halpha cross section i need the absorption cross section for the absorption of an H-alpha photon by a hydrogen atom, in the correct state of course, which I'm pretty sure is neutral hydrogen, n=2. I am needing this for a project, so i also need a reliable source where this comes...

Is there a book or database that lists all (or many) pairs of isotopes along with the energy at which they have the higest probability of fusion and what that probability is? Or is there a program that uses models to make a guess given a pair? Or a formula I could use to make the guess myself...

Hai all, I need some help in understanding the calculation of total ionization cross section. As per the literatures, for a gas capable of multiple ionization, the total cross section is a charge-weighted sum of partial ionization cross sections. To be more elaborate, consider the case of...

As seen in the picture, this question is about an object moving in the x-y plane. But I don't get why in equation 8.9 the cross terms vanish? If anyone can help me, that would be really nice.

Homework Statement I want to find the ionization cross section in a mass spectrometer for the gas Argon. The value obtained should be in the 2x10-16 cm2 range. Homework Equations Q = ionization cross section I = K(V,B)xNxQxdxIe Where I = (0.17 x 10-11, K(V,B) =1, d = 0.1 cm, and Ie = 5 x...

Hi, in class I'm doing a Suzuki Cross Coupling reaction based on "Nickel-Catalyzed SuzukiMiyaura Couplings in Green Solvents" by Stephen D. Ramgren, Liana Hie, Yuxuan Ye, and Neil K. Garg. The reaction involved the bromo-aryl reacting with the boronic acid in heated t-amyl alcohol in the...

Homework Statement I am making an old exam of a particle physics course, and i know how to calculate the cross section for example for bhabha or moller scattering. now one of the questions on the old exam is: Explain why e-+ e+ -> γ is zero, but i am not sure why this is, can someone explain...

1) Alpha particles can react with 48-Ca to produce protons. Consider a beam of alpha particles of current 20nA fired at a think target of Ca of thickness $$1mg/cm^2$$. A detector subtending a solid angle of 4*10^-3 steradians, records 20 protons per second. Determine the total cross section (in...

Homework Statement Two horizontal parallel conducting rods are connected such that a conducting crossbar free to slide along them has a constant current I running through it (Figure 1) . The rods are separated by a distance ℓ and are in an external uniform magnetic field of magnitude B directed...

Hi all, I am very confused on how to define the vector product or cross product in a physical sense. I know the vector product is a psuedovector, and that it is the area of a parallelogram geometrically. However, I know it used used to describe rotation in physics. As with torque, magnetism and...

Homework Statement A motorcyclist must cross a ravine. The far side of the ravine is 2.0 meters higher than the launch point, a ramp that makes an angle of 40◦ with the horizontal. If the ravine is 10.0 meters wide, what minimum speed v must the biker have when leaving the ramp to successfully...

Homework Statement Find the set of points of M such that: AM x BC=AM x AC (Vectors) The Attempt at a Solution [/b] AM x (BM+MC) =AMx(AM+MC) AMxBM+AMxMC=AMxAM +AM x MC Then AMxBM=0 MA X MB=0 I am new to this lesson and this is my first time i solve such a question and i had no idea...

Mod note: Member warned about posting with no effort. 1. Homework Statement Expand to the general case to explore how the cross product behaves under scalar multiplication k (a x b) = (ka) x b = a x (kb). The Attempt at a Solution would this be the right general case to portray the situation?

I am working on fixing a heavy walnut cedar chest lid that has bowed convexly from the chest. It is about 1/4" high in the center of a 24" deep lid. The lid is ~2' x 5'. It is made from 3/4" walnut with 3/4" x 3" ribbing on the top. I thought that adding in some C-channel or square tubing would...

Homework Statement Why does ## \frac{ e^+ + e^- \rightarrow \mu^+ + \mu^- }{e^+ + e^- \rightarrow \tau^+ + \tau^- } \rightarrow 1## at high energies? Would it be the same if it was ## \frac{ e^+ + e^- \rightarrow \mu^+ + \mu^- }{e^+ + e^- \rightarrow e^+ + e^- }##? Homework EquationsThe...

I'm looking at deep inelastic scattering of a low-energy inelastic electron scattering from a stationary proton target. I am given ##E## and ## \theta ## where ##\theta ## is the scaterring angle. ##E=4.879 GeV , \theta=10^{0} ## I am given a figure of cross section...

I have a result for the differential cross section d\sigma/d\eta dP_T^2, but I want to obtain the corresponding differential yields dN/d\eta dP_T^2. How to relate yields to cross section?

Homework Statement In this problem, you will estimate the cross section for an earth-asteroid collision. In all that follows, assume that the Earth is fixed in space and that the radius of the asteroid is much less than the radius R of the earth. The mass of the Earth is M_e, and the mass of...