Recent content by PhysyCola

Update: I believe I have now found a solution, which I will post below. Define the four vectors ##\begin{align} \vec{X}_1 & = (ct_1,\vec{r}_1)^T \\ \vec{X}_2 & = (ct_2,\vec{r}_2)^T \end{align}## that correspond to the displacements of the ends of the interval ##\vec{w}## in the wave-front, so...

Sorry yes, putting ##\Delta \vec{x} = w## was a grave transgression; I might have the solution. I will update this post if I achieve it!

Well, you could define two four vectors ##\begin{align} \vec{X}_1 & = (ct, \vec{x}_1) \\ \vec{X}_2 & = (c(t+\Delta t), \vec{x}_2) \end{align}## such that their difference gives ##\begin{align} \vec{R}= \vec{X}_2 - \vec{X}_1 = (c\Delta t, \Delta \vec{x}) \end{align}## where we have defined...

Yeah, sorry for not being specific; it is indeed a plane wavefront corresponding to an EM wave. I might be getting myself in a pickle here, but wouldn't ##\vec{U}## be a good option to consider, seeing as the direction of the rays remains unchanged? Or ##\vec{K}## due to the nature of the...

Homework Statement For a plane, monochromatic wave, define the width of a wavefront to be the distance between two points on a given wavefront at a given instant in time in some reference frame. Show that this width is the same in all frames using 4-vectors and in-variants. Homework...

Hi tburke2, I believe that you can solve the system by considering the displacement x of the particle as the displacement from some support that oscillates in the same way as your forcing. This would lead to a lagrangian of: L =1/2mx'^2 - 1/2kx^2 were x = x_o - z, where x_o = F_o cos(wt) and z...

Hey there Eric. If you are still having trouble with this problem, you could consider the total energy of the system. In polar coordinates (where r is the distance of the alpha particle from the lead nucleus), the kinetic energy of the system can be written as, noting that the mass is...

Hey there Calpalned. I have worked the problem through, and I am not sure that your answer is correct. Are you sure you have evaluated the cross product correctly?

Hey there everyone, I am a physics-undergraduate student in the first year of my degree looking to both help others, and be helped!