Recent content by raggle

You're right about the first equation, it should be $$ T=\frac{1}{2}mR^2(\dot\theta^2+\dot\phi^2\sin^2\theta) + \frac{1}{2}mR^2\sin^2\theta\dot\phi^2 $$ You're also right about the second equation, I thought the moment of inertia of a hoop was ##\frac{1}{2}mR^2## but it's actually ##mR^2##...

Homework Statement 'Consider the system consisting of a bead of mass m sliding on a smooth circular wire hoop of mass 2m and radius R in a vertical plane, and the vertical plane containing the hoop is free to rotate about the vertical axis. Determine all relative equilibria of the bead.'...

Homework Statement A long light inflexible rod is free to rotate in a vertical plane about a fixed point O. A particle of mass m is fixed to the rod at a point P a distance ℓ from O. A second particle of mass m is free to move along the rod, and is attracted to the point O by an elastic force...

Oh wait I think i just got it. I can put those functions of z into the arbitrary constant vector c can't I? Thanks!

Yeah that's what I'm confused about. My reasoning is that I have \frac{\partial \textbf{B}}{\partial t} in terms of \textbf{E}, and since \textbf{E} is a function of z and t I get the functions of z from partially integrating wrt t. Should they be 0?

Homework Statement Given \textbf{E}(z,t) = E_{0}cos(kz+ωt)\textbf{i} Find B Homework Equations ∇ x E = -\frac{\partial\textbf{B}}{\partial t}The Attempt at a Solution Taking the curl of \textbf{E} gives (0, -ksin(kz+\omega t), 0) so \frac{\partial\textbf{B}}{\partial t} = (0,ksin(kz+\omega...

Homework Statement A parallel plate capacitor consists of two plates, each of area A, separated by a small distance d. in this gap, a dielectric of relative permittivity εr and thickness d/2 is fitted tight against one of the plates, leaving an air gap of thickness d/2 between it and the other...

Homework Statement I'm going over some EM notes and I found a derivation for the potential energy of a dipole in an E field which first found the torque on the dipole and then integrated. I had a go at a derivation that goes the other way, starting from the potential of the 2 charges. I've ran...