Recent content by Toby_phys

Homework Statement N point particles of mass mα, α = 1,...,N move in their mutual gravitational field. Write down the Lagrangian for this system. Use Noether’s theorem to derive six constants of motion for the system, none of which is the energy Homework Equations Noethers Theorem: If a...

Homework Statement A solenoid of volume V, current I and n turns per unit length has an LIH core, relative permitivity is \mu_r. This core is then slid out so that a fraction f of the solenoid's length is filled with air/vacuum (and 1-f is filled with the core). Neglecting hysteresis, what...

Homework Statement A gas effuses into a vacuum though a small hole of area A. Show that if the particles effused into an evacuated sphere and the particles condensed where they collided that there would be a uniform coating. (7.6 of Blundell and Blundell) Homework Equations Angular...

There was a part A that was to show this is the case $$dU=C_vdT+\left[f-T\left(\frac{\partial f}{\partial T}\right)_L\right]dL$$ The second term drops out

Homework Statement For a stretched rubber band, it is observed experimentally that the tension ##f## is proportional to the temperature ##T## if the length ##L## is held constant. Prove that: (b) adiabatic stretching of the band results in an increase in temperature; (c) the band will...

##dq=0## for adiabatic process I think

A possible ideal-gas cycle operates as follows: 1. From an initial state (##p_1##, ##V_1##) the gas is cooled at constant pressure to (##p_1##, ##V_2##); Let's call the start and end temperature ##T_1## and ##T_2## 2.The gas is heated at constant volume to (##p_2##, ##V_2##);Lets call the...

An electron can tunnel between potential wells. Its state can be written as: $$ |\psi\rangle=\sum^\infty_{-\infty}a_n|n\rangle $$ Where $|n \rangle$ is the state at which it is in the $n$th potential well, n increases from left to right. $$...

Why are the states counted in momentum space?? I haven't seen a derivation where this is necessary

So I worked through the Boltzmann distribution and got: $$ P\propto e^{\frac{-E}{k_BT}} $$ Where $E$ is the energy. So surely this means the kinetic energy (and therefore speed) of particles is distributed over a Boltzmann distribution. Or in equation: $$ P\propto e^{\frac{-mv^2}{2k_BT}} $$...

Homework Statement Particles of mass ##m## and charge ##q## are initially traveling in a beam along the ##z## direction with speed ##v## when they enter a long magnetic quadrupole lens, where there is no E-field and the magnetic flux density is ##B = Ay\hat{i} + Ax\hat{j}##, and where A is a...

Homework Statement Evaluate the following line integrals, showing your working. The path of integration in each case is anticlockwise around the four sides of the square OABC in the x−y plane whose edges are aligned with the coordinate axes. The length of each side of the square is a and one...

Yes, I think :) $$\frac{dE}{dt}=\frac{15Ba^2}{32}^2\frac{\dot{\theta}^2}{R_l+R_d}=\frac{15Ba^2}{32}^2\frac{4E}{ma^2(R_l+R_d)}$$ Which is seperable.Edit - I have worked through it all and it works, thank you

I thought about that but I couldn't see how to do it

Mechanical energy is lost at the same rate that energy is dissipated through the resistances. I could go into forces and go right back to first principles but I feel that would be far too long