Homework Statement
A rigid cylinder of radius ##R## and mass ##\mu## has a moment of inertia ##I## around an axis going through the center of mass and parallel to the central axis of the cylinder. The cylinder is homogeneous along its central axis, but not in the radial and angular directions...
So then the rest of the solution would proceed `as I've outlined? Use the expression for curl in spherical coordinates, find which component of B is non-zero and then turn the crank to find Poynting's vector and compare with the time derivative of the electrostatic energy? Regarding units I'm...
Homework Statement
A spherical capacitor has internal radius ##a## and external radius ##b##. At time ##t = 0##, the charge of the
capacitor is ##Q_0## Then the two shells are connected by a resistor in the radial direction of resistance ##R##. Find the Poynting vector and the energy...
Yes that is what I meant by time in the lab frame. Thank you for reinforcing the distinction between the time the clock shows and the time in the lab frame for me.
Possibly. It doesn't directly mention a reference frame. But even so am I correct in how I'm finding the time in the lab frame? Or is there a way to use the Lorentz transformations more directly?
Homework Statement
A rectangular structure carries clocks at its four corners. The clocks are synchronized in the structure’s rest frame, in which it has length L =4ft and width W = 3ft. In our laboratory frame the rectangle is moving in the positive x direction at speed v = 0.8c. As the clock...
Homework Statement
Show that it is impossible for an ultra-relativistic particle with ##pc>>Mc^2## to disintegrate into two identical massive particles of mass m.
Homework Equations
Conservation of four momentum
The Attempt at a Solution
The four momentum of the ultra-relativistic particle...
Homework Statement
A triangular lattice of lattice spacing ##a=2 ## angstroms is irradiated with x-rays at time zero of wavelength 20 angstroms at an incident angle of ##\alpha =135##.
1) What is the maximum wavelength of the incident x-rays?
2) What is the scattering angle ##\Omega## for...
Homework Statement
Consider an inertial laboratory frame S with coordinates (##\lambda##; ##x##). The Lagrangian for the
relativistic harmonic oscillator in that frame is given by
##L =-mc\sqrt{\dot x^{\mu} \dot x_{\mu}} -\frac {1}{2} k(\Delta x)^2 \frac{\dot x^{0}}{c}## where ##x^0...
Homework Statement
Consider the crystal in the attached image (https://ibb.co/ftMrBH) (a triangular lattice of white atoms with a triangular basis of grey atoms attached to them at angles of 0, 60 and 120. From a previous problem the fractional coordinates of the atoms in the basis are (0,0)...
Homework Statement
Low-energy electron diffraction (LEED) experiments are carried on to study a deposition of argon (Ar) and
xenon (Xe) on the surface of a graphite single crystal. In the regime of vapor pressure considered, 75% of Ar
and 25% of Xe are adsorbed on the (hexagonal) crystalline...
Homework Statement
Derive the relativistic Euler equation by contracting the conservation law $$\partial _\mu {T^{\mu \nu}} =0$$ with the projection tensor $${P^{\sigma}}_\nu = {\delta^{\sigma}}_\nu + U^{\sigma} U_{\nu}$$ for a perfect fluid.
Homework Equations
$$\partial _\mu {T^{\mu \nu}} =...
Homework Statement
The surface tension of a layer of water obeys ## \sigma = a- bT##, where ##T## is the temperature. Find the change in temperaure, ##\Delta T## when the area is increased isentropically. Homework Equations
## dU = dQ -dW## , ##dW = \sigma dA##, ##dU = C_A dT + [\sigma...
Homework Statement
The coefficient of thermal expansion and isothermal compressibility of a gas are given by ##\alpha_P =\frac{V-b}{TV}## and ##\kappa_T = \frac{V-b}{PV}## find:
a) The equation of state
b) If the heat capacity at constant volume ##C_V## is constant, what is ##\delta U##?
c)...
Homework Statement
Show that ##(\frac{\partial S}{\partial G})_Y = -\frac{C_Y}{TS}##
Homework Equations
##G = H-TS, (\frac{\partial H}{\partial T})_Y = C_Y##
The Attempt at a Solution
##dG = dH -TdS -SdT## and ##H## is a state variable so ## dH =\frac{\partial H}{\partial T} dT +...