Wednesday, July 29, 2015

CQW holiday project: gravitational field of a cube

show that the lowest two non-vanishing multipole components of the gravitational field of a cubical planet are the monopole and the octupole. what's the next-lowest non-vanishing multipole?

(a solution without a multipole expansion and the added bonus question on the shape of the surface of a lake on such a planet is discussed in the paper "the gravitational field of a cube" by J.M. Chappell, A. Iqbal, D. Abbott and M. Chappell)

with that, we wish all readers of CQW a nice summer vacation and hope to see you again in october. if you came across an interesting question that would fit our blog, you're invited to appear as a guest author: please contact us for that purpose under cosmologyquestionoftheweek"[AT]"gmail"[DOT]"com.

Wednesday, July 22, 2015

temperature measurement

imagine a device which is able to measure the thermal radiation power $S(\nu)$ at a given frequency $\nu$. would it be possible to determine unambiguously the temperature of a blackbody by carrying out measurements at two frequencies $\nu_1$ and $\nu_2$?

Wednesday, July 15, 2015

wrong sign in the induction equation

imagine that the induction equation would read $\mathrm{rot}\vec{E} = +\partial_{ct}\vec{B}$ instead of $\mathrm{rot}\vec{E} = -\partial_{ct}\vec{B}$. can you think of as many consequences as possible this would have?

Wednesday, July 8, 2015

magnetic charges and energy conservation

imagine to extend Maxwell electrodynamics with a magnetic charge density $\rho_m$. would the resulting set of equations still obey energy-momentum conservation? what changes would this yield in the Poynting-law?

Wednesday, July 1, 2015

too many Maxwell equations?

why are there 2 scalar and 2 vectorial Maxwell equations in electrodynamics, which provide 8 relations in total for only two vector fields, i.e. 6 field components? is the system of equations overdetermined?