Answer Happy

(AG) A chef wishes to bake a cake in the heat of a neutron star, and so they carve out a cubical cavity with side length 1 and fill it with unmagnetized cake batter with some magnetic susceptibility tensor X. Neutron star interior is, as the name suggests, comprised entirely of neutrons and retains no charge or atomic structure, and therefore is not a magnetic or dielectric material, or even a conductor, that is, consider those 5 walls of the cubical oven to be grounded. The thin atmosphere of the neutron star is filled with an ungodly magnetic field that can be a quadrillion times stronger than the Earth's: consider this magnetic field B to run through the interior of the neutron star as well in a constant direction. Consider also the 6th wall of the oven to be this layer of atmosphere with a constant surface current K. When the chef determines the cake is finished they remove it from the oven and observes a magnetization of the dessert even after being removed from the magnetic field, that is, a magnetic moment baked in. In summary, the chef has found themself with a 3D Cartesian boundary value problem with 5 vanishing boundaries, a constant magnetic field B, magnetic susceptibility X, as well as a surface current K on the remaining face of the cube. Ignoring all relativistic, thermal, quantum, and gravitational effects, calculate the magnetization M of the cake in terms of the given vectors and tensor.

4.2 Ungodly Cooking (AG) A chef wishes to bake a cake in the heat of a neutron star, and so they carve out a cubical cavity with side length 1 and fill it with unmagnetized cake batter with some magnetic susceptibility tensor x. Neutron star interior is, as the name suggests, comprised entirely of neutrons and retains no charge or atomic structure, and therefore is not a magnetic or dielectric material, or even a conductor, that is, consider those 5 walls of the cubical oven to be grounded. The thin atmosphere of the neutron star is filled with an ungodly magnetic field that can be a quadrillion times stronger than the Earth’s; consider this magnetic field B to run through the interior of the neutron star as well in a constant direction. Consider also the 6th wall of the oven to be this layer of atmosphere with a constant surface current K. When the chef determines the cake is finished they remove it from the oven and observes a magnetization of the dessert even after being removed from the magnetic field, that is, a magnetic moment baked in. In summary, the chef has found themself with a 3D Cartesian boundary value problem with 5 vanishing boundaries, a constant magnetic field B, magnetic susceptibility X, as well as a surface current K on the remaining face of the cube. Ignoring all relativistic, thermal, quantum, and gravitational effects, calculate the magnetization M of the cake in terms of the given vectors and tensor.