g Consider a dielectric sphere of radius Rand permittivity 1moved into a region of space containing a dielectric of permittivity 2and originally threaded by a constant electric field E0. Find the new electric field everywhere after the sphere is moved into place. To make it clear, the same problem can be stated as: Given a sphere of radius Rand permittivity 1submerged into a medium with permittivity 2and a field which, far from the sphere, is uniform with magnitude E0, find the field everywhere in space.

Newton's law of cooling states that the rate of change in the temperature t(t) of a body is proportional to the difference between the temperature of the medium m(t) and the temperature of the body. that is, startfraction dt over dt endfraction equals upper k left bracket upper m left parenthesis t right parenthesis minus upper t left parenthesis t right parenthesis right bracket , where k is a constant. let kequals0.04 left parenthesis min right parenthesis superscript negative 1 and the temperature of the medium be constant, m(t) font size decreased by 3 equivalent font size decreased by 3 294 kelvins. if the body is initially at 369 kelvins, use euler's method with hequals0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes.