Two parallel plates, each having area a = 3490cm2 are connected to the terminals of a battery of voltage vb = 6 v as shown. the plates are separated by a distance d = 0.36cm. you may assume (contrary to the drawing) that the separation between the plates is small compared with either linear dimension of the plate. a dielectric having dielectric constant κ = 3.6 is now inserted in between the plates of the capacitor as shown. the dielectric has area a = 3490 cm2 and thickness equal to half of the separation (= 0.18 cm) . what is the charge on the top plate of this capacitor?

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)