An air-filled spherical capacitor is constructed with concentric spherical conducting shells; inner and other shells of radii ri = 7.00 cm and ro = 14.0 cm, respectively. (a)Use Gauss’s law to determine the electric field at a point r between the two shells (ri < r < ro). Assume that the charge on the inner shell is +Q and on the outer shell is –Q. (3pts) (b)Determine an expression for the potential difference, Vro-Vri, between the two spherical shells. (3pts) (c)Calculate the capacitance of this capacitor. (4pts)

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)