an ion with charge q is distance r from a molecule with polarizability (alpha). find an expression for the magnitude force f(ion on dipole).
express your answer in terms of the variables q, r,(alpha) and appropriates constants.

The space between two 15-in.-long concentric cylinders is filled with glycerin (viscosity = 8.5 × 10-3 lb·s/ft2). the inner cylinder has a radius of 1 in. and the gap width between cylinders is 0.1 in. determine (a) the torque and (b) the power required to rotate the inner cylinder at 180 rev/min. the outer cylinder is fixed. assume the velocity distribution in the gap to be linear.