Charge and Mass of the Electron 7
Consider a latex sphere of mass m and charge q, falling under the influence of
gravity between two horizontal plates. In falling, the sphere is subjected to an opposing
force due to air resistance. The speed of the sphere quickly increases until a constant
terminal speed is reached, at which time the weight of the sphere, mg, minus the buoyant
force is exactly equal to the air resistance force. The value of the air resistance force on a
sphere was first derived by Sir George Stokes and is given as 6 π η r s where η is the
coefficient of viscosity of air, r is the radius of the sphere and s is its terminal speed. If
the buoyant force of the air is neglected, the equation of motion of the sphere is:
mg − 6πηrs = 0