Chapter 24, Problem 96GP

Let us try to estimate the maximum “static electricity” charge that might result during each walking step across an insulating floor. Assume the sole of a person’s shoe has area A ≈ 150 cm², and when the foot is lifted from the ground during each step, the sole acquires an excess charge Q from rubbing contact with the floor. (a) Model the sole as a plane conducting surface with Q uniformly distributed across it as the foot is lifted from the ground. If the dielectric strength of the air between the sole and floor as the foot is lifted is E_S = 3 × 10⁶ N/C, determine Q_max, the maximum possible excess charge that can be transferred to the sole during each step. (b) Modeling a person as an isolated conducting sphere of radius r ≈ 1 m, estimate a person’s capacitance. (c) After lifting the foot from the floor, assume the excess charge Q quickly redistributes itself over the entire surface area of the person. Estimate the maximum potential difference that the person can develop with respect to the floor.