Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

two insulating balls each weigh 0.10 grams and hang from a common point by ident

ID: 2274558 • Letter: T

Question

two insulating balls each weigh 0.10 grams and hang from a common point by identical threads 30 cm long. Each ball carries a charge of +8.0 nC and repels the other ball. If after two hours, the balls are found to be only 4.0 cm apart, what is the rate at which the charge has leaked off

Explanation / Answer

let the final charges on the balls be 'x' nC. final separation b/w the balls = 0.04 m Attractive gravitational force on the balls = G*m1*m2/r^2 => Fg = (6.67*10^-11 *0.1*10^-3*0.1*10^-3)/(0.04)^2 => Fg = 4.169 * 10^-16 N Repulsive electrostatic force on the balls = k*q1*q2/r^2 => Fe = (9*10^9* x*10^-9 *x*10^-9)/(0.04)^2 => Fe = 5.625 *10^-6* x^2 N For static equilibrium, Fe = Fg => 5.625 *10^-6* x^2 = 4.169 * 10^-16 => x = 8.61 *10^-6 C so, final charge on the balls = 8.61 *10^-6 nC = 8.61* 10^-15 C Initial charge on the balls = 8 *10^-9 C charge leaked = 8*10^-9 - 8.61*10^-15 = 8 *10^-9 C rate at which charge has leaked off = (8*10^-9)/(2*60*60) = 1.11 *10^-12 Coulomb/second