Question

Two point charges totaling 8.00 µC exert a repulsive force of 0.150 N on one another when separated by 0.802 m. What is the charge on each?
smallest charge
largest charge

(b) What is the charge on each if the force is attractive?
smallest charge
largest charge

Answer 1

q1 + q2 = 8 uC

Electrostatic force is given by

F = kq1q2/r^2

when force is repulsive, means both charge is positive

q1q2 = F*r^2/k

q1q2 = 0.15*0.802^2/(9*10^9)

q1q2 = 1.072*10^-11

q1 + q2 = 8*10^-6 C

from above equation

q1*(8*10^-6 - q1) = 1.072*10^-11

Solve this quadratic equation

q1 = 1.7*10^-6 C (Smallest Charge)

q2 = 6.3*10^-6 C (Largest Charge)

B.

when force is attractive means both charge are of opposite signs

q1 + q2 = 8*10^-6

q1*q2 = -0.150*0.802^2/(9*10^9) = 1.072*10^-11

q1*(8*10^-6 - q1) = -1.072*10^-11

Solve this quadratic equation

q1 = -1.17*10^-6 C (Smallest Charge)

q2 = 9.17*10^-6 C (Largest Charge)