Question

Common transparent tape becomes charged when pulled from a dispenser. If one piece is placed above another, the repulsive force can be great enough to support the top piece's weight. Assuming equal point charges (only an approximation), calculate the magnitude of the charge if electrostatic force is great enough to support the weight of a 12.0 mg piece of tape held 0.55 cm above another. (The magnitude of this charge is consistent with what is typical of static electricity.)

Answer 1

q = 2 10⁻⁸ C

Step-by-step explanation:

For this exercise we use the translational equilibrium equation

F_e -A =

F_e = W

the electric force is given by Coulomb's law

F_e =
`k (q_1q_2)/(r^2)`

in this case they indicate that the loads on the tapes are equal

F_e = k q² / r²

we substitute

k q² / r² = m g

q =
`\sqrt{ (mg r^2)/(k) }`

calculate

q =
`\sqrt { ( 12 \ 10^(-3) \ 9.8 (0.55 \ 10^(-2))^2 )/(9 \ 10^9) }`

q =
`\sqrt{ 3.9526 \ 10^(-16)`

q = 1,999 10⁻⁸ C

q = 2 10⁻⁸ C