Answer:
36.1 nC
Explanation:
The electrostatic force F = kqq'/r² since q = q', F = kq²/r² where q = charge on tape, r = distance between tapes = 1.00 cm = 1 × 10⁻² m and k = 9 × 10⁹ Nm²/C².
Given that F = weight of 12.0 mg piece of tape, F = mg where m = mass of tape = 12.0 mg = 12 × 10⁻³ kg and g = acceleration due to gravity = 9.8 m/s²
So, kq²/r² = mg
q²/r² = mg/k
q² = mgr²/k
taking square-root of both sides,
q = √(mg/k)r
So, substituting the values of the variables into the equation, we have
q = √(mg/k)r
q = √(12 × 10⁻³ kg × 9.8 m/s²/ 9 × 10⁹ Nm²/C²)1 × 10⁻² m
q = √(117.6 × 10⁻³ kgm/s²/9 × 10⁹ Nm²/C²)1 × 10⁻² m
q = √(13.07 × 10⁻¹² C²/m²)1 × 10⁻² m
q = 3.61 × 10⁻⁶ C/m × 1 × 10⁻² m
q = 3.61 × 10⁻⁸ C
q = 36.1 × 10⁻⁹ C
q = 36.1 nC
