Question

(a) 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 10.0 mg piece of tape held 1.00 cm above another. (b) Discuss whether the magnitude of this charge is consistent with what is typical of static electricity.

Solution

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Electrostatic force should provide for the gravitational pull:

\begin{align*}k\dfrac{q^2}{r^2}&=mg\\\\ \implies q&=r\sqrt{\dfrac{mg}{k}}\\\\&=0.01\:\text{m}\:\sqrt{\dfrac{10^{-5}\:\text{kg}\cdot 9.81\:\dfrac{\text{m}}{\text{s}^2}}{9\cdot10^9 \:\dfrac{\text{Nm}^2}{\text{C}^2}}}\\\\&=\boxed{\textcolor{#c34632}{1.04\:\text{nC}}}\end{align*}

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