Question

20. (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.

Answer 1

Answer:

$1.04461\times 10^{-9}\ C$

Explanation:

Charge of particle = q

The particles have same charge

r = Distance between charge

k = Coulomb constant = $8.99\times 10^9\ Nm^2/C^2$

m = Mass of particle = 10 mg

g = Acceleration due to gravity = 9.81 m/s²

Electrostatic force is given by

$F=k\frac{q_1q_2}{r^2}$

According to Newton's second law

$F=mg$

Here, both the electrostatic and inertial force is conserved

$mg=k\frac{q^2}{r^2}\\\Rightarrow q=\sqrt{\frac{mgr^2}{k}}\\\Rightarrow q=\sqrt{\frac{10\times 10^{-6}\times 9.81\times 0.01^2}{8.99\times 10^9}}\\\Rightarrow q=1.04461\times 10^{-9}\ C$

The charge of the particles is $1.04461\times 10^{-9}\ C$

The charge of the particles is very low as compared to typical static electricity