Two 0.1 g Styrofoam balls are strung like beads on a vertical insulating thread.

Question

Two 0.1 g Styrofoam balls are strung like beads on a vertical insulating thread. The upper ball is free to move but the lower ball is glued to the string. Imagine that both are given an equal amount of negative charge so that the upper ball is suspended above the lower ball and their centers are 4.0 cm apart. (You can assume each ball repels the other as if it were a point charge located at the center). Roughly what fraction of the electrons originally on each ball have been added to each ball? (Styrofoam is mostly made of low mass atoms having roughly equal numbers of protons and neutrons.)

Explanation / Answer

Fraction of the electrons originally on each ball have been added to each ball which given as :

Felec / Fgrav = (k e2 / r2) x (r2 / G mp me)

Felec / Fgrav = k e2 / G mp me

where, k = constant value = 9 x 109 Nm2/C2

e = charge on electron = -1.6 x 10-19 C

G = gravitational constant value = 6.67 x 10-11 Nm2/kg2

mp = mass of proton = 1.67 x 10-27 kg

me = mass of electron = 9.11 x 10-31 kg

then, we have

Felec / Fgrav = (9 x 109 Nm2/C2) (-1.6 x 10-19 C)2 / (6.67 x 10-11 Nm2/kg2) (1.67 x 10-27 kg) (9.11 x 10-31 kg)

Felec / Fgrav = (23.04 x 10-29 Nm2) / (101.4 x 10-69 Nm2)

Felec / Fgrav = 2.27 x 1039

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