A charge Q is transferred from an initially uncharged plastics ball to an identical ball 12 cm away. The force

Use Coulomb's law

|F| = |Q₁| · |Q₂| / (4·π·ε₀·r²)

Since both ball carry charge of same magnitude , but opposite sign:

Q₁ = Q₂ = Q

=>

|F| = Q² / (4·π·ε₀·r²)

=>

Q = √( |F|·4·π·ε₀·r² )

= √( 17 × 10⁻³N · 4 · π · 8.8542×10⁻¹²C²N⁻¹m⁻² · (0.12m)² )

= 1.65×10⁻⁷C

Hence:

Q = n·e

<=>

n = Q/e = 1.65×10⁻⁷C / 1.6022×10⁻¹⁹C

= 1.03×10¹²

About one trillion electrons were transferred from one ball to the other.

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Where did the 1.6002e-19 come from ?