12 Ball
June 23rd, 2009
12 Ball
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A charge Q is transferred from an initially uncharged plastics ball to an identical ball 12 cm away. The force
of attraction is then 17 mN. How many electrons were transferred from one ball to the other?
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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