How to find the ratio of electrical forces between two charges separated by a specific distance? (Electrostatics)
Answers
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We know
charge of an electron = -1.67 ×10⁻¹⁹ C
charge of an proton = 1.67 ×10⁻¹⁹ C
Mass of electron = 9.1 × 10⁻³¹ kg
Mass of proton = 1.67 × 10⁻²⁷ kg
(a). (i)
(Coulomb force/Gravitational force)
= {(9 ×10⁹×(-1.6×10⁻¹⁹)1.6×10⁻¹⁹)/r²}/{(6.67×10⁻¹¹×9.1×10⁻³¹×1.67×10⁻²⁷)/r²}
= 23.04×10⁻²⁹/101.36×10⁻⁶⁹
= 0.2273×10⁻⁴⁰
=2.27×10⁻³⁹
(ii)(Coulomb force/Gravitational force)
= {(9×10⁹×(1.6×10⁻²⁹)²/r²)}/{6.67×10⁻¹¹×(1.67×10⁻²⁷)²/r²}
=1.24×10³⁶
(b)
Force F = 9×10⁹(-1.6×10⁻¹⁹)×1.6×10⁻¹⁹/(10⁻¹⁰)²
F = 2.304 × 10⁻⁸ N
And we know Force F = mass × acceleration
Hence acceleration of electron = F/m = 2.304 × 10⁻⁸ N/ 9.1 × 10⁻³¹ kg
a₁ = 2.5 × 10²² m/s²
and acceleration of proton a₂ = 2.304 × 10⁻⁸ N/1.67 × 10⁻²⁷ kg
a₂ = 1.4 × 10¹⁹ m/s²
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