Coulomb's law for electrostatic force between two point charges

Asked by admin @ 13/08/2021 in Physics viewed by 303 People

Coulombs' law for electrostatic force between two point charges and Newton's law for gravitational force between two stationary point masses, both have inverse-square dependence on the distance between the charges/masses.

(a) Compare the strength of these forces by determining the ratio of their magnitude
(i) for an electron and a proton and (ii) for two protons.
(b) Estimate the accelerations for electron and proton due to the electrical force of their mutual attraction when they are 1Å (= 10−10 m) apart? mp = 1.67 ✕ 10−27 kg m e = 9.11 ✕ 10−31 kg.

Answered by admin @ 13/08/2021

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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