Coulomb's 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 and masses respectively,
(a) Compare the strength of these forces by determining the ratio of their magnitudes (i) for an electron and a proton and (ii) for two protons.
(b) Estimate the accelerations of electron an proton due to the electrical force of the mutual attraction when they are `=10^(-10)m` apart?
`(m_(p) = 1.67 xx 10^(-27) kg, m_(e) = 9.11 xx 10^(-31) kg)`

Explanation

(a) (Electrons) `F_(e), F_(e)` (Proton)
`|F_(e)| = k((e)(e))/r^(2)`………..(1)

`|F_(g)| =G(m_(e).m_(p))/r^(2)`…….(2)
Required ratio,
`|F_(e)/F_(g)| = (ke^(2))/(Gm_(e).m_(p))`
`=(9 xx 10^(9) xx (1.6 xx 10^(-19))^(2)/(6.67 xx 10^(-11) xx (9.1 xx 10^(-31))(1.67 xx 10^(-27))))`
`=2.273 xx 10^(39)`
`|F_(e)| gt gt gt gt |F_(g)|`

`|F_(e)| = k((e)(e))/r^(2)`..........(3)

`|F_(g)| = G.(m_(p)^(2))/r^(2)`......(4)
Required ratio,
`|F_(e)|/|F_(g)| = (ke^(2))/(Gm_(p)^(2))`
`=(9 xx 10^(9) xx (1.6 xx 10^(-19))^(2))/((6.67 xx 10^(-11))(1.67 xx 10^(-27))^(2))`
`=1.349 xx 10^(36)`
`|F_(e)| gt gt gt gt gt |F_(g)|`

Electric force exerted between electron and proton,
`F_(e) =k((e)(e))/r^(2)`
`=(9 xx 10^(9) xx (1.6 xx 10^(-19))^(2))/(10^(-10))^(2)`
`therefore F_(e) = 2.304 xx 10^(-8)` N.........(5)
Now, here `F_(e) = m_(e)a_(e) = m_(p)a_(p)`
(i) `a_(e) =F_(e)/m_(e) = (2.304 xx 10^(-8))/(9.1 xx 10^(-31))`............(6)
`=2.532 xx 10^(22) m//s^(2)`
(ii) `a_(p) = F_(e)/m_(p) = (2.304 xx 10^(-8))/(1.67 xx 10^(-27))`
`=1.380 xx 10^(19) m//s^(2)`