A positive ion A and a negative ion B has charges and , and masses and respectively. At an instant, the ions are separated by a certain distance r. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is , where the

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Solution

Q.
A positive ion A and a negative ion B has charges $6.67 \times 10^{- 19} C$ and $9.6 \times 10^{- 10} C$ , and masses $19.2 \times 10^{- 27} kg$ and $9 \times 10^{- 27} kg$ respectively. At an instant, the ions are separated by a certain distance r. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is $P \times 10^{- 13}$ , where the value of P is __________.

Take $\frac{1}{4 π ε_{0}} = 9 \times 10^{9} {Nm}^{2} C^{- 1}$ and universal gravitational constant as $6.67 \times 10^{- 11} {Nm}^{2} {kg}^{- 2}$ ) [2025]

Ans.
(Bonus)

$F_{e} = \frac{k q_{1} q_{2}}{r^{2}} and F_{g} = \frac{G m_{1} m_{2}}{r^{2}}$

$\frac{F_{e}}{F_{g}} = \frac{k q_{1} q_{2}}{G m_{1} m_{2}}$

$= \frac{9 \times 10^{9} \times 6.67 \times 10^{- 19} \times 9.6 \times 10^{- 10}}{6.67 \times 10^{- 11} \times 19.2 \times 10^{- 27} \times 9 \times 10^{- 27}}$

$= \frac{10^{- 20}}{2 \times 10^{- 65}} = \frac{1}{2} \times 10^{45}$

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