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Question

Physics Question on coulombs law

The ratio of magnitude of electrostatic force and gravitational force for an electron and a proton is

A

6.6×10396.6 \times 10^{39}

B

2.4×10392.4 \times 10^{39}

C

6.6×10296.6 \times 10^{29}

D

2.4×10292.4 \times 10^{29}

Answer

2.4×10392.4 \times 10^{39}

Explanation

Solution

Here, for an electron and a proton Electrostatic force, Fe=14πε0e2r2\left|F_{e}\right|=\frac{1}{4\pi\varepsilon_{0}} \frac{e^{2}}{r^{2}} Gravitational force, Fg=Gmempr2\left|F_{g}\right|=\frac{G\,m_{e}m_{p}}{r^{2}} FeFg=14πε0e2Gmemp\therefore \frac{\left|F_{e}\right|}{\left|F_{g}\right|}=\frac{1}{4\pi\varepsilon_{0}} \frac{e^{2}}{G\,m_{e}m_{p}} =9×109×(1.6×1019)26.67×1011×9×1031×1.66×1027=\frac{9\times10^{9}\times\left(1.6\times10^{-19}\right)^{2}}{6.67\times10^{-11}\times9\times10^{-31}\times1.66\times10^{-27}} =2.4×1039=2.4\times10^{39}