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Electric Charges And Fields

Question

Is the electric force between two electrons greater than the gravitational force between them? If so by what factor?

Solution

Electrostatic force =

\frac{K Q_{1} Q_{2}}{r^{2}}

Gravitational force=

\frac{G m_{1} m_{2}}{r^{2}}

On dividing the two we get,

\frac{\frac{{KQ}_{1} Q_{2}}{r^{2}}}{\frac{{Gm}_{1} m_{2}}{r^{2}}}

\Rightarrow

\frac{9.0 \times 10^{9} \times {(1.6 \times 10^{- 19})}^{2}}{6.67 \times 10^{- 11} \times {(9.1 \times 10^{- 31})}^{2}}

\Rightarrow

4 \times 10^{42}

Therefore, Electrostatic force between two electrons is greater than gravitational force by a factor of 10⁴².