Question

the electric field produced due to an electron is sufficient to balance the gravitational force on another electron located above the first. Find the distance between two electrons.​

Answer 1

The distance between the two electrons will be $r = 1.6 \times 10 ^{-4} m$ .

Explanation :

We know charge carried by 1 electron = $1.6 \times 10^{-19} C$

And also mass of one electron = $9.1 \times 10 ^{-31} kg$

Since the both electrons are in equilibrium due to gravitational and electrostatic forces , so the equilibrium condition will be :

$F_e = F_g$

Or,$\frac{K \times e \times e}{r^2}= mg$

Or,$\frac{9 \times 10 ^9 \times 1.6 \times 10 ^{-19)^2}}{r^2}= 9.1 \times 10 ^ {-31 } \times 10$

Or, $r^2= \frac{(1.6 \times 10 ^{-19})^2}{10 ^ {-30}}$

Or, $r^2 = 1.6 \times 1.6 \times 10 ^{-8}$

Or, r =$1.6 \times 10 ^{-4} m$

So,the distance between two electrons to be in equilibrium  is$1.6 \times 10 ^{-4} m$ .