Question

There are two small uncharged spheres placed at a distance of 1 m from each other. N number of electrons are transferred from one sphere to another. The force between the spheres is now measured to be equal to 2 newton, then the value of N is

a) 4.8 × 10^5
b) 6.1 × 10^2
c) 2.8 × 10^6
d) 9.3 × 10^13

Answer 1

After transfer of N electrons, one body will have charge -Ne and the other body will have charge +Ne.

Now, they experience force of 2 Newton.

$\rm \: F = \dfrac{k {(Ne)}^{2} }{ {d}^{2} }$

$\rm \implies \: 2 = \dfrac{9 \times {10}^{9} \times {(N \times 1.6 \times {10}^{ - 19} )}^{2} }{ {1}^{2} }$

$\rm \implies \: 2 = 9 \times {10}^{9} \times {(N \times 1.6 \times {10}^{ - 19} )}^{2}$

$\rm \implies \: 2 = 9 \times {10}^{9} \times {N}^{2} \times 2.56 \times {10}^{ - 38}$

$\rm \implies \: {N}^{2} = 0.86 \times {10}^{28}$

$\rm \implies \: N \approx 0.93 \times {10}^{14}$

$\rm \implies \: N \approx 9.3 \times {10}^{13}$

So, option d) is corrected !