1. Initial charges on identical conducting spheres

Given:

• $q_1 = 2.1\,\text{nC}$
• $q_2 = -0.1\,\text{nC}$

When two identical conducting spheres are brought into contact, the total charge gets equally distributed.

So total charge, $q_{\text{total}} = 2.1 + (-0.1) = 2.0\,\text{nC}$

Hence charge on each sphere after contact: $q = \frac{2.0}{2} = 1.0\,\text{nC}$

Thus after separation: $q_1' = q_2' = 1.0\,\text{nC} = 1.0 \times 10^{-9}\,\text{C}$

2. Apply Coulomb's law

Distance between spheres: $r = 0.5\,\text{m}$

Electrostatic force: $F = \frac{1}{4\pi\varepsilon_0}\frac{q_1'q_2'}{r^2}$

Given: $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9$

Substitute values: $F = 9\times 10^9 \times \frac{(1\times 10^{-9})(1\times 10^{-9})}{(0.5)^2}$

$F = 9\times 10^9 \times \frac{10^{-18}}{0.25}$

$F = 9\times 10^9 \times 4\times 10^{-18}$

$F = 36\times 10^{-9}\,\text{N}$

3. Required integer

The force is written as: $\underline{\hspace{2cm}} \times 10^{-9}\,\text{N}$

So the required integer is: $\boxed{36}$

4. Comparison with stored answer

Stored correct answer = 36.

Our derived answer matches it.