Spot welding of two steel sheets each $2 \: mm$ thick is carried out successfully by passing $4 \: kA$ of current for $0.2$ seconds through the electrodes. The resulting weld nugget formed between the sheets is $5 \: mm$ in diameter. Assuming cylindrical shape for the nugget, the thickness of the nugget is________$mm$.

$$\begin{array}{|l|l|} \hline \text{Latent heat of fusion for steel} & 1400 \: kJ/kg \\ \hline \text{Effective resistance of the weld joint} & 200 \: \mu \Omega \\ \hline \text{Density of steel} & 8000 \: kg/m^3 \\ \hline \end{array}$$