A cylindrical wire of radius 0.5 mm and conductivity $$5 \times 10^7$$ S m$$^{-1}$$ is subjected to an electric field of 10 mV m$$^{-1}$$. The expected value of current in the wire will be $$x^3\pi$$ mA. The value of $$x$$ is ______.

The radius of the cylindrical wire is $$r = 0.5$$ mm $$= 0.5 \times 10^{-3}$$ m, the conductivity is $$\sigma = 5 \times 10^7$$ S m$$^{-1}$$, and the applied electric field is $$E = 10$$ mV m$$^{-1} = 10 \times 10^{-3} = 10^{-2}$$ V m$$^{-1}$$.

The current density is given by $$J = \sigma E = 5 \times 10^7 \times 10^{-2} = 5 \times 10^5$$ A m$$^{-2}$$.

The cross-sectional area of the wire is $$A = \pi r^2 = \pi \times (0.5 \times 10^{-3})^2 = \pi \times 0.25 \times 10^{-6} = 0.25\pi \times 10^{-6}$$ m$$^2$$.

The current through the wire is $$I = J \times A = 5 \times 10^5 \times 0.25\pi \times 10^{-6} = 1.25 \times 10^{-1} \times \pi = 0.125\pi$$ A $$= 125\pi$$ mA.

Comparing with the given expression $$I = x^3 \pi$$ mA, we get $$x^3 = 125$$, which gives $$x = 5$$.

Therefore, the value of $$x$$ is $$5$$.