We can find the current flowing through the wire using Ohm's law: [tex]I= \frac{\Delta V}{R} [/tex] where I is the current, [tex]\Delta V[/tex] is the potential difference applied to the wire, and R is the resistance of the wire.
We can now rewrite both [tex]\Delta V[/tex] and R. In fact, we know that the potential difference applied to the wire is equal to the product between the intensity of the electric field E applied and the length L of the wire: [tex]\Delta V = EL[/tex] Instead, the resistance R is related to the properties of the wire, through the relationship [tex]R= \frac{\rho L}{A} [/tex] where [tex]\rho[/tex] is the resistivity of the material (iron) and A is the cross-sectional area of the wire.
Substituting both formulas into the first one, we get [tex]I= \frac{EA}{\rho} [/tex] The section of the wire is [tex]A=\pi r^2 = \pi (2.3 \cdot 10^{-3}mm)^2=1.66 \cdot 10^{-5}m^2[/tex] And by using [tex]E=0.063 V/m[/tex] and [tex]\rho = 9.71 \cdot 10^{-8}\Omega m[/tex] (iron resistivity), we find [tex]I= \frac{(0.063 V/m)(1.66 \cdot 10^{-5}m^2)}{9.71 \cdot 10^{-8}\Omega m}=10.8 A [/tex]
