A steel wire 20 m long is at 12 V. Find the current density.

To find the current density in the steel wire taken, we apply the formula: j = I / S = (U / R) / S = U / (R * S) = U / (ρ * l / S * S) = U / (ρ * l).

Constants and variables: U – voltage on the steel wire (U = 12 V); ρ is the specific electrical resistance of steel (ρ = 0.103 … 0.137 Ohm * mm2 / m, we take ρ = 0.12 Ohm * mm2 / m); l – wire length (l = 20 m).

Let’s calculate: j = U / (ρ * l) = 12 / (0.12 * 20) = 5 A / mm2.

Answer: The current density in the steel wire taken is 5 A / mm2.