What is the mass of a copper wire with a diameter of 2 mm, from which the winding of the electromagnet

What is the mass of a copper wire with a diameter of 2 mm, from which the winding of the electromagnet coil is made, if a current of 1 A flows through the coil at a voltage of 2 V?

Task data: d (diameter of the specified copper wire) = 2 mm (0.002 m); I (current in the coil of the electromagnet) = 1 A; U (coil voltage) = 2 V.

Constants: ρ (specific electrical resistance of copper) = 1.7 * 10 ^ -8 Ohm * m; according to the condition ρm (copper density) = 9 g / cm3 = 9000 kg / m3.

To calculate the mass of the indicated copper wire, we use the equality: U / I = R (wire resistance) = ρ * l / S = ρ * (V / S) / S = ρ * (m / ρm) / S2 = 4 ^ 2 * ρ * m / (ρm * Π ^ 2 * d ^ 4) and m = U * ρm * Π ^ 2 * d ^ 4 / (I * 4 ^ 2 * ρ).

Calculation: m = U * ρm * Π ^ 2 * d ^ 4 / (I * 4 ^ 2 * ρ) = 2 * 9000 * 3.14 ^ 2 * 0.0024 / (1 * 4 ^ 2 * 1.7 * 10 ^ -8) = 10.44 kg.

Answer: The mass of the indicated copper wire is 10.44 kg.