A copper wire with a radius of 0.1 mm and a resistance of 1 k is connected across a 20 V power supply. Determine the current density in the wire.

Step-by-step solution

Given, radius of the wire, r = 0.1 mm = 10⁻⁴ m Resistance of the wire, R = 1 k = 10^3 Voltage across the wire, V = 20 V Current in the wire is given by Ohm's law: I = V R = 20 10^3 = 2 10⁻² A Cross-sectional area of the wire: A = r^2 = (10⁻⁴)^2 = 10⁻⁸ m ^2 Current density J is the current per unit area: J = I A = 2 10⁻² 10⁻⁸ = 2 10^6 A/m ^2 J 2 3.1416 10^6 0.6366 10^6 A/m ^2 = 6.37 10^5 A/m ^2