A 2 mm diameter, 10 m long electric wire is tightly wrapped with a 1 mm thick plastic cover (k = 0.15 W/m·°C). A current of 10 A flows and the voltage drop along the wire is 8 V. The wire is exposed to a medium at 30 °C with h = 24 W/m^{2}·°C. Determine (a) the steady temperature at the wire–plastic interface (answer in °C) and (b) the critical radius of the cover (answer in mm), and hence state whether doubling the cover thickness raises or lowers the interface temperature.