A copper wire with diameter d = 1.4 mm and specific electrical resistance of r el = 0.020 · 10 −6 Ω m is surrounded by a plastic insulation of thickness δ = 1.0 mm, which has a thermal conductivity of...

A copper wire with diameter d = 1.4 mm and specific electrical resistance of r_el
= 0.020 · 10⁻⁶
Ω m is surrounded by a plastic insulation of thickness δ = 1.0 mm, which has a thermal conductivity of λ = 0.15W/K m. The outer surface of the insulation will be maintained at a temperature of ϑ_W2
= 20 ◦C. What is the largest current which can be applied to the wire if the inner temperature of the insulation is not allowed to rise above 30 ◦C?