Consider an infinitely long, hollow cylindrical wire. The wire has outer diameter b and the cylindrical hole at its center has diameter a.
Find the magnetic field everywhere if a known current i flows from left to right and the current is uniformly spread over the region between a and b.
Find the force that this wire would exert on a thin, straight length of wire W located a distance 2b from the axis of the cylinder if that thin wire had a current 3i

Along wire of diameter 1 mm is submerged in an oil bath of temperature ∞ 31°c. the wire has an electrical resistance per unit length of 0.01 ω/m. if a current of 103 a flows through the wire and the convection coefficient is 500 w/m2·k, what is the steady-state temperature of the wire? from the time the current is applied, how long does it take for the wire to reach a temperature that is within 1°c of the steady-state value? the properties of the wire are 8000 kg/m3, 500 j/kg·k, and 20 w/m·k.