A long hollow cylindrical thick-walled conductor (inner radius 1.50cm, outer radius 4.00cm) carries a current of 24.0A distributed uniformly across its cross section. A long thin wire runs down the center of the cylinder and carries a current of 32.0A in the opposite direction. What is the magnitude of the magnetic field 3.00cm from the axis?

Athin electrical heater is inserted between a long circular rod and a concentric tube with inner and outer radii of 20 and 40 mm. the rod (a) has a thermal conductivity of ka = 0.15 w/(m*k), while the tube (b) has a thermal conductivity of kb = 0.8 w/(m*k) and its outer surface is subjected to convection with a fluid of temperature t= -15°c and heat transfer coefficient 60 w/(m2 *k). the thermal contact resistance between the cylinder surfaces and the heater is negligible. (a) determine the electrical power per unit length of the cylinders (w/m) that is required to maintain the outer surface of cylinder b at 15°c. (b) what is the temperature at the center of cylinder a?