An approximation for the magnetic field at the edge of a certain C-shaped magnet is Show that this approximation is consistent with Maxwell’s equations in free space.
Find the magnitude and direction of the force on a square loop of current which has sides length b = 10 cm, positioned with its left edge a distance c = 12 cm from the magnet opening, and carrying a current of 2.6 A counterclockwise. Let and a = 30 cm.
If the loop is rotated by an angle 20º about the x axis, how much torque does it experience and it which direction?

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?