A square loop that is .5 m on a side has 20 turns and carries a current of 3 A The loop lies in the x-y plane. An external field of 5 T is uniform and points in a direction that is 30 degrees from the z-axis. (a) Find the magnetic dipole moment of the loop. (b) Find the torque on the loop. Show your work.

Solenoids and electromagnets are widely used in power generation and distribution. A solenoid formed from a length of wire has 80 turns. The solenoid carries a constant current of 13 Aand the strength of the magnetic field produced is measured to be 3×10-3 T at its center. What is the length of the wire that forms the solenoid? Show your work.

To generate the data shown at the right, the dipole magnet was moved closer to the sensor (holding for 10-20 seconds at each distance). The magnet was then moved back away from the sensor in a similar fashion. This provided two data points at each distance (except the closest) to be averaged. Each data point was corrected for the background magnetic field measured at 0.5 meters (no change observed at longer distances). The absolute values of the corrected field are given in the table.Use the data provided below to determine the dependence of the magnetic field on distance, based on a linear trendline.

Please show work and circle answer on paper