You are working on a design for an electromagnetic compass. A single circular loop of wire with an area ofA=1.4mm²is fixed to the face of the compass, and initially lies in a horizontal plane. While active, your circuit is designed to have a counter-clockwise direct current ofI=4.5A running through the loop, as seen from above. The compass is in a gimbal which allows the loop to rotate along any axis. You are field testing your compass in an area where the earth's magnetic field has a strength ofB=41T. Randomized Variables A=1.4mm² I=4.5A B=41T =37

A. Calculate the maximum magnitude of the torque, (in Nm), exerted on the current loop by the earth's magnetic field while current is running through the loop.

B. Towards which direction will the top of the compass (which is pointed out of the page) rotate when the current in the loop is on?

C. About which of the following axes will the loop rotate when the current is first turned on in the loop?

D. Calculate the magnitude of the torque (in Nm) exerted on the loop when the angle between the normal to the current loop and the earth's magnetic field is = 37.

E. A torque of = 6.0 10^-14 Nm is required to produce a large enough motion of the compass to be detected with the unaided eye. To produce this effect, you decide to use multiple loops of wire, but keep all other parameters the same. What is the minimum number of loops required?

N wire loop W E S