You are working on a design for an electromagnetic compass. A single circular loop of wire with an area of A $=1\mathrm{.}7$ mm$2$ is 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 of I $=4\mathrm{.}9$ A 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 of B $=42$ T$.$