# Problem: People have proposed driving motors with the earth's magnetic field. This is possible in principle, but the small field means that unrealistically large currents are needed to produce noticeable torques. Suppose a 20-cm-diameter loop of wire is oriented for maximum torque in the earth's field.What current would it need to carry in order to experience a very modest 1.0 × 10−3 N⋅m torque?

###### FREE Expert Solution

Torque for a loop in a magnetic field:

$\overline{){\mathbf{\tau }}{\mathbf{=}}{\mathbf{B}}{\mathbf{I}}{\mathbf{A}}}$

A = π(d/2)2 = π(20cm/2)2(1m/100cm)2 = 0.01π m2

###### Problem Details

People have proposed driving motors with the earth's magnetic field. This is possible in principle, but the small field means that unrealistically large currents are needed to produce noticeable torques. Suppose a 20-cm-diameter loop of wire is oriented for maximum torque in the earth's field.

What current would it need to carry in order to experience a very modest 1.0 × 10−3 N⋅m torque?