A square loop of copper wire is pulled through a region of uniform magnetic field as shown. Rank the pulling forces \(F_A\), \(F_B\), \(F_C\), and \(F_D\) that must be applied to keep the loop moving with constant speed (\(\vec{v}\)):
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When considering the forces on a conducting loop in a magnetic field, the force is strongest where the field is most aligned and the length of the wire interacts with the magnetic flux.
When a conducting loop is moved through a magnetic field, the induced emf and the resulting current will generate forces on the segments of the wire. The forces are given by:
\[
F = I L B
\]
Where \(I\) is the induced current, \(L\) is the length of the wire, and \(B\) is the magnetic field strength.
- \(F_A\) acts on the side entering the magnetic field, with the least magnetic interaction.
- \(F_B\) and \(F_D\) are the forces acting on the loop's sides where the magnetic field is strongest, as they are directly aligned with the field.
- \(F_C\) is the force acting on the side of the wire where the magnetic field is cutting through the loop the most efficiently.
Therefore, the ranking is:
\[
F_C>F_B = F_D>F_A
\]
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