A square conducting loop of side length carries a steady conventional current
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Magnetism and Electromagnetism · Magnetism and Electromagnetism
Problem
A square conducting loop of side length ℓ carries a steady conventional current I. The loop is mounted so it can rotate about a vertical axis passing through its center. A uniform horizontal magnetic field of magnitude B points due east. At a particular instant the plane of the loop makes an angle θ with the magnetic field direction (the normal to the loop’s plane therefore makes an angle 90∘−θ with the field).
(a) For the side of the loop that is nearest the observer, express the angle between the current direction in that side and the magnetic field in terms of θ. Briefly explain your reasoning.
(b) Rank the magnitudes of the magnetic forces on the four sides of the loop at this instant. Clearly state any equalities and justify the ranking in terms of geometric considerations.
(c) Explain why the net translational (linear) force on the loop as a whole is zero even though individual sides experience non-zero forces.
(d) Using your analysis, determine the values of θ (within 0∘≤θ≤90∘) for which the loop experiences (i) maximum torque and (ii) zero torque about the rotation axis. Justify each answer in terms of the forces identified earlier.