Physics

Physics

Problem

A straight current-carrying conductor is placed in a uniform magnetic field and the angle θ\theta between the conductor and the magnetic field is slowly varied from 0∘0^{\circ} to 180∘180^{\circ}. a. Part 1: (a) Describe qualitatively how the magnitude of the magnetic force on the conductor depends on θ\theta, and sketch a labelled graph of force versus θ\theta for the full range 0∘≤θ≤180∘0^{\circ} \leq \theta \leq 180^{\circ}. b. Part 2: (b) From your graph, identify the values of θ\theta at which the force is zero and at which it attains its maximum value. Explain the physical reasons for these special angles. c. Part 3: (c) Using appropriate trigonometric reasoning, compare the magnitude of the force at θ=45∘\theta = 45^{\circ} with that at θ=90∘\theta = 90^{\circ}, expressing your answer as a simple fraction of the maximum force.
Intuitive explanation

The key is understanding how the magnetic force on a current-carrying conductor depends on its orientation relative to the field. The force follows F=BILsin⁡θF = BIL\sin\theta, where θ\theta is the angle between the conductor and field direction—so the force is zero when they're parallel and maximum when perpendicular. As you rotate the conductor from 0°0° to 180°180°, watch how sin⁡θ\sin\theta changes: it rises to a peak at 90°90°, then falls back down symmetrically.

Intuitive explanation

The key is understanding how the magnetic force on a current-carrying conductor depends on its orientation relative to the field. The force follows F=BILsin⁡θF = BIL\sin\theta, where θ\theta is the angle between the conductor and field direction—so the force is zero when they're parallel and maximum when perpendicular. As you rotate the conductor from 0°0° to 180°180°, watch how sin⁡θ\sin\theta changes: it rises to a peak at 90°90°, then falls back down symmetrically.

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