Mathematics

Mathematics

Problem

A science exhibition model uses an aluminium strip of length 0.30 m carrying a current of 15 A inside a uniform magnetic field of 0.2 T. The strip is to be oriented so that the force on it is exactly one-half of the maximum possible value. Solve the following: a. (i) Determine the angle, measured from the direction of the magnetic field, at which the strip must be kept to obtain one-half of the maximum force. b. (ii) For the angle found in part (i), calculate the actual magnitude of the force acting on the strip.
Intuitive explanation

The key here is understanding that the magnetic force on a current-carrying conductor depends on the angle between the wire and the field: F=BILsin⁡θF = BIL\sin\theta. The maximum force occurs when the strip is perpendicular to the field (θ=90°\theta = 90°), but you want exactly half that maximum. This means you need to find the angle where sin⁡θ=0.5\sin\theta = 0.5, then use that to orient your strip correctly.

Intuitive explanation

The key here is understanding that the magnetic force on a current-carrying conductor depends on the angle between the wire and the field: F=BILsin⁡θF = BIL\sin\theta. The maximum force occurs when the strip is perpendicular to the field (θ=90°\theta = 90°), but you want exactly half that maximum. This means you need to find the angle where sin⁡θ=0.5\sin\theta = 0.5, then use that to orient your strip correctly.

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