A 0.30 m section of wire is placed in a uniform magnetic field of 0.80 T. The wire carries a current of 1.50 A. The angle between the magnetic field and the wire is [math: 35.0∘] 35.0 ^\circ . What is the magnitude of the force experienced by the wire?

Question

BlackTom AI · Accepted Answer

We start by identifying the formula for the magnetic force on a current-carrying wire: F = I L B sin(theta).

Given values: I = 1.50 A, L = 0.30 m, B = 0.80 T, theta = 35.0 degrees.

Compute the product of the scalar factors: I × L × B = 1.50 × 0.30 × 0.80 = 0.36 N (in the sense of the force magnitude before including the angle factor).

Now include the angle with sin(theta): sin(35.0°) ≈ 0.574.

Therefore, F = 0.36 × 0.574 ≈ 0.2066 N, which rounds to about 0.21 N.

Option-by-option analysis:
- 0.29 N: This would require a larger sine factor or larger product I×L×B. Using the given numbers, sin(35°) ≈ 0.574 cannot produce 0.29 N when multiplied by 0.36. This option reflects a miscalculation of either the angle factor or the product of I, L, and B.
- 0.25 N: This is closer to the correct value but still higher than the precise calculation. It might arise from rounding choices or slight misestimate of sin(35°), but the exact computation with sin(35°) yields about 0.2066 N.
- 0.21 N: This matches the calculated result when using F = I L B sin(35°). After computing 0.36 × sin(35°) with sin(35°) ≈ 0.574, the product is approximately 0.2066 N, which rounds to 0.21 N.
- 0.36 N: This corresponds to ignoring the sin(theta) factor entirely, i.e., assuming sin(θ) = 1. That would only be correct if the field were aligned with the wire, which is not the given case (theta = 35°). Hence this option overestimates the true magnitude.

Summary: The correct approach is to multiply I, L, and B to get 0.36 N, then multiply by sin(35°) to get about 0.2066 N. The option that reflects this final value most closely is 0.21 N, while the other choices stem from misapplying the angle factor or miscalculating the product.

A 0.30 m section of wire is placed in a uniform magnetic field of 0.80 T. The wire carries a current of 1.50 A. The angle between the magnetic field and the wire is [math: 35.0∘] 35.0 ^\circ . What is the magnitude of the force experienced by the wire?Single choice

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