A straight wire segment of length 25 cm carries a current of 33.0 A and is immersed in a uniform

step 1 In this question, we have a wire of length 25 centimetres with a current of 33 amps flowing thro

A straight wire segment of length 25 cm carries a current of...

A straight wire segment of length $25 \mathrm{cm}$ carries a current of $33.0 \mathrm{A}$ and is immersed in a uniform external magnetic field. The magnetic force on the wire segment has magnitude 4.12 N. (a) What is the minimum possible magnitude of the magnetic field? (b) Explain why the given information enables you to calculate only the minimum possible field magnitude.

A straight wire segment of length $25 \mathrm{cm}$ carries a current of $33.0 \mathrm{A}$ and is immersed in a uniform external magnetic field. The magnetic force on the wire segment has magnitude 4.12 N. (a) What is the minimum possible magnitude of the magnetic field?
(b) Explain why the given information enables you to calculate only the minimum possible field magnitude.

Key Concepts

Determination of Minimum Magnetic Field Magnitude

In problems where only the force, current, and conductor length are known, and the angle between the current and the magnetic field is unspecified, one can only determine the minimum magnetic field strength. This minimum is calculated under the condition of maximum force (i.e., when sin(?) = 1), since any deviation from a perpendicular orientation would require a stronger magnetic field to produce the same force.

Angle Dependence in Magnetic Force

The sin(?) term in the magnetic force equation highlights the role of the relative orientation between the current and the magnetic field. When the conductor is perpendicular to the field (? = 90°), sin(?) is one, yielding the maximum force. This dependence is crucial for understanding that any misalignment reduces the force and directly affects the calculation of the magnetic field’s magnitude.

Uniform Magnetic Field

A uniform magnetic field is characterized by having the same magnitude and direction at every point in the region of interest. This simplification allows for straightforward application of the force equation across all parts of a current-carrying conductor immersed in such a field, making it easier to analyze the resulting forces.

Magnetic Force on a Current-Carrying Conductor

This concept describes the force experienced by a current-carrying conductor in a magnetic field, governed by the relation F = I L B sin(?), where I represents the current, L is the length of the conductor, B is the magnetic field strength, and ? is the angle between the current direction and the field. It forms a fundamental basis for understanding interactions between electricity and magnetism in many applications.

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