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An infinitely long uniform solid wire of radius a carries a uniform dc current of density j. The magnetic field at a distance r from the center of the wire is proportional to (A) r for r a (B) 0 for r a (C) r for r a (D) 0 for r a

An infinitely long uniform solid wire of radius a carries a uniform dc current of density j. The magnetic field at a distance r from the center of the wire is proportional to (A) r for r a (B) 0 for r a (C) r for r a (D) 0 for r a

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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**Magnetic Field Around a Long Uniform Solid Wire Carrying Uniform DC Current** An infinitely long, uniformly solid wire with a radius \( a \) carries a uniform direct current (dc) of density \( \overline{j} \). The magnetic field at a distance \( r \) from the center of the wire is proportional to: **Options:** (A) \( r \) for \( r < a \) and \( 1/r^2 \) for \( r > a \) (B) 0 for \( r < a \) and \( 1/r \) for \( r > a \) (C) \( r \) for \( r < a \) and \( 1/r \) for \( r > a \) (D) 0 for \( r < a \) and \( 1/r^2 \) for \( r > a \) **Explanation:** To determine the correct relationship of the magnetic field with distance \( r \), one must consider the fundamental properties of magnetic fields generated by currents in wires and apply Ampère’s Law. **Details:** - For point \( r \) inside the wire (\( r < a \)): - The magnetic field \( \overline{B} \) is directly proportional to the distance \( r \) from the center. - For point \( r \) outside the wire (\( r > a \)): - The magnetic field \( \overline{B} \) is inversely proportional to the distance \( r \) from the center. Based on these principles, the correct option would be: (C) \( r \) for \( r < a \) and \( 1/r \) for \( r > a \). This understanding is essential for studying the behaviors of magnetic fields in materials and is a fundamental concept in electromagnetism.
Transcribed Image Text:**Magnetic Field Around a Long Uniform Solid Wire Carrying Uniform DC Current** An infinitely long, uniformly solid wire with a radius \( a \) carries a uniform direct current (dc) of density \( \overline{j} \). The magnetic field at a distance \( r \) from the center of the wire is proportional to: **Options:** (A) \( r \) for \( r < a \) and \( 1/r^2 \) for \( r > a \) (B) 0 for \( r < a \) and \( 1/r \) for \( r > a \) (C) \( r \) for \( r < a \) and \( 1/r \) for \( r > a \) (D) 0 for \( r < a \) and \( 1/r^2 \) for \( r > a \) **Explanation:** To determine the correct relationship of the magnetic field with distance \( r \), one must consider the fundamental properties of magnetic fields generated by currents in wires and apply Ampère’s Law. **Details:** - For point \( r \) inside the wire (\( r < a \)): - The magnetic field \( \overline{B} \) is directly proportional to the distance \( r \) from the center. - For point \( r \) outside the wire (\( r > a \)): - The magnetic field \( \overline{B} \) is inversely proportional to the distance \( r \) from the center. Based on these principles, the correct option would be: (C) \( r \) for \( r < a \) and \( 1/r \) for \( r > a \). This understanding is essential for studying the behaviors of magnetic fields in materials and is a fundamental concept in electromagnetism.
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