Table 24.1 notes that the magnetic field 10 cm from a wire carrying a 1 A current is 2 μT. What

Name: Problem 1, Chapter 24: College Physics: A Strategic Approach
Uploaded: 2020-11-04T02:33:17-08:00
Duration: 2 min
Channel: Vishal Gupta
Description: Table 24.1 notes that the magnetic field 10 cm from a wire carrying a 1 A current is 2 μT. What is the field 1 cm from the wire?

step 1 We know that magnetic field due to a current carrying conductor depends directly on the current

Question

Table 24.1 notes that the magnetic field $10 \mathrm{cm}$ from a wire carrying a $1 \mathrm{A}$ current is $2 \mu \mathrm{T}$. What is the field $1 \mathrm{cm}$ from the wire?

   Table 24.1 notes that the magnetic field $10 \mathrm{cm}$ from a wire carrying a $1 \mathrm{A}$ current is $2 \mu \mathrm{T}$. What is the field $1 \mathrm{cm}$ from the wire?

College Physics: A Strategic Approach

Randall D. Knight,… 4th Edition

Chapter 24, Problem 1

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Solved by Expert Vishal Gupta

11/04/2020

Step 1

This relationship can be expressed as B ∝ I/r. Show more…

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Table 24.1 notes that the magnetic field $10 \mathrm{cm}$ from a wire carrying a $1 \mathrm{A}$ current is $2 \mu \mathrm{T}$. What is the field $1 \mathrm{cm}$ from the wire?

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Key Concepts

Magnetic Field Around a Long Straight Wire

A long, straight current-carrying wire produces a magnetic field that loops around the wire. The magnitude of this field at any point a distance r from the wire is given by the formula B = (?0 I)/(2?r), where ?0 is the permeability of free space and I is the electric current. This relation is a result of fundamental laws in electromagnetism and is crucial for calculating the magnetic field at various distances from the wire.

Inverse Proportionality of Magnetic Field with Distance

The magnetic field generated by a straight wire decreases in magnitude as the distance from the wire increases. Specifically, the field is inversely proportional to the distance (B ? 1/r), meaning that if the distance from the wire is reduced by a certain factor, the field strength increases by the same factor. Understanding this relationship allows one to predict how changes in distance affect the magnetic field intensity.

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