An investigator places a sample 1.0 cm from a wire carrying a large current; the strength of the

Name: Problem 2, Chapter 24: College Physics: A Strategic Approach
Uploaded: 2020-11-04T02:34:07-08:00
Duration: 2 min 43 s
Channel: Vishal Gupta
Description: An investigator places a sample 1.0 cm from a wire carrying a large current; the strength of the magnetic field has a particular value at this point. Later, she must move the sample to a 5.0 cm distance, but she would like to keep the field the same. By what factor must she increase the current?

step 1 High, in the given problem, an investigator places a sample 1 .0 centimeter from a wire carrying

Question

An investigator places a sample $1.0 \mathrm{cm}$ from a wire carrying a large current; the strength of the magnetic field has a particular value at this point. Later, she must move the sample to a $5.0 \mathrm{cm}$ distance, but she would like to keep the field the same. By what factor must she increase the current?

   An investigator places a sample $1.0 \mathrm{cm}$ from a wire carrying a large current; the strength of the magnetic field has a particular value at this point. Later, she must move the sample to a $5.0 \mathrm{cm}$ distance, but she would like to keep the field the same. By what factor must she increase the current?

College Physics: A Strategic Approach

Randall D. Knight,… 4th Edition

Chapter 24, Problem 2

Instant Answer

Solved by Expert Vishal Gupta

11/04/2020

Step 1

Step 1: We start by using Biot-Savart's law, which states that the magnetic field due to a straight current-carrying conductor is given by $B = \frac{{\mu_0 I}}{{2\pi r}}$, where $B$ is the magnetic field, $\mu_0$ is the permeability of free space, $I$ is the Show more…

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An investigator places a sample $1.0 \mathrm{cm}$ from a wire carrying a large current; the strength of the magnetic field has a particular value at this point. Later, she must move the sample to a $5.0 \mathrm{cm}$ distance, but she would like to keep the field the same. By what factor must she increase the current?

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Key Concepts

Magnetic Field due to a Current-Carrying Wire

A long straight conductor carrying a current produces a magnetic field that circles the wire. According to Ampère's law, the magnitude of this field at any point is given by the formula B = (??I)/(2?r), where B is the magnetic field, I is the current, and r is the distance from the wire. This fundamental relationship shows how the magnetic field strength is directly proportional to the current and inversely proportional to the distance from the wire.

Inverse Proportionality of the Magnetic Field with Distance

The formula B = (??I)/(2?r) demonstrates that if the distance from the wire (r) increases, the magnetic field (B) decreases proportionally. To maintain the same field strength at a larger distance, the current must be increased by the same factor by which the distance increases, demonstrating the inverse relationship between field strength and distance.

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