A long, straight wire carries a current I. If the magnetic field is 1 T at a distance of r, what is the magnetic field at a distance of 5r from the wire? Express your answer in teslas.
A long, straight wire carries a current I. If the magnetic field is 1 T at a distance of r, what is the magnetic field at a distance of 5r from the wire? Express your answer in teslas.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Magnetic Field of a Straight Wire
**Problem Statement:**
A long, straight wire carries a current \( I \). If the magnetic field is \( 1 \, \text{T} \) at a distance of \( r \), what is the magnetic field at a distance of \( 5r \) from the wire?
**Express your answer in teslas.**
**Solution:**
\[
B = 0.2 \, \text{T}
\]
**Explanation:**
The magnetic field around a long, straight wire is inversely proportional to the distance from the wire. Therefore, when the distance increases, the magnetic field decreases proportionally. Given that the magnetic field is \( 1 \, \text{T} \) at a distance \( r \), at a distance \( 5r \), the magnetic field would be \( \frac{1}{5} \) of the original magnetic field, resulting in \( 0.2 \, \text{T} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a931645-54a1-474a-bda2-4c874edd548a%2F6e6cddc2-3575-418f-b37d-67410082a432%2Fih0ol4i_processed.png&w=3840&q=75)
Transcribed Image Text:### Magnetic Field of a Straight Wire
**Problem Statement:**
A long, straight wire carries a current \( I \). If the magnetic field is \( 1 \, \text{T} \) at a distance of \( r \), what is the magnetic field at a distance of \( 5r \) from the wire?
**Express your answer in teslas.**
**Solution:**
\[
B = 0.2 \, \text{T}
\]
**Explanation:**
The magnetic field around a long, straight wire is inversely proportional to the distance from the wire. Therefore, when the distance increases, the magnetic field decreases proportionally. Given that the magnetic field is \( 1 \, \text{T} \) at a distance \( r \), at a distance \( 5r \), the magnetic field would be \( \frac{1}{5} \) of the original magnetic field, resulting in \( 0.2 \, \text{T} \).
![**Problem Statement:**
A long, straight wire lies on the \( y \) axis and carries a current \( I \) in the positive \( y \) direction. A second parallel wire carries the same current and is positioned such that it intersects the \( x \) axis at \( x = 3.0 \, \text{m} \). Where on the \( x \) axis is the magnetic field zero?
**Instructions:**
Express your answer with the appropriate units.
**Response Box:**
- **\( x = \)** [Value] [Units]
**Explanation:**
This problem involves finding the point along the \( x \) axis where the magnetic field generated by the two parallel wires cancels out, resulting in a net magnetic field of zero. The two wires, carrying equal currents in the same direction, create magnetic fields that interact. The location on the \( x \) axis where the fields cancel depends on the relative distances between the observation point and each wire.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a931645-54a1-474a-bda2-4c874edd548a%2F6e6cddc2-3575-418f-b37d-67410082a432%2Foad8wpf_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A long, straight wire lies on the \( y \) axis and carries a current \( I \) in the positive \( y \) direction. A second parallel wire carries the same current and is positioned such that it intersects the \( x \) axis at \( x = 3.0 \, \text{m} \). Where on the \( x \) axis is the magnetic field zero?
**Instructions:**
Express your answer with the appropriate units.
**Response Box:**
- **\( x = \)** [Value] [Units]
**Explanation:**
This problem involves finding the point along the \( x \) axis where the magnetic field generated by the two parallel wires cancels out, resulting in a net magnetic field of zero. The two wires, carrying equal currents in the same direction, create magnetic fields that interact. The location on the \( x \) axis where the fields cancel depends on the relative distances between the observation point and each wire.
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