### 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.

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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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Concept explainers

Magnetic Field Of Coaxial Cable

The word coaxial means same axis. So for a long straight cable to be coaxial, it must have concentric cylindrical shaped conductor around it. Coaxial cable (popularly called ‘coax’) has various applications ranging from current conductors to radiofrequency signal transmitters. This cable has lower emission losses and provides protection from electromagnetic interference which allows signals with less power to transmit over longer distances.For example, currents produced in the pickup of a stereo turntable generally travel to the amplifier through a coaxial cable.The self-inductance of a coaxial cable is another important characteristic, because it influences the propagation of electrical signals in the cable.

Question

### 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.

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