Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

A long wire carrying 100A is perpendicular to the magnetic field lines of a uniform magnetic field of magnitude 5.0 mT. At what distance from the wire is the net magnetic field equal to zero?

Point on the line parallel to the wire at a distance $r = 4.0 \times 10^{- 3} m$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given

$B_{e x t} = 5.0 \times 10^{- 3} T$ , the field lines are perpendicular to the wire i=100A.

Step 2: Understanding the concept

We can use the equation for the field produced by the long current-carrying wire at a point away from the wire. The distance should be such that the field produced by the wire is exactly the same as the given field.

Formula:

Magnetic field due to a long straight wire at distance r from the wire carrying current i

$B_{r} = \frac{μ_{0} i}{2 π r}$

Step 3: Calculate distance from the wire where the net magnetic field is zero

Since the long wire is kept in an external magnetic field, the field due to wire (B_w) and external magnetic field (B_ext) will cancel out when their magnitudes are the same, and the direction is opposite. So, the set points which will satisfy this condition lie on the line parallel to the wire at distance r.

$\begin{matrix} B_{r} = \frac{μ_{0} i}{2 π r} = B_{e x t} \\ r = \frac{μ_{0} i}{2 π B_{e x t}} \\ r = \frac{1.26 \times 10^{- 6} \times 100}{2 \times π \times 5.0 \times 10^{- 3}} \\ r = 4.0 \times 10^{- 3} m \end{matrix}$

Hence, the Point on the line parallel to the wire at a distance $r = 4.0 \times 10^{- 3} m$

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Fundamentals Of Physics

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Short Answer

A long wire carrying 100A is perpendicular to the magnetic field lines of a uniform magnetic field of magnitude 5.0 mT. At what distance from the wire is the net magnetic field equal to zero?

Step by Step Solution

Step 1: Given

Step 2: Understanding the concept

Step 3: Calculate distance from the wire where the net magnetic field is zero

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Fundamentals Of Physics

Answers without the blur.

Short Answer

A long wire carrying 100A is perpendicular to the magnetic field lines of a uniform magnetic field of magnitude 5.0 mT. At what distance from the wire is the net magnetic field equal to zero?

Step by Step Solution

Step 1: Given

Step 2: Understanding the concept

Step 3: Calculate distance from the wire where the net magnetic field is zero

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