Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

Shows four identical currents i and five Amperian paths (a through e) encircling them. Rank the paths according to the value of $\oint \vec{B} . d \vec{s}$ taken in the directions shown, most positive first.

The ranking of the paths according to the value of $\oint \vec{B} . d \vec{s}$ , the most positive first is $d > a = e > b > c$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given

Figure 29.33

Step 2: Determining the concept.

Using Ampere’s law, find the values $\oint \vec{B} . d \vec{s}$ along each path. Comparing them, rank the paths according to the value $\oint \vec{B} . d \vec{s}$ .

The formula is as follows:

$\oint \vec{B} . d \vec{s} = μ_{0} i_{e n c}$

Where,

$\vec{B}$ = is the magnetic field, $d \vec{s}$ = is the infinitesimal segment of the integration path,

$μ_{0}$ = is the empty's permeability,

$i_{e n c}$ = is the enclosed electric current by the path.

Step 3: Determining the path according to the value of ∮B→.ds→.

According to Ampere’s law,

$\oint \vec{B} . d \vec{s} = μ_{0} i_{e n c}$

From the given figure, it can interpret that,

For path (a),

role="math" localid="1663002871558" $\oint \vec{B} . d \vec{s} = μ_{0} (3 i - i) \oint \vec{B} . d \vec{s} = μ_{0} i$

Hence, the path of (a) is $\oint \vec{B} . d \vec{s} = μ_{0} i$ .

Step 4: Determining the path (b).

For path (b),

$\oint \vec{B} . d \vec{s} = μ_{0} (2 i - i) \oint \vec{B} . d \vec{s} = μ_{0} i$

Hence, the path of (b) is $\oint \vec{B} . d \vec{s} = μ_{0} i$ .

Step 5: Determining the path (c).

For path (c),

$\oint \vec{B} . d \vec{s} = μ_{0} (3 i + i) \oint \vec{B} . d \vec{s} = 4 μ_{0} i$

Hence, the path of (c) is $\oint \vec{B} . d \vec{s} = 4 μ_{0} i$ .

Step 6: Determining the path (d),

For path (d),

$\oint \vec{B} . d \vec{s} = μ_{0} (3 i + i) \oint \vec{B} . d \vec{s} = 4 μ_{0} i$

Hence, the path of (d) is $\oint \vec{B} . d \vec{s} = 4 μ_{0} i$ .

Step 7: Determining the path (e).

For path (e),

$\oint \vec{B} . d \vec{s} = μ_{0} (3 i - i) \oint \vec{B} . d \vec{s} = 2 μ_{0} i$

Hence, the path of (e) is $\oint \vec{B} . d \vec{s} = 2 μ_{0} i$ .

Hence, the ranking of the paths according to the value of $\oint \vec{B} . d \vec{s}$ , the most positive first is $d > a = e > b > c$ .

Ampere’s law gives the relation between magnetic flux and current enclosed by the loop.

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Fundamentals Of Physics

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Short Answer

Shows four identical currents i and five Amperian paths (a through e) encircling them. Rank the paths according to the value of $\oint \vec{B} . d \vec{s}$ taken in the directions shown, most positive first.

Step by Step Solution

Step 1: Given

Step 2: Determining the concept.

Step 3: Determining the path according to the value of ∮B→.ds→.

Step 4: Determining the path (b).

Step 5: Determining the path (c).

Step 6: Determining the path (d),

Step 7: Determining the path (e).

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Shows four identical currents i and five Amperian paths (a through e) encircling them. Rank the paths according to the value of ∮B→.ds→taken in the directions shown, most positive first.

Step by Step Solution

Step 1: Given

Step 2: Determining the concept.

Step 3: Determining the path according to the value of ∮B→.ds→.

Step 4: Determining the path (b).

Step 5: Determining the path (c).

Step 6: Determining the path (d),

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