Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

Question: In Fig 29-55, two long straight wires (shown in cross section) carry currents $i_{1} = 30.0 mA$ and $i_{1} = 40.0 mA$ directly out of the page. They are equal distances from the origin, where they set up a magnetic field. To what value must current $i_{1}$ be changed in order to rotate $20.0 °$ clockwise?

The value of current $i_{1}$ is $i_{1} = 61.3 m A$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given

i) Currents flowing through the two long straight wires are $i_{1} = 30.0 m A$ and $i_{2} = 40.0 m A$

ii) The rotation of net magnetic field $\vec{B}$ is $θ = 20.0 °$ .

Step 2: Determine the formula for the magnetic field as:

Use the concept of the magnetic force due to current in straight wires and trigonometry.

Formulae:

$B_{s t r a i g h t} = \frac{μ_{0} i}{4 π R}$

$\tan θ = \frac{B_{y}}{B_{x}}$

Step 3: Calculate the value to which current i1 must be changed in order to rotate 20.0° clockwise

The value of current $i_{1}$ :

The magnetic field due to a current in straight wire is

$B_{s t r a i g h t} = \frac{μ_{0} i}{4 π R}$

The distances of the $B_{1}$ and $B_{2}$ are the same; hence they are directly proportional localid="1663143974221" $i_{1}$ and $i_{2}$ respectively.

$B_{1} α i_{1}$ and

$B_{2} α i_{2}$

According to the right hand rule, is going to the y axis and is going along x axis.

The angle of the net field is

$\tan θ = \frac{B_{y}}{B_{x}}$

$\tan θ = \frac{B_{2}}{B_{1}}$

$θ = \tan^{- 1} (\frac{i_{2}}{i_{1}})$

Substitute the values and solve as:

$θ = \tan^{- 1} (\frac{40.0 mA}{30.0 mA})$

$θ = 53.13 °$

In the problem, the net field rotation is

$θ' = θ - 20.0 °$

$θ' = 53.13 ° - 20.0 °$

$θ' = 33.13 °$

The final value of the current is:

$\tan θ' = \frac{i_{2}}{i_{1}}$

$i_{1} = \frac{i_{2}}{\tan θ'}$

Substitute the values and solve as:

$i_{1} = \frac{40.0 mA}{\tan (33.13 °)}$

$i_{1} = 61.3 mA$

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Fundamentals Of Physics

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Short Answer

Step by Step Solution

Step 1: Given

Step 2: Determine the formula for the magnetic field as:

Step 3: Calculate the value to which current i1 must be changed in order to rotate 20.0° clockwise

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Fundamentals Of Physics

Answers without the blur.

Short Answer

Question: In Fig 29-55, two long straight wires (shown in cross section) carry currents i1=30.0 mA and i1=40.0 mA directly out of the page. They are equal distances from the origin, where they set up a magnetic field. To what value must current i1 be changed in order to rotate 20.0° clockwise?

Step by Step Solution

Step 1: Given

Step 2: Determine the formula for the magnetic field as:

Step 3: Calculate the value to which current i1 must be changed in order to rotate 20.0° clockwise

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