Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

A particle of charge q moves in a circle of radius r with speed v. Treating the circular path as a current loop with an average current, find the maximum torque exerted on the loop by a uniform field of magnitude B.

The maximum torque exerted on the loop by a magnetic field is $τ_{m a x} = \frac{1}{2} q v r B$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given

Radius of a circle is r.

The charge on particle q.

The speed of particle is v.

The magnitude of magnetic field is B.

Step 2: Understanding the concept

Here, we need to use the equations of torque exerted on a current loop by a magnetic field. For the maximum torque, we can consider .

Formulae:

$τ = N i A B sin θ i = \frac{q}{T} T = \frac{2 π r}{v} A = π r^{2}$

Step 3: Calculate the maximum torque exerted on the loop by a magnetic field.

We have the equation for torque exerted on the current loop as

$τ = N i A B sin θ$

For the maximum torque, $s i n θ$ should be maximum, so consider . Here we are also considering the current loop of moving charge, so N=1.

$τ_{m a x} = i A B$

Now, the current due to the moving charge can be expressed as

$i = \frac{q}{T}$

But we have the equation of period in terms of velocity as

$T = \frac{2 π r}{v}$

So, the equation for current will become

$i = \frac{q v}{2 π r}$

Also, the area of cross-section is

$A = π r^{2}$

Substituting the equation of current and area in the equation of maximum torque, we get,

$\begin{matrix} τ_{m a x} = \frac{q v}{2 π r} \times π r^{2} \\ τ_{m a x} = \frac{1}{2} q v r B \end{matrix}$

Hence, the maximum torque exerted on the loop by a magnetic field is $τ_{m a x} = \frac{1}{2} q v r B$

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Fundamentals Of Physics

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Short Answer

A particle of charge q moves in a circle of radius r with speed v. Treating the circular path as a current loop with an average current, find the maximum torque exerted on the loop by a uniform field of magnitude B.

Step by Step Solution

Step 1: Given

Step 2: Understanding the concept

Step 3: Calculate the maximum torque exerted on the loop by a magnetic field.

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Fundamentals Of Physics

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Short Answer

A particle of charge q moves in a circle of radius r with speed v. Treating the circular path as a current loop with an average current, find the maximum torque exerted on the loop by a uniform field of magnitude B.

Step by Step Solution

Step 1: Given

Step 2: Understanding the concept

Step 3: Calculate the maximum torque exerted on the loop by a magnetic field.

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