Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

A magnetic field forces an electron to move in a circle with radial acceleration $3.0 \times 10^{14} m / s^{2}$ in a particular magnetic field. (a) What is the speed of the electron if the radius of its circular path is $15 cm$ ? (b)What is the period of the motion?

a) Speed of the electron is $6.7 \times 10^{6} m / s$ .

b) Period of motion is $1.4 \times 10^{- 7} s$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given

1) Radial acceleration, $a = 3 \times 10^{14} m / s^{2}$

2) Radius of the circular path,

$r = 15 cm = 0.15 m$

Step 2: Understanding the concept of centripetal acceleration

The centripetal acceleration of the object depends on the velocity and radius of the orbit. Using the equation of centripetal acceleration, we can calculate the speed of an electron moving in a circular direction. Using the value of the speed of an electron and the equation of period, we can find the period of motion of an electron.

Formula:

$a = \frac{V^{2}}{r}$ …(i)

$T = \frac{2 π r}{V}$ …(ii)

Step 3: (a) Calculate the speed of the electron if the radius of its circular path is 15cm

From equation (i), we can write,

$a = \frac{V^{2}}{r}$

By rearranging this equation, we get,

$v = \sqrt{a r} = \sqrt{3 \times 10^{14} m / s^{2} \times 0.15 m} = 6.7 \times 10^{6} m / s$

Therefore, the speed of electron is $6.7 \times 10^{6} m / s$ .

Step 4: (b) Calculate the period of the motion

From equation (ii), we can write

$T = \frac{2 π r}{V}$

Substitute the value of given radius and speed calculated in part (a), we get

$T = \frac{2 π \times 0.15 m}{6.7 \times 10^{6} m / s} = 1.4 \times 10^{- 7} s$

Therefore, the time period of rotation of electron is $1.4 \times 10^{- 7} s$ .

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Fundamentals Of Physics

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Short Answer

A magnetic field forces an electron to move in a circle with radial acceleration $3.0 \times 10^{14} m / s^{2}$ in a particular magnetic field. (a) What is the speed of the electron if the radius of its circular path is $15 cm$ ? (b)What is the period of the motion?

Step by Step Solution

Step 1: Given

Step 2: Understanding the concept of centripetal acceleration

Step 3: (a) Calculate the speed of the electron if the radius of its circular path is 15cm

Step 4: (b) Calculate the period of the motion

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A magnetic field forces an electron to move in a circle with radial acceleration 3.0×1014m/s2 in a particular magnetic field. (a) What is the speed of the electron if the radius of its circular path is 15cm? (b)What is the period of the motion?

Step by Step Solution

Step 1: Given

Step 2: Understanding the concept of centripetal acceleration

Step 3: (a) Calculate the speed of the electron if the radius of its circular path is 15cm

Step 4: (b) Calculate the period of the motion

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A magnetic field forces an electron to move in a circle with radial acceleration $3.0 \times 10^{14} m / s^{2}$ in a particular magnetic field. (a) What is the speed of the electron if the radius of its circular path is $15 cm$ ? (b)What is the period of the motion?