Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

Answers without the blur.

Just sign up for free and you're in.

Short Answer

In Fig. 28-30, a charged particle enters a uniform magnetic field with speed $v_{0}$ , moves through a halfcirclein time $T_{0}$ , and then leaves the field
. (a) Is the charge positive or negative?
(b) Is the final speed of the particle greater than, less than, or equal to $v_{0}$ ?
(c) If the initial speed had been $0.5 v_{0}$ , would the time spent in field have been greater than, less than, or equal to $T_{0}$ ?
(d) Would the path have been ahalf-circle, more than a half-circle, or less than a half-circle?

The charge on the particle is negative.
The final speed of the particle is equal to $v_{0} .$
If the initial speed is $0.5 v_{0}$ , then the time spent in the magnetic field $\vec{B}$ is equal to $T_{0} .$
The path would have been a half circle.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Determine the formula for the radius

Consider the formula for the radius of the charge as:

$r = \frac{mv}{| q | B}$

Here, r is radius, B is magnetic field, v is velocity, m is mass,q is charge on particle

Step 2: (a) Determine the charge on the particle

The charge on the particle:

In order to get the force on the particle downwardaccording to the right hand rule, the charge on the particle must be negative.

Hence, the charge on the particle is negative.

Step 3: (b) Determinewhether the final speed of the particle is greater than, less than, or equal to v0

The final speed of the particle greater than, less than, or equal to $v_{0}$ :

Magnetic field does not do any work on the charge particle. It only changes the direction of velocity in magnetic field region.

Hence, the speed of the particle does not change.

Hence, its final speed is the same as the initial speed.

Step 4: (c) Determine if the initial speed is 0.5v0 , then whether the time spent in the magnetic field B→ is greater than, less than, or equal to T0

If the initial speed is $0.5 v_{0}$ , then whether the time spent in the magnetic field $\vec{B}$ is greater than, less than, or equal to $T_{0}$ :

$r = \frac{m v}{| q | B}$

If velocity is $\frac{1}{2} v_{0},$ then using the above relation,

$r = \frac{1}{2} (\frac{m v}{q B})$

Hence, radius will get halved.

Consider the formula:

$T = \frac{2 π r}{v}$

Since the speed is halved and the radius is halved, the period will not change. It will be the same as the initial time $T_{0} .$

Hence, if the initial speed is $0.5 v_{0}$ , then the time spent in the magnetic field $\vec{B}$ is equal to $T_{0} .$

Step 5: (d) Determinewhether the path would have been a half circle, more than half circle, or less than a half circle

Path is half circle, more than half circle, or less than a half circle:

The path will be half circle. Speed does not change the direction; only the magnetic force changes the direction.

Hence, the path would have been a half circle.

Therefore, use the right hand rule to find the force on the particle and usethe relation of radius and magnetic field to find the radius of different particles.

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Determine the formula for the radius

Step 2: (a) Determine the charge on the particle

Step 3: (b) Determinewhether the final speed of the particle is greater than, less than, or equal to v0

Step 4: (c) Determine if the initial speed is 0.5v0 , then whether the time spent in the magnetic field B→ is greater than, less than, or equal to T0

Step 5: (d) Determinewhether the path would have been a half circle, more than half circle, or less than a half circle

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Determine the formula for the radius

Step 2: (a) Determine the charge on the particle

Step 3: (b) Determinewhether the final speed of the particle is greater than, less than, or equal to v0

Step 4: (c) Determine if the initial speed is 0.5v0 , then whether the time spent in the magnetic field B→ is greater than, less than, or equal to T0

Step 5: (d) Determinewhether the path would have been a half circle, more than half circle, or less than a half circle

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics