Explanation 1) Concept: We use the concept of conservation of mechanical energy and magnetic and centripetal force . We can rearrange the energy conservation equation for velocity. Also from the centripetal force and magnetic force equation, we can write the equation for velocity. Equating these two velocities’ equations and plugging the value of slope from the graph r V 1 2 , we can find the magnetic field. 2) Formulae: i) P . E i + K . E i = P . E f + K . E f ii) F B = q v B iii) F c p = m v 2 r 3) Given: i) Scale on y axis is r s = 3.0 m m ii) Scale on x axis is V s 1 2 = 40.0 V 1 2 iii) Figure 28-38 is the graph of radius vs. potential. 4) Calculations: P . E i + K . E i = P . E f + K . E f Here potential energy is the electrical potential energy. We can write q V i + 1 2 m v i 2 = q V f + 1 2 m v f 2 Initially kinetic energy is zero, and finally potential energy is zero. We can write q V i = 1 2 m v f 2 Rearranging it for velocity, we get v f = 2 q V i m … … … … … . . ( 1 ) The magnetic force provides the centripetal force, so we can write F c p = F B m v f 2 r = q v f B Rearranging for velocity, we get v f = q B r m … … … … ( 2 ) From equation (1) and (2), we can write q B r m = 2 q V i m 1 2 q B m r V i 1 2 = 2 q m 1 2 We can find the slope r V i 1 2 from the graph

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ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

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Magnetic Force

A magnetic force arises when a charged particle or a current-carrying conductor is placed in a magnetic field. It is created because of the movement of the charged particles.

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Chapter 28, Problem 20P

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To find:

Magnitude of magnetic field.

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Chapter 28, Problem 19P

Chapter 28, Problem 21P

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Magnitude of magnetic field.

Solution Summary: The author explains the concept of conservation of mechanical energy and magnetic and centripetal force. Equating these two velocities’ equations and plugging the value of slope from the graph, they can find the magnetic field.

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To find: Magnitude of magnetic field.

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Chapter 28 Solutions

To find:

Magnitude of magnetic field.