(a) Explanation Given Info: The particle is negatively charged. The mass ( m ) of the particle is 2.58 × 10 − 15 kg . The uniform magnetic field ( B → ) of the region is − ( 0.120 T ) k ^ . The velocity ( v → ) of the particle at particular instant is ( 1.05 × 10 6 m / s ) ( − 3 i ^ + 4 j ^ + 12 k ^ ) . The force ( F → ) exerted on particle is 2.45 N . Formula to calculate the force exerted is, F → = q v → × B → q is the charge of the particle, v → is the velocity of the particle, and B → is the uniform magnetic field of the region through which the particle moves. Substitute ( 1.05 × 10 6 m / s ) ( − 3 i ^ + 4 j ^ + 12 k ^ ) for v → , − ( 0.120 T ) k ^ for B → , and 2.45 N for F → . 2.45 N = q [ ( ( 1.05 × 10 6 m / s ) ( − 3 i ^ + 4 j ^ + 12 k ^ ) ) × ( − ( 0.120 T ) k ^ ) ] = q [ [ ( − 3.15 × 10 6 m / s ) i ^ + ( 4.20 × 10 6 m / s ) j ^ + ( 12.60 × 10 6 m / s ) k ^ ] × ( − ( 0.120 T ) k ^ ) ] = q [ 3.780 × 10 5 ( i ^ × k ^ ) − 5.04 × 10 5 ( j ^ × k ^ ) − 15.12 × 10 5 ( k ^ × k ^ ) ] m ⋅ T / s Substitute − j ^ for ( i ^ × k ^ ) , i ^ for ( j ^ × k ^ ) , and 0 for ( k ^ × k ^ ) (b) To determine The acceleration of the particle. (c) To determine To explain: The reason for the path of particle to be helix, and to calculate the radius of circular component of the helical path. (d) To determine The cyclotron frequency of the charged particle. (e) To determine The co-ordinates of x , y , and z for time t = 2 T .

Sears And Zemansky's University Physics With Modern Physics

13th Edition

ISBN: 9780321897961

Author: YOUNG, Hugh D./

Publisher: Pearson College Div

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Question

Chapter 27, Problem 63E

(a)

To determine

The charge of the particle.

(b)

To determine

The acceleration of the particle.

(c)

To determine

To explain: The reason for the path of particle to be helix, and to calculate the radius of circular component of the helical path.

(d)

To determine

The cyclotron frequency of the charged particle.

(e)

To determine

The co-ordinates of x, y, and z for time t=2T.

Expert Solution & Answer

Chapter 27 Solutions

Sears And Zemansky's University Physics With Modern Physics

Ch. 27 - Prob. 1DQ Ch. 27 - Prob. 2DQ Ch. 27 - Prob. 3DQ Ch. 27 - Prob. 4DQ Ch. 27 - Prob. 5DQ Ch. 27 - Prob. 6DQ Ch. 27 - Prob. 7DQ Ch. 27 - Prob. 8DQ Ch. 27 - Prob. 9DQ Ch. 27 - Prob. 10DQ

Ch. 27 - Prob. 11DQ Ch. 27 - Prob. 12DQ Ch. 27 - Prob. 13DQ Ch. 27 - Prob. 14DQ Ch. 27 - Prob. 15DQ Ch. 27 - Prob. 16DQ Ch. 27 - Prob. 17DQ Ch. 27 - Prob. 18DQ Ch. 27 - Prob. 19DQ Ch. 27 - Prob. 20DQ Ch. 27 - Prob. 1E Ch. 27 - Prob. 2E Ch. 27 - Prob. 3E Ch. 27 - Prob. 4E Ch. 27 - Prob. 5E Ch. 27 - Prob. 6E Ch. 27 - Prob. 7E Ch. 27 - Prob. 8E Ch. 27 - Prob. 9E Ch. 27 - Prob. 10E Ch. 27 - Prob. 11E Ch. 27 - Prob. 12E Ch. 27 - Prob. 13E Ch. 27 - Prob. 14E Ch. 27 - Prob. 15E Ch. 27 - Prob. 16E Ch. 27 - Prob. 17E Ch. 27 - Prob. 18E Ch. 27 - Prob. 19E Ch. 27 - Prob. 20E Ch. 27 - Prob. 21E Ch. 27 - Prob. 22E Ch. 27 - Prob. 23E Ch. 27 - Prob. 24E Ch. 27 - Prob. 25E Ch. 27 - Prob. 26E Ch. 27 - Prob. 27E Ch. 27 - Prob. 28E Ch. 27 - Prob. 29E Ch. 27 - Prob. 30E Ch. 27 - Prob. 31E Ch. 27 - Prob. 32E Ch. 27 - Prob. 33E Ch. 27 - Prob. 34E Ch. 27 - Prob. 35E Ch. 27 - Prob. 36E Ch. 27 - Prob. 37E Ch. 27 - Prob. 38E Ch. 27 - Prob. 39E Ch. 27 - Prob. 40E Ch. 27 - Prob. 41E Ch. 27 - Prob. 42E Ch. 27 - Prob. 43E Ch. 27 - Prob. 44E Ch. 27 - Prob. 45E Ch. 27 - Prob. 46E Ch. 27 - Prob. 47E Ch. 27 - Prob. 48E Ch. 27 - Prob. 49E Ch. 27 - Prob. 50E Ch. 27 - Prob. 51E Ch. 27 - Prob. 52E Ch. 27 - Prob. 53E Ch. 27 - Prob. 54E Ch. 27 - Prob. 55E Ch. 27 - Prob. 56E Ch. 27 - Prob. 57E Ch. 27 - Prob. 58E Ch. 27 - Prob. 59E Ch. 27 - Prob. 60E Ch. 27 - Prob. 61E Ch. 27 - Prob. 62E Ch. 27 - Prob. 63E Ch. 27 - Prob. 64E Ch. 27 - Prob. 65E Ch. 27 - Prob. 66E Ch. 27 - Prob. 67E Ch. 27 - Prob. 68E Ch. 27 - Prob. 69E Ch. 27 - Prob. 70E Ch. 27 - Prob. 71E Ch. 27 - Prob. 72E Ch. 27 - Prob. 73E Ch. 27 - Prob. 74E Ch. 27 - Prob. 75E Ch. 27 - Prob. 76E Ch. 27 - Prob. 77E Ch. 27 - Prob. 78E Ch. 27 - Prob. 79E Ch. 27 - Prob. 80E Ch. 27 - Prob. 81E Ch. 27 - Prob. 82E Ch. 27 - Prob. 83E Ch. 27 - Prob. 84E Ch. 27 - Prob. 85E Ch. 27 - Prob. 86E Ch. 27 - Prob. 87E Ch. 27 - Prob. 88E Ch. 27 - Prob. 89E Ch. 27 - Prob. 90E Ch. 27 - Prob. 91E

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