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In a situation like that shown in Fig. 27.18, the charged particle is a proton (q = 1.60 × 10-¹9 C, m = 1.67 × 10-27 kg) and the uniform, 0.500-T magnetic field is directed along the x-axis. At t = 0 the proton has velocity components u, = 1.50 x 10³ m/s, U₁ = 0, and U₂ = 2.00 x 10 m/s. Only the magnetic force acts on the proton. (a) At t = 0, find the force on the proton and its acceleration. (b) Find the radius of the resulting helical path, the angular speed of the proton, and the pitch of the helix (the distance traveled along the helix axis per revolution).

In a situation like that shown in Fig. 27.18, the charged particle is a proton (q = 1.60 × 10-¹9 C, m = 1.67 × 10-27 kg) and the uniform, 0.500-T magnetic field is directed along the x-axis. At t = 0 the proton has velocity components u, = 1.50 x 10³ m/s, U₁ = 0, and U₂ = 2.00 x 10 m/s. Only the magnetic force acts on the proton. (a) At t = 0, find the force on the proton and its acceleration. (b) Find the radius of the resulting helical path, the angular speed of the proton, and the pitch of the helix (the distance traveled along the helix axis per revolution).

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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EXAMPLE 27.4 HELICAL PARTICLE MOTION IN A MAGNETIC FIELD In a situation like that shown in Fig. 27.18, the charged particle is a proton x = 1.60 × 10-¹⁹ C, m = 1.67 × 10-27 kg) and the uniform, 0.500-T magnetic field is directed along the x-axis. At t = 0 the proton has velocity components u = 1.50 x 105 m/s, Uy = 0, and v₂ = 2.00 x 10 m/s. Only the magnetic force acts on the proton. (a) At t = 0, find the force on the proton and its acceleration. (b) Find the radius of the resulting helical path, the angular speed of the proton, and the pitch of the helix (the distance traveled along the helix axis per revolution).
Transcribed Image Text:EXAMPLE 27.4 HELICAL PARTICLE MOTION IN A MAGNETIC FIELD In a situation like that shown in Fig. 27.18, the charged particle is a proton x = 1.60 × 10-¹⁹ C, m = 1.67 × 10-27 kg) and the uniform, 0.500-T magnetic field is directed along the x-axis. At t = 0 the proton has velocity components u = 1.50 x 105 m/s, Uy = 0, and v₂ = 2.00 x 10 m/s. Only the magnetic force acts on the proton. (a) At t = 0, find the force on the proton and its acceleration. (b) Find the radius of the resulting helical path, the angular speed of the proton, and the pitch of the helix (the distance traveled along the helix axis per revolution).
This particle's motion has components both parallel (v₁) and perpendicular (v₁) to the magnetic field, so it moves in a helical path. X
Transcribed Image Text:This particle's motion has components both parallel (v₁) and perpendicular (v₁) to the magnetic field, so it moves in a helical path. X
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