a electron = m/s 2 in the -- direction -- positive z-direction negative z-direct

Question

aelectron =  m/s2 in the  -- direction -- positive z-direction negative z-direction negative y-direction positive x-direction negative x-direction positive y-direction

Example 19.2 A Proton Moving in a Magnetic Field Goal Calculate the magnetic force and acceleration when a particle moves at an angle other than ninety degrees to the field.

Problem A proton moves at 8.30 106 m/s along the x-axis. It enters a region in which there is a magnetic field of magnitude 2.80 T, directed at an angle of 60.0° with the x-axis and lying in the xy-plane (Fig 19.8).

(a) Find the initial magnitude and direction of the magnetic force on the proton.

(b) Calculate the proton's initial acceleration.

Strategy Finding the magnitude and direction of the magnetic force requires substituting values into the equation for magnetic force, Equation 19.1, and using the right-hand rule. Applying Newton's second law solves part (b).
Figure 19.8 The magnetic force on a proton is in the positive z-direction when and lie in the xy-plane. Solution (a) Find the magnitude and direction of the magnetic force on the proton. Substitute v = 8.30 106 m/s, the magnetic field strength B = 2.80 T, the angle, and the charge of a proton into Equation 19.1. F = qvB sin
F = (1.60 10-19 C)(8.30 106 m/s)(2.80 T)(sin 60°)
F =  N Apply the right-hand rule number 1 to find the initial direction of the magnetic force. Point the fingers of the right hand in the x-direction (the direction of ), and then curl them towards . The thumb points  -- direction -- upwards, in the positive z-direction. to the right, in the positive x-direction. backwards, in the negative y-direction. forwards, in the positive y-direction. to the left, in the negative x-direction. downwards, in the negative z-direction. . (b) Calculate the proton's initial acceleration. Substitute the force and the mass of a proton into Newton's second law. ma = F (1.67 10-27 kg)a = F
a =  m/s2
Remarks The initial acceleration is also in the positive z-direction. Because the direction of changes, however, the subsequent direction of the magnetic force also changes. In applying right-hand rule number 1 to find the direction, it was important to take into consideration the charge. A negatively charged particle accelerates in the opposite direction.

Explanation / Answer

acceleration = F/m
   = qvB sin /me
   = 3.22x10-12/9.11x10-31
   = 3.53x1018 m/s2
direction -- positive z-direction

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