3Motion of a charged particle in the magnetic field

What does “the whole picture” mean?
A bubble chamber image of the tracks of subatomic
particles. The tracks curve because the charged
particles are affected by the presence of a magnetic field.

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To investigate the effect of a magnetic field on moving charged particles;

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An electron beam tube (Figure) can be used to demonstrate the magnetic force on a moving charge. A beam of electrons is produced by an ‘electron gun’, and magnets or electromagnets are used to apply a magnetic field.

The deflection tube uses an electron gun to inject electrons into a region of nearly uniform magnetic field perpendicular to the beam. In this region a magnetic field acts on the charge, producing a uniform acceleration in the direction perpendicular to the magnetic field and to the velocity of the electrons. Each electron experiences an acceleration that is always at right angles to its velocity.

The factors that determine the size of the force on a moving charge in a uniform magnetic field. It will depend on:
■■ the magnetic flux density B (strength of the
magnetic field)
■■ the charge Q on the particle
■■ the speed v of the particle.

The magnetic force F on a moving particle at right angles to a magnetic field is given by the equation:
F = Bqv
The direction of the force can be determined from Fleming’s left-hand rule. The force F is always at 90° to the velocity of the particle. Consequently, the path described by the particle will be an arc of a circle.

Suppose we have such a particle with a charge q, moving at a speed v, at right angles to a magnetic field of flux density B. In a time t, the charge will move a distance L = v∙t and is equivalent to a current I = q / t.
Force on the current
F = BIL = B ∙ q / t ∙ v ∙ t = Bqv
If the field and current are at an angle q, then the formula will be modified to F = Bqv sinϑ

The force F is always at right angles to the particle’s velocity v, and its direction can be found using the Fleming’s left-hand rule.

WHITEBOARD ACTIVITY

1. What is the direction of the magnetic force on a positive charge that moves as shown in each of the six cases shown below:

(a) Left (West)
(b) Into the page
(c) Up (North)
(d) No force
(e) Right (East)
(f) Down (South)

2. What is the maximum force on an aluminum rod with a  charge that you pass between the poles of a 1.50 T permanent magnet at a speed of 5.00 m/s? In what direction is the force?

F = 7.50∙10-7 N
Perpendicular to both the magnetic field lines and the velocity

What has been learned
What remained unclear
What is necessary to work on