MOVING PARTICLES

The world of atomic physics is populated by a great variety of particles – electrons, protons, neutrons, positrons, and many more. Many of these particles are electrically charged, and so their motion is influenced by electric and magnetic fields. Indeed, we use this fact to help us to distinguish one particle from another. Figure 25.1 shows the tracks of particles in a detector called a bubble chamber. A photon (no track) has entered from the top and collided with a proton; the resulting spray of nine particles shows up as the gently curving tracks moving downwards. The tracks curve because the particles are charged and are moving in a magnetic field. The tightly wound spiral tracks are produced by electrons that, because their mass is small, are more dramatically affected by the field.
In this chapter, we will look at how charged particles behave in electric and magnetic fields and how this knowledge can be used to control beams of charged particles. At the end of the chapter, we will look at how this knowledge was used to discover the electron and to measure its charge and mass.

You can use your knowledge of how charged particles and electric currents are affected by fields to interpret diagrams of moving particles. You must always remember that, by convention, the direction of conventional electric current is the direction of flow of positive charge. When electrons are moving, the conventional current is regarded as flowing in the opposite direction.
An electron beam tube (Figure 25.2) can be used to demonstrate the magnetic force on moving charged particles. A beam of electrons is produced by an ‘electron gun’, and magnets or electromagnets are used to apply a magnetic field.

You can use such an arrangement to observe the effect of changing the strength and direction of the magnetic field, and the effect of reversing the field.

If you are able to observe a beam of electrons like this, you should find that the force on the electrons moving through the magnetic field can be predicted using Fleming’s left-hand rule (see Chapter 24). In Figure 25.3, a beam of electrons is moving from right to left, into a region where a magnetic field is directed into the plane of the paper. Since electrons are negatively charged, they represent a conventional current from left to right. Fleming’s left-hand rule predicts that, as the electrons enter the field, the force on them will be upwards and so the beam will be deflected up the page. As the direction of the beam changes, so does the direction of the force. The force due to the magnetic field is always at ${90^ \circ }$ to the velocity of the electrons. It is this force that gives rise to the motor effect. The electrons in a wire experience a force when they flow across a magnetic field, and they transfer the force to the wire itself. In the past, most oscilloscopes, monitors and television sets made use of beams of electrons. The beams were moved about using magnetic and electric fields, and the result was a rapidly changing image on the screen.

PRACTICAL ACTIVITY 25.1

 

Electron beam tubes

Figure 25.4 shows the construction of a typical tube. The electron gun has a heated cathode. The electrons have sufficient thermal energy to be released from the surface of the heated cathode. These electrons form a cloud around the cathode. The positively charged anode attracts these electrons, and they pass through the anode to form a narrow beam in the space beyond. The direction of the beam can be changed using an electric field between two plates (as in Figure 25.4), or a magnetic field created by electromagnetic coils.

Question

 

1) Figure 25.5 shows how radiation from a radioactive material passes through a region of uniform magnetic field.
State and explain whether each type of radiation has positive or negative charge, or is uncharged.

Magnetic force on a moving charged particle

Imagine a charged particle moving in a region of uniform magnetic field, with the particle’s velocity at right angles to the field. We can make an intelligent guess about the factors that determine the size of the force on the particle (Figure 25.6). It will depend on:
- the magnetic flux density B (strength of the magnetic field)
- the charge Q on the particle
- the speed ν 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 ${90^ \circ }$ to the velocity of the particle. Consequently, the path described by the particle will be an arc of a circle.

If the charged particle is moving at an angle $\theta $ to the magnetic field, the component of its velocity at right angles to B is $v\,sin\theta $. Hence, the equation becomes:

$F = BQv\,sin\theta $

where B is the magnetic flux density, Q is the charge on the particle, v is the speed of the particle and $\theta $ is the angle between the magnetic field and the velocity of the particle.

We can show that the two equations $F = BIL$ and $F = BQv$ are consistent with one another, as follows.
Since current I is the rate of flow of charge, we can write:

$I = \frac{Q}{t}$

Substituting in $F = BIL$ gives:

$F = \frac{{BQL}}{t}$

Now, $\frac{l}{t}$ is the speed ν of the moving particle, so we can write:

$F = BQv$

For an electron, with a charge of $−e$, the magnitude of the force is:

$F = Bev\,(e = 1.60 \times {10^{ - 19}}C)$

The force on a moving charged particle is sometimes called the ‘Bev force’; it is this force acting on all the electrons in a wire that gives rise to the ‘BIL force’.
Here is an important reminder: the force F is always at right angles to the particle’s velocity v, and its direction can be found using Fleming’s left-hand rule (Figure 25.7).