Introduction
You may wonder why it is important to study charged particles? What use are they to us in everyday life? Well, without charged particles we wouldn’t have an electric current – unthinkable in our technological age. But there are more applications you may not have thought of. Laser printers and photocopiers use charged particles to get the toner to stick to the paper and car companies use charged particles to ensure that spray guns paint cars evenly. The Large Hadron Collider accelerates positively charged protons to 99% the speed of light, then collides them head on to try and recreate the conditions that existed when the Universe was 1/100th of a billionth of a second old. Scientists then study these collisions to try and explain what mass is and what 96% of the universe is made of.
In this section we will study how charged particles move in electric and magnetic fields. We will then study the different types of particle accelerator and their applications.
Force Fields
The idea of a field should be familiar to you. In Physics, a field means a region where an object experiences a force without being touched. For example, there is a gravitational field around the Earth. This attracts masses towards the Earth’s centre. Magnets cause magnetic fields and electric charges have electric fields around them.
Electric Fields
In an electric field, a charged particle will experience a force. We use lines of force to show the strength and direction of the force. The closer the field lines the stronger the force. Field lines are continuous they start on positive charge and finish on negative charge. The direction is taken as the same as the force on a positive “test” charge placed in the field.
Electric fields have a number of applications and play an important role in everyday life. For example,
- the cathode ray tube (the basis for traditional television and monitor systems)
- paint spraying, e.g. for cars
- photocopying and laser printing
- pollution control.
Stray electric fields can also cause problems, for example during lightning storms there is a risk of damage to microchips within electronic devices caused by static electricity.
If an electric field is applied to a conductor it will cause the free electrons in the conductor to move
Electric Field Patterns
These are called radial fields. The lines are like the radii of a circle. The strength of the field decreases as we move away from the charge.
The field lines are equally spaced between the parallel plates. This means the field strength is constant. This is called a uniform field.
Work Done
We have seen already that electric fields are similar to gravitational fields. Consider the following:
If a mass is lifted or dropped through a height then work is done i.e. energy is changed.
If the mass is dropped then the energy will change to kinetic energy.
If the mass is lifted again then the energy will change to gravitational potential energy.
Change in gravitational potential energy = work done
Now consider a negative charge moved through a distance in an electric field
If the charge moves in the direction of the electric force, the energy will appear as kinetic energy. If a positive charge is moved against the direction of the force, as shown in the diagram, the energy will be stored as electric potential energy.
Definition of potential difference and the volt
Potential difference (p.d.) is defined to be a measure of the work done in moving one coulomb of charge between two points in an electric field. Potential difference (p.d.) is often called voltage. This gives the definition of the volt.
There is a potential difference of 1 volt between two points if 1 joule of energy is required to move 1 coulomb of charge between the two points, 1 V = 1 J C−1
This relationship can be written mathematically: Ew = QV
Where Ew is energy (work done) in joules (J), Q is the charge in coulombs (C) and V is the potential difference (p.d.) in volts (V).
If the small positive charge, above, is released there is a transfer of energy to kinetic energy, i.e. the charge moves. Again, using the conservation of energy means that;
Ew = EK
QV = ½mv2
Example: A positive charge of 3.0 µC is moved from A to B. The potential difference between A and B is 2.0 kV.
(a) Calculate the electric potential energy gained by the charge–field system.
(b) The charge is released. Describe the motion of the charge.
(c) Determine the kinetic energy when the charge is at point A.
(d) The mass of the charge is 5.0 mg. Calculate the speed of the charge
(a) Q = 3.0 µC = 3.0 × 10−6 C Ew = QV
V = 2.0 kV = 2.0 × 103 V Ew = 3.0 × 10−6 × 2.0 × 103
Ew = ? Ew = 6.0 × 10−3 J
(b) The electric field is uniform so the charge experiences a constant unbalanced force. The charge accelerates uniformly towards the negative plate A
(c) By conservation of energy, EK = Ew = 6.0 × 10−3 J
(d) m = 5.0 mg = 5.0 × 10−6 kg EK = ½mv2
EK = 6.0 × 10−3 J 6.0 × 10−3 = 0.5 × 5.0 × 10−6 × v2
v = ? v2 = 2.4 × 10−3
. v = 49 m s−1
Charged Particles in Magnetic Fields
The discovery of the interaction between electricity and magnetism, and the resultant ability to produce movement, must rank as one of the most significant developments in physics in terms of the impact on everyday life.
This work was first carried out by Michael Faraday whose work on electromagnetic rotation in 1821 gave us the electric motor. He was also involved in the work which brought electricity into everyday life, with the discovery of the principle of the transformer and generator in 1831. Not everyone could see its potential. William Gladstone (1809–1898), the then Chancellor of the Exchequer and subsequently four-time Prime Minister of Great Britain, challenged Faraday on the practical worth of this new discovery – electricity. Faraday’s response was ‘Why, sir, there is every probability that you will soon be able to tax it!’ The Scottish physicist, James Clark Maxwell (1831–1879), built upon the work of Faraday and wrote down mathematical equations describing the interaction between electric and magnetic fields. The computing revolution of the 20th century could not have happened without an understanding of electromagnetism.
Magnetic Field Around A Current Carrying Wire
In 1820 the Danish physicist Oersted discovered that a magnetic compass was deflected when an electrical current flowed through a nearby wire. This was explained by saying that when a charged particle moves a magnetic field is generated. In other words, a wire with a current flowing through it (a current-carrying wire) creates a magnetic field.
Moving charges experience a force in a magnetic field
A magnetic field surrounds a magnet. When two magnets interact, they attract or repel each other due to the interaction between the magnetic fields surrounding each magnet.
A moving electric charge behaves like a mini-magnet as it creates its own magnetic field. This means it experiences a force if it moves through an external magnetic field (in the same way that a mass experiences a force in a gravitational field or a charge experiences a force in an electric field.)
Simple rules can be used to determine the direction of force on a charged particle in a magnetic field.
Movement of a negative charge in a magnetic field
One common method is known as the right-hand motor rule. This is shown in the figure on the right. The thumb gives the motion (M), the first finger gives the field (F) and the second finger is the direction of electron current (I).
Movement of a positive charge in a magnetic field
For a positive charge, the direction of movement is opposite to the direction worked out above. It is easiest to work out which way a negative charge would move using the right hand rule and then simply reverse this.
If a charge travels parallel to the magnetic field, it will not experience an additional force. The direction of the force is determined using the same right hand rule. The speed of the charge will not change, only the direction of motion changes.
Electron curves out of the page Electron curves to the right No change in direction
The Electric Motor
When a current-carrying wire is placed between the poles of a permanent magnet, it experiences a force. The direction of the force is at right-angles to:
- the direction of the current in the wire;
- the direction of the magnetic field of the permanent magnet
We can utilize this principle in the electric motor;
An electric motor must spin continuously in the same direction. Whichever side of the coil is nearest the north pole of the field magnets above must always experience an upwards force if the coil is to turn clockwise.
That side of the coil must therefore always be connected to the negative terminal of the power supply. Once the coil reaches the vertical position the ends of the coil must be connected to the opposite terminals of the power supply to keep the coil turning. This is done by split ring commutator.
In order for the coil to spin freely there cannot be permanent fixed connections between the supply and the split ring commutator. Brushes rub against the split ring commutator ensuring that a good conducting path exists between the power supply and the coil regardless of the position of the coil.
Particle Accelerators
Particle accelerators are used to probe matter. They have been used to determine the structure of matter and investigate the conditions soon after the Big Bang. Particle accelerators are also used produce a range of electromagnetic radiations which can be used in many other experiments.
There are three main types of particle accelerators:
- linear accelerators
- cyclotrons
- synchrotrons
Regardless of whether the particle accelerator is linear or circular, the basic parts are the same:
- a source of particles (these may come from another accelerator)
Accelerators using electrons use thermionic emission in the same way as a cathode ray tube. At the Large Hadron Collider (LHC) at CERN the source of particles is simply a bottle of hydrogen gas. Electrons are stripped from the hydrogen atoms leaving positively charged protons. These are then passed through several smaller accelerator rings before they reach the main beam pipe of the LHC.
- beam pipes (also called the vacuum chamber)
Beam pipes are special pipes which the particles travel through while being accelerated. Inside is a vacuum to ensure that the particles do not collide with other atoms such as air molecules.
- accelerating structures (a method of accelerating the particles)
In the beam pipes there are special accelerating regions where there is a rapidly changing electric field. At the LHC, as protons approach the accelerating region, the electric field is negative and the protons accelerate towards it. As they move through the accelerator, the electric field becomes positive and the protons are repelled. The protons increase their kinetic energy and are accelerated to almost the speed of light.
- a system of magnets (electromagnets or superconducting magnets as in the LHC)
Newton’s first law states that an object travels with a constant velocity (both speed and direction) unless acted on by an external force. The particles in the beam pipes would go in a straight line if they were not constantly going past powerful, fixed magnets which cause them to travel in a circle. There are over 9000 superconducting magnets at the LHC in CERN. These operate best at temperatures very close to zero Kelvin and this is why the whole machine needs to be cooled down. If superconducting magnets were not used, they would not be able to steer and focus the beam within such a tight circle and so the energies of the protons which are collided would be much lower.
- a target
In some accelerators the beam collides directly with a stationary target, such as a metal block. In this method, much of the beam energy is simply transferred to the block instead of creating new particles. In the LHC, the target is an identical bunch of particles travelling in the opposite direction. The two beams are brought together at four special points on the ring where massive detectors are used to analyse the collisions.
Cyclotron
