1. CfE Higher Unit 2 – Particles and Waves
Magnetic Fields
CfE Higher
Unit 2 – Particles and Waves

2. Learning Intentions
To be able to state a moving charge produces a magnetic field
To be able to describe the force acting on a charged particle in a magnetic field

3. Magnetic Fields
A moving charge produces a magnetic field in addition to its electric field. (An electric charge produces an electric field whether it is moving or still).
If the direction of the current is reversed, the direction of the magnetic field also reverses (as shown above).

4. Magnetic Fields
Therefore, any current carrying conductor such as a wire will produce a magnetic field.
(Interaction of a current carrying wire with magnets can produce a force on the wire. This is the principle behind the operation of an electric motor).

5. Movement of Charge in a Magnetic Field
The direction of a negative charge in a magnetic field can be determined using the RIGHT HAND RULE. The direction of the resultant force is given by the direction of the thumb (thrust).

6. Movement of Charge in a Magnetic Field
If we consider a single charge q moving with constant velocity (v) PERPENDICULAR to a uniform magnetic field (B), as shown.
There will be a force on the moving charge due to this interaction with its own magnetic field with the external magnetic field. The resultant trajectory of this particle is circular motion.

7. Movement of Charge in a Magnetic Field
The magnetic field is acting on the particle from all directions and the resultant force acts perpendicular to the field (has a central force), so this is why it moves in a circle.

8. Movement of Charge in a Magnetic Field
The direction of this force is perpendicular to both B and v. The rule for moving charges is known as the RIGHT HAND RULE for NEGATIVE charges. The direction of the resultant force is given by the direction of the thumb (thrust).

9. Movement of Positive Charges in a Magnetic Field
For positive charges the direction of the force is in the exact opposite direction - since the right hand rule is for negative charges.
If the charge is travelling parallel to the magnetic field, there is no force (the charge must cut across the field lines).
If the particle travels at an angle to the magnetic field , only the component of field strength perpendicular to the velocity will contribute to the force.
The size of the force depends on the charge Q, the magnetic field strength B and the velocity v. B, v and F are all vectors.

10. Particle Accelerators
Particle accelerators use electric and magnetic fields to accelerate charged particles to very high speeds (to produce other particles and/or nuclear reactions).
This acceleration of particles is called ELECTROSTATIC ACCELERATION.

11. Linear Accelerators (LINACS)
LINACS increase the velocity of the charged particle by repeated use of electric fields to increase the kinetic energy of the particle.
The acceleration of the particle takes place between the electrodes (it travels at constant speed inside the electrodes).
The electrodes continually change polarity (alternate) so that the force on the particles is always in the same (forward) direction.

12. LINACS cont…
Since the particle is gaining speed, each electrode is longer than the previous one, giving the same transit time. The particles are kept in the centre by a series of magnets.

13. Cyclotrons
A cyclotron works by using a series of magnets to keep the particles in a circular orbit.
It consists of two hollow shaped 'dees'. A high alternating p.d. is applied across the dees (inside the dees, the electric field is zero).
Each time a particle enters the gap it is accelerated.

14. Cyclotrons
As the speed is increased the radius of the path due to the magnetic field increases as shown i.e. the charged particles follow an increasing spiral path.
Cyclotrons are used in medicine to produce particle beams for radiotherapy.

15. Synchrotrons
A Synchrotron has a single hollow ring of large radius with many magnets positioned around a circumference. The magnets guide the charged particles through the required circular path.
Oscillating electric fields are used to accelerate particles but the synchrotron can repeat the process millions of times.

16. Synchrotrons
The Large Hadron Collider at CERN is an example of a synchrotron. Two beams protons / antiprotons are accelerated in opposite directions until they acquire enough energy.
They are then collided in an experimental area. This is how the fundamental particles of the standard model are detected.