1. CfE Higher Physics Particles and Waves
“Anyone who is not shocked by the quantum theory has not understood it.“ N.Bohr

2. Forces on Charged Particles
Key Areas
Key Area –
Forces on Charged Particles
Electric fields around charged particles and between charged parallel plates
Movement of charged particles in an electric field
Voltage, Potential Difference, Work and Charge
Movement of charged particles in a magnetic field
Particle accelerators
Electrostatic precipitators and electrostatic propulsion

3. Learning Intentions State what is meant by an electric field.
Compare and contrast electric and gravitational fields.
Describe the electric field pattern around positive and negative point charges.
Carry out calculations using Coulomb’s Law to find the force between charged particles.
Describe the electric field pattern around pairs of point charges.

4. What will happen with these charges?
Summarise this in one sentence...
Opposite charges attract each other and like charges repel each other.

5. Forces on Charged Particles
You will have previously learned about gravitational fields around planets.
A gravitational field is a region in which a mass experiences a force.
An electric field is a region in which a charge experiences a force.

6. Comparing Gravitational and Electric Fields
In many ways, the gravitational field of a planet is very similar to the electric field of a point charge.
Both fields have the same shape with lines of force (field lines) radiating outwards.

7. Comparing Gravitational and Electric Fields
The main difference between these 2 fields is that gravitational forces can only attract masses whereas electric fields can attract or repel charges.

8. Comparing Gravitational and Electric Fields
We can compare the way in which the strengths of these fields decrease with distance:
They have a very similar mathematical basis!

9. Forces on Charged Particles
This is Newton’s Law of Universal Gravitation which we have already met:
This is Coulomb’s Law for point charges:

10. Forces on Charged Particles
These formulae are very similar...
These parts look very similar!
These parts are both constants!
Re-writing these equations...

11. Forces on Charged Particles
Coulomb’s Law for point charges:
F = Force (N)
Q1 = Charge 1 (C)
Q2 = Charge 2 (C)
Ɛ0 = Permittivity of free space (8.85 x Fm-1)
r = distance (m) r Q1 Q2 F F

12. Example
An electron is placed 2.45 mm away from a 4.25 x C negatively charged plastic sphere in a vacuum. Calculate the size of the repulsive force experienced by the electron.

13. Forces on Charged Particles
So a charged particle experiences a force as a result of the electric field of another charged particle.
The direction of this force depend on the polarity of the charges (positive or negative).
The magnitude of this force depends on the size of both charges and the distance between them.

14. Electric Field around Point Charges
The pattern of electric field lines around a point charge is altered by the presence of another charge. The fields on the 2 particles combine:

15. Learning Intentions
Describe the use of static electric charge in each of the following applications:
Xerography
Paint Spraying
Electrostatic Precipitators
Describe some of the risks and dangers associated with static electricity.

16. Static Electricity - Xerography

17. Static Electricity – Paint Spraying

18. Static Electricity –Electrostatic Precipitator

19. Static Electricity and Electronics
Voltages that cannot be perceived by humans can damage microchips and computer processors.
For this reason electronic engineers need to wear an anti-static wrist strap to earth themselves before working.

20. Danger of Static Electricity
When 2 substances or materials move against one another, a static charge can develop.
This static charge will be larger if the speed of movement increases.
If the potential difference between one object another gets high enough, charges can jump causing a spark which can cause an electric shock or a fire.

21. Danger of Static Electricity
Earth rods are connected to the base of wind turbines to prevent engineers from getting fatal static shocks.
An aircraft needs to be earthed before being re-fuelled to prevent an explosion.

22. Danger of Static Electricity
Lightning occurs when there is a separation of static charge within a cloud or between a cloud and the ground.
For reasons not fully understood, a channel of air becomes ionized and conducts electric charge in a lightning strike.
The temperature of a bolt may exceed 50,000 K!

23. Learning Intentions
Describe the electric field pattern between 2 charged parallel metal plates.
Describe and explain the movement of charged particles in an electric field.
Describe how an inkjet printer works.
Describe how a parallel plate particle accelerator works.
State the definition of the volt.
Calculate the velocity of a charged particle using the principle of conservation of energy and the work done by the electric field in a particle accelerator.
Explain why charges projected into an electric field follow a parabolic path.
Describe how a CRO works.

24. Electric Field between Charged Parallel Metal Plates
The electric field lines between 2 charged metal plates are parallel and show the direction in which a positive charge would accelerate:
Positively Charged Metal Plate
Electric Field Lines
Negatively Charged Metal Plate

25. Electric Field between Charged Parallel Metal Plates
The accelerating force experienced by a charge between 2 parallel charged plates is constant.
As the particle moves away from one plate, the repulsive force gets weaker, but as it gets closer to the other the attractive force gets stronger.

26. Force on Charged Particles between Parallel Plates
When a charged particle is placed or projected between 2 charged parallel plates, it will accelerate parallel to the electric field lines: + + -

27. The Inkjet Printer

28. Parallel Plate Accelerator
Electrons, for example, can be accelerated using the following system: - +
What will happen to the electron? e-
As a result of the unbalanced electrostatic force acting on the electron, it will be accelerated to a high velocity before passing through the gap.

29. The Definition of the Volt
When a charge of 1 Coulomb moves across a potential difference of 1 Volt, the work done by the electric field on the charge is 1 Joule.
So, 1 Volt can be defined as “1 Joule per Coulomb”.
The work done by the electric field in accelerating a charge is:
The work done in accelerating an electron is:
e = charge of an electron.
e = 1.60 x C V e- - +

30. Calculating the Velocity of the Electron...
The electron is accelerating, so it is gaining kinetic energy.
Using the definition of the volt, the work done by the electric field in accelerating the electron is given by.
By the principle of conservation of energy, the kinetic energy gained by the electron must have come from the work done by the electric field.
We can rearrange this to calculate the velocity of the electron as it leaves the accelerator.

31. Example: Calculating the velocity of the electron...
Calculate the velocity of an electron which is accelerated by
a potential difference of 150 V.
The kinetic energy gained by the electron is given by:
Ek = ½mv2
The work done on the electron is given by:
Ew = QV Q = e = 1.60 x C and V = 150 V
So...
Ew = (1.60 x 10-19) x 150
Ew = 2.40 x J
Ew = Ek so Ew = ½mev2
Ew = 2.40 x J and me = 9.11 x kg
Therefore 2.40 x = ½(9.11 x 10-31) v2
Rearranging for v gives:
v = 7260 ms-1 (to 3 s.f.)

32. Parabolic Paths + + + + + + + + + + + + - - - - - - - - - - -
When a charge is projected into an electric field, its motion can be considered as being in 2 separate directions:
Constant velocity perpendicular to the field according to Newton’s first law.
Acceleration parallel to the field.
The combination of these 2 separate motions results in a parabolic path. Does this look familiar? +

33. Parabolic Paths
The deflection of electrons using charged metal plates is used in CROs (Cathode Ray Oscilloscopes).
As a voltage is applied across the metal plates in the evacuated tube, the beam of electrons will move up, down, left or right and the display on the screen will change accordingly.

34. Learning Intentions
State that every moving charge has an associated magnetic field.
Describe the magnetic field pattern around a current-carrying wire.
Describe and explain the movement of a charged particle in a magnetic field.
Describe the following technologies and how they use the effect of magnetic fields on moving charges:
Nuclear fusion reactors.
Cyclotron
Synchrotron
Mass Spectrometer
Define gravitational, electrical and magnetic fields.

35. Magnetic Field around a Current-carrying Conductor
When a wire has an electric current flowing through it, an associated magnetic field is produced.
The direction of the magnetic field can be found using the “Right Hand Grip Rule”.
N.B. The thumb points in the direction of conventional current flow (opposite direction to electron flow).

36. Magnetic Field around a Current-carrying Conductor
The magnetic field around a current carrying conductor can be attracted or repelled by another magnetic field causing the conductor to move/rotate.
This is the principle of an electric motor.

37. Moving Charges
When any electric charge moves, it has a magnetic field associated with it.
This is true even if the charges are not confined to a wire.
This means that moving charges can be steered or directed using magnetic fields.

38. Force Acting on a Moving Charge
A moving charge is deflected when it moves through a magnetic field because a force is acting.
We can use a simple hand-rule to figure out the direction in which this force will act.
We use the left hand for positive charges and the right hand for negative charges.

39. Nuclear Fusion Reactors
The charged particles in a super-heated plasma in a fusion reactor could be contained using a magnetic field.

40. Particle Accelerator - Cyclotron
A cyclotron is a particle accelerator which accelerates charged particles using an electric field.
It uses a magnetic field to deflect the particles into a spiral pathway until they achieve the required speed and exit the accelerator.

41. Cyclotron – Use in Medicine
A cyclotron is used alongside a PET scanner to produce Positron-Emitting Radiopharmaceuticals (PERs).
PERs are drugs that contain radioactive nuclei which undergo beta decay by the emission of positrons.
The cyclotron accelerates protons to extremely high speeds before firing them at non-radioactive nuclei.
The resulting nuclear reaction results produces a radioactive nucleus since the contents of the nucleus is no longer stable.
Cyclotron
PET Scanner

42. Particle Accelerator - Synchrotron
Particles in a synchrotron are accelerated in a linear accelerator before being steered in a circular path by electromagnets.
When the required speed has been attained, the particles can be collided with others for particle physics research.

43. Mass Spectrometer
Chemists use mass spectrometers to identify particles according to their mass to charge ratio.
The mass and charge of unknown particles affect how they are deflected by a magnetic field.
The results recorded by the detector can be compared to those of known samples.

44. Summary of Fields.
Earth
Moon
A gravitational field is a region in which a mass experiences a force.
An electric field is a region in which a charge experiences a force.
A magnetic field is a region in which a moving charge experiences a force.