1. Motion of Charges in Electric Fields

2. Electric Potential Difference

3. Electric Potential Energy

4. The electron-Volt (eV)

5. Example Question 1 A charge of 5mC experiences a force of 0.2N in an electric field. It is moved a distance of 20cm against this force. Find the potential difference through which the charge has moved.

6. Example Question 2 An electron is accelerated from rest through a potential difference of 2000V. Find its kinetic energy in electron-volts and in Joules.

7. Uniform Electric Fields Consider the uniform field between two parallel plates, d metres apart, with a potential difference of ΔV volts between them. Consider moving a small positive charge q from the negative plate to the positive plate. Because it is a uniform field of constant strength E there is a constant force (F = qE) on this charge throughout its travel. To move this charge we have to do work on it.

8. Uniform Electric Fields

9. Example Question 3 Calculate the strength of the uniform field is between two parallel plates, 20cm apart, with a potential difference of 800V between them.

10. Acceleration in Uniform E-Field

11. Motion Anti-Parallel to Field Motion Parallel or Antiparallel to the Field If the particle is initially stationary, it accelerates in the direction of the force acting on it. This is identical to the motion of a body dropped in the Earth's gravitational field If the particle is initially moving in the same direction as the force acting on it, it will accelerate in the direction in which it is initially moving. This is identical to the motion of a body projected vertically downward in the Earth’s gravitational field

12. Motion Anti-Parallel to Field If the particle is initially moving in the opposite direction to the force acting on it, it will slow down come to a halt and then accelerate back along the path which it initially travelled. This is identical to the motion of a body projected vertically upward in the Earth’s gravitational field In this case motion will be in two directions so take the original direction of motion as positive All of theses motions are in a straight line with constant acceleration so Newton’s equations of motion can be applied

13. Example Question 4 Two large flat parallel plates have a potential difference of 200V applied to them. The plates are 10.0cm apart. An alpha particle, initially adjacent to the positive plate, accelerates towards the negative plate. Find: a) the time the proton takes to move between the plates: b) the final velocity of the proton (just before it hits) c) verify this final velocity using conservation of energy

15. Example Question 5 Two large flat parallel plates, 10.0cm apart, have a potential difference of 200V between them. A proton is fired upwards towards the positive plate, through a hole in the negative plate. The initial speed of the proton is 100 000 ms -1. Find: a) the force on the proton; b) the acceleration of the proton; c) the time before the proton returns to the negative plate; d) the distance the proton moves upwards in the space between the plates.

17. Example Question 6 Two parallel plates 20cm long and 5cm apart have a potential difference of 1000V between them. In an electron gun, electrons are accelerated through a potential difference of 4000V. On leaving the electron gun these electrons enter the field between the parallel plates at right angles to the field, as depicted in the diagram below. Find: a) the time taken for the electrons to transverse this field; b) the deflection of the electrons on leaving the field

18. Example Question 6

19. Application: The Cyclotron

20. Parts of a Cyclotron: Ion Source In the original cyclotron this was a heated filament A small quantity of hydrogen gas was introduced into the apparatus. Electrons emitted by the heated filament were accelerated by the electric field between the dees, and when they collided with hydrogen molecules they could eject one of the hydrogen electrons creating ions Modern cyclotrons have the source of ions, created by passing a gas through an electric arc, located outside the evacuated chamber These ions are then injected into the space between the dees. This is to preserve as good a vacuum as possible in the apparatus

21. Parts of a Cyclotron: The Dees These are two hollow semicircular containers made of a non- magnetic metal (eg copper) They are open at the diameter so that ions may pass freely from one dee to the other. An alternating potential difference is applied between the dees. The metal is non-magnetisable so as not to interfere with the external magnetic field that is applied to the apparatus

22. Parts of a Cyclotron: Evacuated Outer Container The apparatus is located in an evacuated container, also made of non-magnetisable material The vacuum is maintained in the apparatus so that the ions do not suffer energy losses due to collisions with air molecules

23. Operation of a Cyclotron An alternating potential difference ΔV volts is applied between the two dees. There is an electric field between the dees but no field inside the dees, as they are effectively hollow charged conductors As the ions accelerate between the dees they gain energy ΔE = qΔV Once they pass into a dee their motion is subject only to the external magnetic field They are moving at right angles to this field, and so they follow a circular path. When the ions exit the dees they once again are accelerated by the electric field between them and gain another quantum of energy ΔE = qΔV, as the electric field has reversed its direction (due to the alternating current)

24. Operation of Cyclotron

25. Example Question 7 Cyclotrons are used in hospitals to create radioactive isotopes of elements, which are used in research and for diagnostic purposes. These isotopes have short half lives and need to be created on location when about to be used. A cyclotron has an alternating potential difference of 2500V applied across the dees. Protons ar emitted from the device with an energy of 3.2MeV. Calculate: a) the energy gained by a proton each time it crosses the space between the dees; b) the number of times N that the protons cross the space between the dees