1. The Motion Of Charged Particles in Magnetic Fields
SACE Stage 2 Physics

2. Magnetic Forces on Moving Charges
Magnetic fields are caused by electric currents and exert forces on electric currents.
(2) Electric currents consist of moving electric charges. The force on a current wire is in fact caused by the force on the moving charges.
(3) The charges experience these forces whether they are moving in a conductor or not eg
Directed into
the page + I F B
Force perpendicular to v and B and into the page F v +

3. Magnetic Forces on Moving Charges
Expression for the force on a moving charge,
where v is the speed of the moving charge and  the angle between the vectors v and B.

4. Magnetic Forces on Moving Charges
Direction is given by the R.H palm rule.(Need to reverse direction of thumb for a negative charge)
Size of F = qvB sin 
= qvB when at 90o to the B field
Direction of F is perpendicular and into the plane of page.
NB the force on a positive charge would be perpendicular and out of the plane of the page. B v

5. Direction of the Force
Magnetic forces remain at 90o to both v and B. To do this they must change direction continually.
Cross shows B is directed into the plane of the page
      v F
Charge undergoes circular motion, changing velocity with out changing speed, no work done on charge and kinetic energy remains constant.

6. Factors which affect the magnitude of the force
Fmax occurs when sin=90o.
F=0 occurs when sin=0o.

7. Example
An electron moving with speed v = 2.00 x 106 ms-1 enters a uniform magnetic field of strength B=4.50T at an angle of  = 400 to the field, as shown in the diagram. Find,
The magnitude of the force on the electron
The direction of the force on the electron
What would be the force on an electron moving left to right in this field?
What would be the force on an electron moving down the page as it enters this field?
=400

8. Example The magnitude of the force on the electron
The direction of the force on the electron
The force is directed out of the page, right hand rule.

9. Example
What would be the force on an electron moving left to right in this field?
F=0N as electron is moving parallel to magnetic field (sin 0 = 0).
What would be the force on an electron moving down the page as it enters this field?

10. Motion of a Charged Particle in a Magnetic Field
     
Magnetic force provides the centripetal acceleration. v F

11. Motion of a Charged Particle in a Magnetic Field
If m, q and B are held constant, higher speed  larger radius.
     
106 m/s F1
2x106 m/s F2 r 2r

12. Example
A Bainbridge mass spectromoter is used to measure the mass of zinc ions (Zn+). The ions enter a magnetic field, of strength B=1.8T with a speed of 4.2 x 104 ms-1 and they move in a circular path of radius r = 1.7cm. What is the mass of the zinc ions?

13. Example
A Bainbridge mass spectromoter is used to measure the mass of zinc ions (Zn+). The ions enter a magnetic field, of strength B=1.8T with a speed of 4.2 x 104 ms-1 and they move in a circular path of radius r = 1.7cm. What is the mass of the zinc ions?

14. Use of Magnetic Fields in Cyclotrons
Particles moving in a cyclotron are subjected to a uniform magnetic field which causes the particles to move in a circular path.
Each time the charged particle enters a Dee it follows a semi-circular path and each time it traverses to the other Dee its speed is greater than before as it is subjected to an Electric field. Its energy has increased by W=qV.

15. Use of Magnetic Fields in Cyclotrons
The period of the charged particle is independent of its speed, this can be shown by the following,

16. Use of Magnetic Fields in Cyclotrons
The Kinetic Energy can be found by,

17. Use of Magnetic Fields in Cyclotrons
Example,
A cyclotron is used to accelerate dueterons (q = 1.6 x 10-19C) of mass 3.34 x kg. The radius of the cyclotron is 30cm and the magnetic field applied to it has strength 1.6T. Find
The period of the particles in their circular path.
The energy (in eV) of the particles leaving the cyclotron.

18. Use of Magnetic Fields in Cyclotrons
The period of the particles in their circular path.

19. Use of Magnetic Fields in Cyclotrons
(b) The energy (in eV) of the particles leaving the cyclotron.