Charge To Mass Ratio of Electrons
- The velocity of an electron beam can be found using a deflection tube
- This consists of electrons accelerated from a cathode (negative terminal) to an anode (positive terminal)
- They are then passed between two oppositely charged parallel horizontal plates and a magnetic field is applied perpendicular to them
- This means an electron beam is passed through a combined electric (E) and magnetic (B) field
- By adjusting the strengths of the E and B fields, the two electric and magnetic forces can be made to balance the path of the electrons and keep the beam horizontal
- When the electron beam remains straight, the electric and magnetic forces on them are equal in magnitude but opposite in direction
- The magnetic field is provided by two coils (Helmhol coils) which provide a uniform field between them
- The force due to an electric field is given by:
F = eE
- The force due to a magnetic field is given by:
F = Bev
- Equating the E and B forces gives:
eE = Bev
- Where:
- e = charge of an electron (C)
- E = electric field strength (N C-1)
- B = magnetic flux density (T)
- v = velocity of the electron beam (m s-1)
- Rearranging for the velocity v, and using the definition of electric field strength between two plates, the equation becomes:
- Where:
- V = voltage between the plates (V)
- d = distance between the plates (m)
Measuring the charge-to-mass ratio of the electrons
- When electrons travel through a magnetic field that is perpendicular to its velocity, they travel in a circular path
- This means the magnetic force, which is perpendicular to its velocity, is equivalent to the centripetal force:
- Where:
- r = radius of the circular path of the electrons (m)
- m = mass of an electron (kg)
- Rearranging this for the charge to mass ratio e/m gives the equation: