• The magnetic force on an isolating moving charged particle, such as an electron, is given by the equation:

F?=?BQv

• Where:
  • F?= magnetic force on the particle (N)
  • B?=?magnetic flux density?(T)
  • Q?= charge of the particle (C)
  • v?= speed of the particle (m s-1)

   

• Current is the rate of flow of?positive?charge
  • This means that the direction of the current for a flow of negative charge (eg. an electron beam) is in the opposite direction to its motion

   

• F,?B?and?v?are mutually perpendicular
  • Therefore if a particle travels?parallel?to a magnetic field, it will not experience a magnetic force

   

The force on an isolated moving charge is perpendicular to its motion and the magnetic field B

• According to?Fleming’s left hand rule:
  • B?is directed into the page, and current?I?(or speed?v) is directed to the right
  • When an electron enters a magnetic field from the?left, and if the magnetic field is directed?into the page, then the force on it will be directed?upwards

   

• The equation shows:
  • If the direction of the electron changes, the magnitude of the force will change too

   

• The force due to the magnetic field is always perpendicular to the velocity of the electron
  • Note:?this is equivalent to?circular motion

   

• Fleming’s left-hand rule can be used again to find the direction of the force, magnetic field and velocity
  • The key difference is that the second finger, representing current?I?(direction of positive charge), can now be used as the?direction of velocity?v?of a?positive?charge

   

Step 1:?Write out the known quantities

• • Speed of the electron,?v?= 5.3 × 107?m s-1
  • Charge of an electron,?Q?= 1.60 × 10-19?C
  • Magnetic flux density,?B?= 0.2 T

   

Step 2: Write down the equation for the magnetic force on an isolated particle

F?=?BQv

Step 3: Substitute in values, and calculate the force on the electron

F?= (0.2) × (1.60 × 10-19) × (5.3 × 107) = 1.696 × 10-12?N