7.8.4 Force on a Moving Charge

• 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