AQA A Level Physics

Revision Notes

7.8.4 Force on a Moving Charge

Calculating Magnetic 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

Force on isolated moving charge, downloadable AS & A Level Physics revision notes

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

Worked Example

An electron is moving at 5.3 × 107 m s-1 in a uniform magnetic field of flux density 0.2 T.

Calculate the force on the electron when it is moving perpendicular to the field.

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

Exam Tip

Remember not to mix this up with F = BIL!

  • F = BIL is for a current-carrying conductor
  • F = BQv is for an isolated moving charge (which may be inside a conductor)

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