Force on a Moving Charge (CIE A Level Physics)

• A moving charge produces its own magnetic field
  • When interacting with an applied magnetic field, it will experience a force

• The force F on an isolated particle with charge Q moving with speed v at an angle θ to a magnetic field with flux density B is defined by the equation

• 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)
  • θ = angle between charge’s velocity and magnetic field (degrees)

• Current is taken as the rate of flow of positive charge (i.e. conventional current)
  • This means that the direction of the current for a flow of negative charge (e.g. a beam of electrons) is in the opposite direction to its motion

• As with a current-carrying conductor, the maximum force on a charged particle occurs when it travels perpendicular to the field
  • This is when θ = 90°, so sin θ = 1

• The equation for the magnetic force becomes:

• F, B and v are mutually perpendicular, therefore:
  • if the direction of the particle's motion changes, the magnitude of the force will also change
  • if the particle travels parallel to a magnetic field, it will experience no magnetic force

Path of a moving charged particle in a magnetic field

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

• From the diagram above, when a beam of electrons enters a magnetic field which is directed into the page: 
  • electrons are negatively charged, so current I is directed to the right (as motion v is directed to the left)
  • using Fleming’s left-hand rule, the force on an electron will be directed upwards

Direction of force on a moving charge

• The direction of the magnetic force on a charged particle depends on
  • the direction of flow of the current
  • the direction of the magnetic field

• This can be found using Fleming's left-hand rule
• The second finger represents the current flow or the flow of positive charge
  • For a positive charge, the current points in the same direction as its velocity 
  • For a negative charge, the current points in the opposite direction to its velocity

Fleming’s left-hand rule allows us to determine the direction of the force on a charged particle

• From the diagram above, when a positive charge enters a magnetic field from left to right, using Fleming's left-hand rule:
  • the first finger (field) points into the page
  • the second finger (current) points to the right
  • the thumb (force) points upwards

• When a charged particle moves in a uniform magnetic field, the force acts perpendicular to the field and the particle's velocity
  
  • As a result, it follows a circular path 

The direction of the magnetic force F on positive and negative particles in a B field in and out of the page