Force on a Moving Charge (AQA A Level Physics): Revision Note

Magnetic force on a moving charge

• 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 $\theta$ to a magnetic field with flux density $B$ is defined by the equation

$F=BQv\sin \theta$

• 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 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 $\theta =90°$, so $\sin \theta =1$

• The equation for the magnetic force becomes:

$F=BQv$

• $F$, $B$ 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

• 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 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

• 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