• The?direction?of the force on a charge moving in a?magnetic field?is determined by the direction of the magnetic field and the current
  • Recall that the direction of the current is in the direction of?conventional?current flow (positive to negative)

   

• When the force, the magnetic field and the current are all mutually perpendicular to each other, the directions of each can be interpreted by?Fleming’s left-hand rule
• On the left hand, with the thumb pointed upwards, first finger forwards and the second finger to the right, ie. all three are perpendicular to each other
  • The?thumb?points in the direction of?motion?of the rod (or the direction of the force) (F)
  • The?first?finger points in the direction of the external?magnetic field?(B)
  • The?second?finger points in the direction of conventional?current?flow (I)

   

Fleming’s left hand rule

• Since this is represented in 3D space, sometimes the current, force or magnetic field could be directed into or out of the page, not just left, right, up and down
• The direction of the magnetic field into or out of the page in 3D is represented by the following symbols:
  • Dots (sometimes with a circle around them) represent the magnetic field directed?out?of the plane of the page
  • Crosses represent the magnetic field directed?into?the plane of the page

   

The magnetic field into or out of the page is represented by circles with dots or crosses

• The way to remember this is by imagining an arrow used in archery or darts:
  • If the arrow is approaching?head-on, such as out of a page, only the very tip of the arrow can be seen (a dot)
  • When the arrow is?receding away, such as into a page, only the cross of the feathers at the back can be seen (a cross)

   

Using Fleming’s left-hand rule:

B?= into the page

F?= vertically downwards

I?= from right to left

• The direction of the magnetic force on positive and negative charged particles depends on
  • The direction of flow of the charged particles
  • The direction of the magnetic field

   

• This can be found using Fleming's left-hand rule by remembering that the second finger represents the?current?flow or the flow of?positive?charge
  • This means that for negative charges, such as electrons, their flow will be in the opposite direction to which the second finger points
  • Therefore, if a particle carries a negative charge, the second finger should be pointed in the?opposite?direction to its motion

   

• For example, when a?positively?charged particle enters a magnetic field?into?the page from?left to right:
  • Using Fleming's left-hand rule, the first finger points into the page and the second finger (current) points to the right
  • This means the force is upwards
  • The particle is then pulled in the direction of this force (upwards). This means the direction of the current also changes direction slightly (slanting upwards)
  • This means the force will?also?change direction since it still needs to keep perpendicular to the current and the field

   

• Therefore, the moving charges will follow a?circular?trajectory
• Examples of the direction of the magnetic force on positive and negative particles are:

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