7.8.2 Fleming's Left Hand Rule

• 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