# 7.8.2 Fleming's Left Hand Rule

### 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)

#### Worked Example

State the direction of the current flowing in the wire in the diagram below. Using Fleming’s left-hand rule:

B = into the page

F = vertically downwards

I = from right to left #### Exam Tip

Don’t be afraid to use Fleming’s left-hand rule during an exam. Although, it is best to do it subtly in order not to give the answer away to other students!

### Direction of the Magnetic Force

• 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

#### Exam Tip

Remember not to get this mixed up with Fleming’s right-hand rule. That is used for a dynamo, where a current is induced in the conductor (not following through it initially). Fleming’s left-hand rule is sometimes referred to as the ‘Fleming’s left-hand rule for motors’. ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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