Magnetic flux density (A-level only): Fleming’s left hand rule.

The idea

Fleming’s left hand rule predicts the direction of the force on a current-carrying conductor in a magnetic field. Hold the left hand with the thumb, first finger and second finger mutually perpendicular. The first finger points along the magnetic flux density B from north to south. The second finger points in the conventional current direction, from positive to negative. The thumb then gives the direction of the force, also called the motor effect force. For a positive charge moving in a field, treat the velocity as conventional current. For a negative charge such as an electron, the current is opposite to the velocity, so reverse the second finger or reverse the predicted force. The rule applies when the current and field are not parallel; the force is greatest when they are perpendicular. Use it with F = BIl sin θ to link direction and magnitude.

What earns the marks

• States that the first finger represents the magnetic flux density B, directed from north to south.
• States that the second finger represents conventional current, from positive to negative.
• States that the thumb represents the direction of the force on the conductor.
• Describes the three digits as mutually perpendicular when the hand is held correctly.
• Applies the rule to a moving positive charge by taking the current direction as the velocity direction.
• Applies the rule to a moving negative charge by reversing the current direction relative to the velocity, or by reversing the force direction.
• Recognises that the force is zero when the current is parallel to the magnetic field and maximum when perpendicular.

Common mistakes and how to put them right

• Using the right hand instead of the left hand.

  Put it right: The right-hand rule gives the direction for a generator effect, so use the left hand for the motor effect force.

• Pointing the second finger along electron flow rather than conventional current.

  Put it right: Conventional current is opposite to electron flow, so reverse the finger for negative charge carriers.

• Treating the first finger as the force and the thumb as the field.

  Put it right: The first finger is the field and the thumb is the force, so swap them to obtain the correct prediction.

Exam tips

• Sketch the left hand with labelled fingers beside your working so the examiner can see the direction reasoning clearly.
• When a question gives an electron beam, state explicitly that conventional current is opposite to the electron velocity before applying the rule.
• Check whether the field and current are perpendicular; if they are parallel, state that the force is zero rather than forcing a direction.