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I dont understand in what scenarios are the three rules applied and are any two of them similar or are they all different?

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All of them in fact mean the same thing: given $\mathbf{A}$ and $\mathbf{B}$, you are finding (/deciding) the direction of $\mathbf{A}\times\mathbf{B}$.

For the situations in which Fleming's rules are of interest, we are interested in just one relation: $$\mathbf{F} = q\mathbf{v}\times\mathbf{B}$$ or its equivalent: $$\mathbf{F} = I\mathbf{l}\times\mathbf{B}$$ where $I\mathbf{l}$ is the current times the length of a conductor, in the direction of the current.

These different rules are just different ways of assigning quantities to fingers. All of them obey your general convention for the cross product, normally given by the "right hand screw rule".

For example, Fleming's right hand rule says that when a conductor is moving ($\mathbf{v}$) along your right hand thumb, and the field $\mathbf{B}$ is along the index finger, then the current (due to $\mathbf{F}$) is along your middle finger. But Fleming's left hand rule with $\mathbf{v}$ along your left hand middle finger and $\mathbf{B}$ along the left hand index finger gives the same direction (left hand thumb) for $\mathbf{F}$.

However, people seem to prefer always associating the thumb with the "Motion", and the middle finger with the "Current", giving rise to the two rules. Because of this, Fleming's right-hand rule is used when a moving conductor ($\mathbf{v}$) develops a current ($\mathbf{F}$ for positive $q$), as in a generator, and the left-hand rule is used when a current ($q\mathbf{v}$, more or less) generates motion (again $\mathbf{F}$), like in a motor.

The right hand palm rule is yet another (and as far as I can see, not very common) rule that says the same thing, which is used, given the current (right hand thumb) and the magnetic field (outstretched fingers), to find the force on the wire (upward normal from the palm i.e. on the side where you can fold fingers). It is completely equivalent to the other rules.

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  • $\begingroup$ Thank you for explaining the Right Hand Rule and the Left Hand Rule. Could you please tell me where the Right Hand Palm Rule is used? $\endgroup$ – dj1 May 7 '15 at 6:26
  • $\begingroup$ @dj1 I updated the answer $\endgroup$ – AV23 May 8 '15 at 18:37

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