- Definition: A current-carrying conductor in a magnetic field is influenced by mutual forces between the conductor’s electromagnetic field and the external magnetic field.
- Electromagnetic Field Creation: A current through a conductor generates concentric magnetic flux lines, establishing an electromagnetic field around it.
- Right-Hand Rule: This rule shows the direction of magnetic flux lines around a current-carrying conductor using the orientation of the right hand.
- Fleming’s Left-Hand Rule: This rule helps determine the direction of the force exerted on a current-carrying conductor placed in a magnetic field.
- DC Motor Operation: The force acting on a current-carrying conductor in a magnetic field explains the rotation mechanism of a DC motor.
Oersted discovered that a compass needle deflects near a current-carrying conductor, showing it exerts a force on the needle. In 1821, Faraday found that a current-carrying conductor also deflects in a magnetic field, indicating mutual forces between them.
When a conductor carries current (I) over its length (l), it generates concentric magnetic flux lines around it. This creates an electromagnetic field along the conductor’s central axis.
Using the right-hand thumb rule, the direction of the magnetic flux lines follows the bent fingers when the thumb points in the direction of current flow.
This current carrying conductor is placed between two poles of a horse shoe magnet of flux density 
. This magnet is tightly fixed to the ground. Conductor is not fixed, rather it is free to move. The length of the conductor is just perpendicular of the permanent magnetic field of the horse shoe.
Thus, the current direction and magnetic field are perpendicular to each other.
Now two magnetic fields (electromagnetic field by the conductor and permanent magnetic field by the horse shoe magnet) are in their action.
The concentric circles of electromagnetic flux due to flowing current (I) through this conductor try to repel the magnetic flux of the permanent magnet at that situation.
Let us consider the force is 
.
Here the direction of the current depends on the orientation of length of the current carrying conductor (l), so vector is taken for length only. The force is the cross product of length vector (
) and the flux density vector (
). Now,
Here, θ is the angle between two vectors and 
is the unit vector of the force in the perpendicular direction with respect to two vectors direction.
In This direction of force the conductor will move to. This consequent can be simplified with an easy rule, i.e. Fleming’s Left Hand rule. By stretching three fingers of left hand in perpendicular manner with each other, if the direction of the current is denoted by middle finger of the left hand and the second finger is for direction of the magnetic flux then the thumb of the left hand denotes the direction of the conductor’s movement.
Now the direction of the current through this conductor depends on the conductor in which orientation the conductor is placed between two poles of the magnet. So the current carrying conductor always faces a force in the vicinity of a permanent magnet or any electro-magnet. Based on this phenomenon DC motor rotates.
