Electrical Engineering ⇒ Topic : Force on a Conductor in a Magnetic Field

FORCE ON A CONDUCTOR IN A MAGNETIC FIELD

The force experienced by a current carrying conductor in a magnetic field is given by

                                                                         F = BIL                                        .............. (1)

                          (a)    Conductor in a magnetic field                                      (b) Conductor in a magnetic field at

                                      at an angle 90⁰ to it.                                                              an angle θ to it.

                                                                                             figure (1)

where F is force on conductor in N, B is magnetic flux density in Wb/m² (also called tesla or T), I is current in the conductor in A, and L is effective length of the conductor in the field in meters.

                                Substituting F = 1 N, I = 1 A, and L = 1 m in Eq. (1), we get

                                                                             B= 1 T

If the conductor is placed at an angle θ to the field, the effective length will be L sin θ. The force on the conductor will be

                                                          F = BIL sin θ                                                             ................ (2)

  The effective length is the length of the conductor lying within and perpendicular to the magnetic field.

If θ = 0, i.e., the conductor is placed parallel to the field, the force on the conductor is

                                                         F = 0                                                                           ...............   (3)

The basic principle of electric motor is that the armature conductor carrying current is placed in a magnetic field. So, it is also called motor principle. The direction of rotation of the armature is defined by the left hand rule. It is illustrated in Figure (2).

                                                                 FIGURE (2)     Fleming's left hand rule.  

  Spread the thumb, first finger, and second finger of the left hand at directions mutually perpendicular to each other. If first finger indicates the direction of flux and second finger indicates the direction of current, the thumb will indicate the direction of rotation of the armature            

When a current-carrying conductor is placed at right angles to  a magnetic field, it is found that the conductor experiences a force which acts in a direction perpendicular to the direction of both the field and the current. Consider a straight current-carrying conductor placed in a uniform magnetic field as shown in Figure (a).

                                 figure (a)

B = magnetic flux density in Wb/m²

/  = current through the conductor in amperes

L = effective length of the conductor in metres i. e. the length of the conductor lying in the magnetic field

∅ = angle which the conductor makes with the direction of the magnetic field

It has been found experimentally that the magnitude of force (F) acting on the conductor is directly proportional to the magnitudes of flux density (B), current (I), length (L) and sin  i. e

where k is a constant of proportionality. Now SI unit of B is so defined that value of k becomes unity.

By experiment, it is found that the direction of the force is always perpendicular to the plane containing the conductor and the magnetic field.

Both magnitude and direction of the force will be given by the following vector equation

The direction of this force is perpendicular to the plane containing . It can be found by using right-hand rule for cross product

Special Cases.                           

Therefore, if a current-carrying conductor is placed parallel to the direction of magnetic field, the conductor will experience no force.

Therefore, a current-carrying conductor will experience a maximum force when it is placed at right angles to the direction of the magnetic field

Direction of force. The direction of force F is always perpendicular to the plane containing and and can be determined by right-hand rule for cross product stated below :

Orient your right hand so that your outstretched fingers point along the direction of the conventional current; the orientation should be such that when you bend your fingers, they must

point along the direction of the magnetic field (B) . Then your extended thumb will point in the direction of the force on the conductor

                   figure (b)              

Thus applying right-hand rule for cross product to Figure (b)t is clear that magnetic force on the conductor is vertically upward.

Note. If the current-carrying conductor is at right angles to the magnetic field, the direction of force can also be found by Fleming's Left-hand rule stated below

Fleming's Left-hand Rule. Stretch out the First finger, second finger and thumb of your left hand so that they are at right angles to one another. If the first finger points in the direction of magnetic field (North to South) and second finger (i.e. middle finger) points towards the direction of current, then the thumb will point in the direction of motion of the conductor.