Electrical Engineering ⇒ Topic : Magnetic force

Magnetic force. It is the force exerted by one magnet on another to attract it or repel it

MAGNETIC FORCE

Electrostatic forces have been discussed in Chapter, where it was stated that if a charge q is placed in an electric field of intensity E, then the electrostatic force experienced by the charge is

                                                                 F_e = q. E newtons                ...........(1)

The force F_e acts along E and the charge experiences the force, whether it is atrest or moving.

 In a similar way, a moving charge q in a magnetic field will experience a magnetic force given by

                                                                F_m  = q(u x B) newtons         ............ (2)

Here, q is the charge in Coulombs,

u is the velocity of the moving charge in m/s, and

B is the magnetic flux density in Wb/m².

The direction of the force is given by the cross product (u x B) and will be perpendicular to the plane determined by u and B as shown in Fig. (a). The magnitude of the force F_m is given as

                                                                     Fm = q.u.B sin θ               ...............(3)

where, θ is the angle between the vectors u and B.

The following cases can be visualised:

Case (a) When θ = 0 : When the charge q moves along the magnetic field, O becomes zero and the force experienced by the charge also becomes zero.

Case (b) When θ = π/2: When θ = π/2, the force is in a direction normal to the direction of the magnetic field and the force experienced by the charge is maximum. The maximum force is given as

                                                     F_m =q.u.B newtons

and this acts normal to the velocity vector. The acceleration of q is given by

                                              FIGURE (a) Illustrating Fm = q. (U x B)

where, m is the mass of the charged particle.

The acceleration acts along F_m. Since the acceleration and the velocity vectors are mutually perpendicular, the component of a along u is zero. Therefore, there is no change in the initial velocity of the charged particle when it is in the magnetic field, but its direction changes. This implies that there is no change in the kinetic energy of the particle in the original direction of motion. But in an electric field, the charge is accelerated in the direction of the field E and the velocity of the particle increases continuously. The particle acquires kinetic energy from the electric field