Force on current carrying conductor on magnetic field

Force on current carrying conductor on magnetic field

A conductor consists of large no. of free electrons. Current on the conductor means drifting of such a free electron in any fixed direction due to the motion of such a free electron each electron experience magnetic force and hence conductor itself experience magnetic force. So, when a current carrying conductor is placed in a uniform magnetic field it experience force.

Consider a conductor having length l, cross-section area A in a uniform magnetic field. If n be the number of electrons per unit volume (electron density), vd be the drift velocity of electron having electronic charge e then the current on the conductor is
Force on current carrying conductor on magnetic field

Due to the motion of electron on magnatic field, each electron experience Lorent’s magnatic force.
Force on current carrying conductor on magnetic field

Total number of current on the conductor is
Force on current carrying conductor on magnetic field
Total force experienced by the conductor is
Force on current carrying conductor on magnetic field


So the force experienced by the conductor is perpendicular to the plane containing l and B.

Special Case:
we have
Force on current carrying conductor on magnetic field
Case-I:
if θ = 90°
Force on current carrying conductor on magnetic field
when the current carrying conductor is placed perpendicular to the magnetic field, magnetic field produces maximum force on the conductor.
Case-II:
if θ = 0° or 180°
Force on current carrying conductor on magnetic field
when the current carrying conductor is placed parallel or anti parallel with magnetic field then magnetic field produces no force on the conductor.

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