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:
Due to the motion of electron on magnetic field, each electron experience Lorent’s magnetic force.
Total number of current on the conductor is:
Total force experienced by the conductor is:
So the force experienced by the conductor is perpendicular to the plane containing l and B.
Special Case:
we have
Case-I:
if θ = 90°
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°
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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