Force on current in magnetic field
From the definition of magnetic induction a charge q moving in a magnetic induction B experiences a force given by
F = q(v×B)
The magnitude of this force is
F = qvB sinθ
The force is mutually perpendicular to B and to the component v = sinθ of the velocity of the charge normal to the field. If the finger of the right hand is curled in the direction in which the vector v = sinθ must be rotated toward the vector B, the thumb will point in the direction of the force in a positive charge.
If a charge moves at right angles to a uniform field. Its path is circular, since the force is constant in magnitude and always perpendicular to the motion. The magnetic force is the centripetal force
When the charges are moving along a conductor in a magnetic field, the force ?F on any element field, the force ?F on any element ?l of the conductor
?F = BI ?l sin θ
Where θ is the angle between the conductor and the flux. The resultant force on the conductors is the vector sum of the contributions of the elements.
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