Current loop as a Magnetic dipole Assignment Help

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A current carrying circular coil behaves as a bar magnet whose magnetic moment is M = NiA; Where N = Number of turns in the coil, i = Current through the coil  and A = Area of the coil

Magnetic field of a current carrying coil is a vector and it's direction is given by right hand thumb rule

 

428_current loop as a magnetic dipole.png

Behaviour of Current loop In a Magnetic Field

(1) Torque :Consider a rectangular current carrying coil PQRS having N turns and area A, placed in a uniform field B, in such a way that the normal  to the coil makes an angle q with the direction of B. the coil experiences a torque given by t = NBiA sinq . Vectorially 1158_current loop as a magnetic dipole2.png

(i) t is zero when θ = 0, i.e., when the plane of the coil is perpendicular to the field.

(ii) t is maximum when θ =90o, i.e., the plane of the coil is parallel to the field.

          113_current loop as a magnetic dipole3.png

            The above expression is valid for coils of all shapes.

1579_current loop as a magnetic dipole1.png

(2) Workdone : If coil is rotated through an angle q from it's equilibrium position then required work.  It is maximum when θ = 180o => W­max = 2 MB

(3) Potential energy : Is given by U = - MB cosθ1085_current loop as a magnetic dipole4.png

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