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Asked by jeeasp7676 | 18 Aug, 2023, 12:32: PM
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Let the square loop is on y-z plane and direction of magnetic field B is in -x axis direction as shown in figure. Axis of rotation OO' is parallel to z-axis
If small angular displacement θ is made to the loop , then the restoring torque τ acting on the loop due to force ( Refer top view figure )
acting on the vertical side of loop is
.............................. (1)
where i is the current passing through loop and l is the side length of loop.
If I is the moment of inertia , then the torque , where is angular acceleration
Hence , eqn.(1) can be written using small angle approximation as
If we compare above expression with the standard SHM equation ,
then we get angular frequency of oscillatory motion of coil as
........................... (2)
Moment of inertia of loop about the given axis of rotation is
By substituting moment of inertia in eqn. (2), we get
Angular frequency ω and period T of oscillation are related as
Hence period of oscillation T is
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