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Asked by jeeasp7676 | 18 Aug, 2023, 12:32: PM

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

Answered by Thiyagarajan K | 19 Aug, 2023, 01:08: PM
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