A square current carrying loop made of thin wire and having a mass m = 10 g can rotate without friction with respect to the vertical axis OO₁ , passing through the centre of the loop at right angles to two opposite sides of the loop. The loop is placed in a homogeneous magnetic field with an induction $B = 10^{- 1} T$ directed at right angles to the plane of the drawing. A current I = 2A is flowing in the loop. Find the period (in sec) of small oscillations that the loop performs about its position of stable equilibrium. (Round off your answer to nearest integer)

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Detailed Solution

$T = 2 π \sqrt{\frac{I}{MB}}$

here $I = \frac{m}{4} \frac{l^{2}}{12} \times 2 + \frac{m}{4} \frac{l^{2}}{4} \times 2 = \frac{{ml}^{2}}{6}$

and

$M = l^{2} i$

$T = 2 π \sqrt{\frac{I}{MB}} = 2 π \sqrt{\frac{m}{6 iB}} = 2 π \sqrt{\frac{0.01}{6 \times 2 \times 0.1}} = 0.57 s$

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