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A square current carrying loop made of thin wire and having a mass m =10g can rotate without friction with respect to the vertical axis O O_1, 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 inductionB = 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 of small oscillations that the loop performs about its position of stable equilibrium. |
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Answer» Solution :`T_0 = 2pi sqrt(m)/(6IB) = 0.57 s` [Hint : Restoring torque equation : `I AB SIN THETA = - I_0 theta,` where `A = a^2` and `I_0 = m/4 [(a^2)/(12) xx 2 + (a/2)^2 xx 2 ]` `= m /4 xx 2/3 a^2` `rarr (m/6 a^2)overset(..)theta = -a^2 B theta rArr overset(..) = - ((6IB)/(M)) theta ]`. |
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