Question

A conductor in the shape of a square frame with side a suspended by an elastic thread is located in a uniform horizontal magnetic field with induction B. In equilibrium the plane of the frame is parallel to the vector B (Fig. 4.25). Having been displaced from the equilibrium position, the frame performs small oscillations about a vertical axis passing through its centre. The moment of inertia of the frame relative to that axis is equal to I, its electric resistance is R. Neglecting the inductance of the frame, find the time interval after which the amplitude of the frame'* deviation angle decreases e-fold.

Answer 1

If φ = angle of deviation of the frame from its normal position, then an e.m.f

is induced in the frame in the displaced position and a current flows in it. A couple

then acts on the frame in addition to any elastic restoring couple c φ. We write the equation of the frame as

Thus where β is defined in the book.

Amplitude of oscillation *** out according to so time required for the oscillations to decrease to 1/e of its value is