A rectangular wire frame, shown below, is placed in a uniform mag… - Vidyadip

Question

A rectangular wire frame, shown below, is placed in a uniform magnetic field directed upward and normal to the plane of the paper. The part AB is connected to a spring. The spring is stretched and released when the wire AB has come to the position A′ B′ (t = 0) How would the induced emf vary with time? Neglect damping.

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Answer

When the spring is stretched and released, the wire AB will execute simple harmonic (sinusoidal) motion, so induced emf will vary periodically. At t = 0, wire is at the extreme position. $\text{v}=0.$ $\text{v}=\text{A}\omega\sin\omega\text{t}$ Induced emf $\varepsilon = \text{Bvl}$ $=\text{BA}\omega\text{l}\sin\omega\text{t}$ Where A = BB′= AA′ is the amplitude of motion and ω is angular frequency.

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