Problem

Problem

A conducting square loop is placed in a magnetic field BB with its plane perpendicular to the field. Now the sides of the loop start shrinking at a constant rate α\alpha . The induced emf in the loop at an instant when its side is aa , is (a) 2aαB2a\alpha B (b) a2αBa^2\alpha B (c) 2a2αB2a^2\alpha B (d) aαBa\alpha B
Intuitive explanation

The key is recognizing that a changing magnetic flux through the loop induces an emf, and here the flux changes because the loop's area is shrinking—not because the field itself is changing. Use Faraday's law: the induced emf equals the rate of change of flux, ε=−dΦdt\varepsilon = -\frac{d\Phi}{dt}. Since Φ=B⋅A\Phi = B \cdot A and the area A=a2A = a^2 decreases as the side length aa shrinks at rate α\alpha, you need to find how fast the area is changing in terms of the given quantities.

Intuitive explanation

The key is recognizing that a changing magnetic flux through the loop induces an emf, and here the flux changes because the loop's area is shrinking—not because the field itself is changing. Use Faraday's law: the induced emf equals the rate of change of flux, ε=−dΦdt\varepsilon = -\frac{d\Phi}{dt}. Since Φ=B⋅A\Phi = B \cdot A and the area A=a2A = a^2 decreases as the side length aa shrinks at rate α\alpha, you need to find how fast the area is changing in terms of the given quantities.

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