A conducting ring of radius r is placed with its plane perpendicular to a time-varying magnetic field B = B₀ + α t, as shown in the figure, where B₀ and α are positive constants. The emf produced in the ring is .

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(3) -π r²α. Given: ring of radius r with its plane perpendicular to ⃗B; B = B₀ + α t. Idea: Faraday's law, ε = -(dΦ)/(dt), with Φ = BA because the field is normal to the ring. Φ = (B₀ + α t) π r². (dΦ)/(dt) = α π r²; the constant part B₀ does not change, so it induces nothing. ε = -π r²α; the minus sign is Lenz's law: the induced current opposes the growing flux. So the emf in the ring is -π r²α.

A conducting ring of radius r is placed with its plane perpendicular to a time-varying magnetic field B = B₀ + α t, as shown in the figure, where B₀ and α are positive constants. The emf produced in the ring is ______.

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