Final answer:
The emf induced in a wedding ring with a 2.2-cm diameter when exposed to a changing magnetic field from 0 T to 2.5 T in 200 μs is calculated using Faraday's law of induction.
Step-by-step explanation:
To find the emf induced in the wedding ring as the magnetic field changes, we will use Faraday's law of electromagnetic induction. The average emf (electromotive force) induced in a loop is given by the change in magnetic flux (ΔΦ) divided by the change in time (Δt):
emf = ΔΦ / Δt
The magnetic flux is the product of the magnetic field (B), the area of the loop (A), and the cosine of the angle (θ) between the field and the normal to the loop. Here, θ is zero since the ring's axis is parallel to the field. As the magnetic field changes uniformly, we can write:
ΔΦ = B⋅A = B⋅(π⋅(r^2))
Given B changes from 0 T to 2.5 T in 200 μs with the radius (r) of the ring being 1.1 cm (half of the diameter):
ΔΦ = 2.5 T ⋅ (π ⋅ (0.011 m)^2)
emf = (ΔΦ) / (Δt) = [2.5 ⋅ (π ⋅ (0.011 m)^2)] / (200 × 10^-6 s)
Calculating this gives us the average induced emf in the ring.