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A square loop has each side of length 2 cm. A magnetic field directed out of the page has magnitude B = 4t² * y (in tesla), where y is measured in metres and t in seconds. The induced EMF in the loop at t = 2.5 s is expressed as x / 10⁴ microvolts. Find the value of x.

1. 4
2. 8
3. 16
4. 32

Correct answer: 8

Solution

Integrating B = 4t² * y over the square loop (side L = 0.02 m) placed with one side at y = 0: Phi = 4t² * L * (L²/2) = 2t² * L³. EMF = |dPhi/dt| = 4t * L³. At t = 2.5 s: EMF = 4 * 2.5 * (0.02)³ = 10 * 8 * 10^(-6) = 8 * 10^(-5) V = 8 * 10^(-5) * 10⁶ muV = 8 * 10 muV = 80 muV... let me recompute carefully.

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