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Magnetic Flux in a Non-Uniform Field

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A square loop of side length L=0.2L = 0.2 m is positioned in the xyxy-plane with one corner at the origin and the opposite corner at (L,L,0)(L,L,0). The region is subject to a non-uniform magnetic field given by B⃗=(αx2)k^\vec{B} = (\alpha x^2)\hat{k}, where α=0.05\alpha = 0.05 T/m². What is the magnetic flux through the loop?

A

6.67 × 10⁻⁵ Wb

B

4.00 × 10⁻⁴ Wb

C

1.33 × 10⁻⁴ Wb

D

2.67 × 10⁻⁵ Wb

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