A square of side L metre lies in the xy plane in a region where the magnetic field is given by ⃗B = B₀(2̂i + 3̂j + 4̂k) T, where B₀ is a constant. The magnitude of the flux passing through the square is Wb.

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(1) 4B₀L². Given: the square lies in the xy plane, so its area vector is ⃗A = L²̂k; ⃗B = B₀(2̂i + 3̂j + 4̂k). Idea: flux counts only the component of ⃗B along the normal to the surface, Φ = ⃗B·⃗A. Φ = B₀(2̂i + 3̂j + 4̂k)· L²̂k. Since ̂i·̂k = ̂j·̂k = 0 and ̂k·̂k = 1: Φ = 4B₀L². Magnitude of the flux = 4B₀L² Wb.

A square of side L metre lies in the xy plane in a region where the magnetic field is given by ⃗B = B₀(2̂i + 3̂j + 4̂k) T, where B₀ is a constant. The magnitude of the flux passing through the square is ______ Wb.

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