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

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

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

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