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A square of side 2 m lies in the x-y plane in a region of magnetic field B = B0(2 i + 3 j + 4 k) T (B0 constant). Find the magnitude of the magnetic flux through the square.

1. 8 B0 Wb
2. 12 B0 Wb
3. 16 B0 Wb
4. sqrt(4*29) B0 Wb

Correct answer: 16 B0 Wb

Solution

The area vector of a loop in the x-y plane points along k, with magnitude (side)² = 4 m². Flux = B.A = (4*B0)*(4) = 16 B0 Wb (only the z-component contributes).

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