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

Step-by-step solution

Magnetic flux through a surface is defined as the dot product of magnetic field B and area vector A : = B A . Given the square in the x – y plane with side length L , its area vector is A = L^2 k . For magnetic field B = B₀(2 i + 3 j + 4 k ) , the dot product with A simplifies due to orthogonality of unit vectors: = B₀(2 i + 3 j + 4 k ) (L^2 k ) = B₀ L^2 (4 k k ) = 4 B₀ L^2 . The magnetic flux through the square is = 4 B₀ L^2 . This matches option B .