Question : A square of side L meters lie in the X-Y plane in a region, where the magnetic field is given by B=B₀(2i+3j+4k)T, where B₀ is constant. The magnitude of flux passing through the square is
a) 2B₀L² Wb
b) 3B₀L² Wb
c) 4B₀L² Wb
d) √29 B₀L² Wb
Doubt by Nisha
Solution :
B=B₀(2i+3j+4k)T
Side of square (a) = L m
Area of Square (A) = L² m²
A = (L²k) m² [The square is lying along the XY plane and we know area vector is always perpendicular to the plane so it must lie along the z-axis.]
A = (L²k) m² [The square is lying along the XY plane and we know area vector is always perpendicular to the plane so it must lie along the z-axis.]
Magnetic Flux (ɸ) = B.A
ɸB = [B₀(2i+3j+4k)].[L²k]
ɸB = B₀L²[(2i+3j+4k).k]
ɸB = B₀L²[(2i+3j+4k).k]
ɸB = B₀L²[(2i+3j+4k).(0i+0j+1k)]
ɸB = B₀L²[2(0)+3(0)+4(1)]
ɸB = 4B₀L²
ɸB = B₀L²[2(0)+3(0)+4(1)]
ɸB = 4B₀L²
ɸB = 4B₀L² Wb
Hence, c) 4B₀L² Wb would be the correct option.
