The following four vector fields are given in Cartesian co-ordinate system. The vector field which does not satisfy the property of magnetic flux density is
\({x^2}{a_x} + {y^2}{a_y} + {z^2}{a_z}\)
Magnetic flux density must have zero divergence throughout the region. Options 1, 2 and 4 each have zero divergence. For the marked field, \(\nabla\cdot(x^2\hat a_x+y^2\hat a_y+z^2\hat a_z)=2x+2y+2z\), which is not identically zero. Thus it cannot be a magnetic flux-density field over general space.
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