Question

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

• A. $y^2\widehat{a_x}+z^2\widehat{a_y}+x^2\widehat{a_z}$
• B. $z^2\widehat{a_x}+x^2\widehat{a_y}+y^2\widehat{a_z}$
• C. $x^2\widehat{a_x}+y^2\widehat{a_y}+z^2\widehat{a_z}$
• D. $y^2{z}^2\widehat{a_x}+x^2{z}^2\widehat{a_y}+x^2{y}^2\widehat{a_z}$

Answer 1

The correct option is C $x^2\widehat{a_x}+y^2\widehat{a_y}+z^2\widehat{a_z}$

The property of a solid magnetic field is
$▽.\overrightarrow{B}=0$
(i.e. solenoidal property)
when, $B=x^2\widehat{a_x}+y^2\widehat{a_y}+z^2\widehat{a_z}$
$▽.\overrightarrow{B}=2x+2y+2z\ne 0$