NIMCET 2024 Paper

The divergence of the vector $\overline{\mathit{A}}$ is given bu $\mathrm{div}\left(\overline{\mathit{A}}\right)=\frac{\partial {\mathit{A}}_{\mathit{x}}}{\partial \mathit{x}}+\frac{\partial {\mathit{A}}_{\mathit{y}}}{\partial \mathit{y}}+\frac{\partial {\mathit{A}}_{\mathit{z}}}{\partial \mathit{z}}$
Here ${\mathit{A}}_{\mathit{x}}=2\mathit{x}+1,{\mathit{A}}_{\mathit{y}}=\left({\mathit{x}}^2-6\mathit{y}\right),{\mathit{A}}_{\mathit{z}}=\left(\mathit{x}{\mathit{y}}^2+3\mathit{z}\right)$
Hence $\mathrm{div}\left(\overline{\mathit{A}}\right)=2-6+3=-1$
If $\mathrm{div}\left(\overline{\mathit{A}}\right)>0$, the field is a source field.
If , the field is a sink field.
If $\mathrm{div}\left(\overline{\mathit{A}}\right)=0$, the field is a solenoidal field.
Since $\mathrm{div}\left(\overline{\mathit{A}}\right)=-1$, the vector field is a sink field.