The rate of change of a vector field is complex. The divergence of a vector field indicates how much the vector field spreads out from a certain point. The divergence of a vector is scalar.

If $\vec{B}=B_x\hat{i}_x+B_y\hat{i}_y+B_z\hat{i}_z \tag{1}$

Its divergence is written as $$\vec{\nabla}.\vec{B}=\frac{\partial{B_x}}{\partial{x}}+\frac{\partial{B_y}}{\partial{y}}+\frac{\partial{B_z}}{\partial{z}}\tag{2}$$

In cylindrical coordinates, the field is …