Answer to Question #159837 in Physics for Haji

Question

Elaborate physical interpretation and significance of Gradient, Divergence & Curl and write down their respective formula.

Answer 1

Divergence is the net flow of field/liquid/substance out of a unit volume.

$$\nabla \cdot \vec{A}=\frac{\partial A_x}{\partial x}+\frac{\partial A_y}{\partial y}+\frac{\partial A_z}{\partial z}$$

Curl gives the measure of angular velocity of a object.

If Curl is zero, it means the object is not rotating.

If Curl is not zero, its magnitude represents the speed of the object and its direction denotes the axis of rotation.

$$\nabla \times \vec{A}$$

Gradient is the rate of change of a parameter P with respect to parameter Q.

$$\nabla \cdot A=\frac{\partial A_x}{\partial x}\vec{i}+\frac{\partial A_y}{\partial y}\vec{j}+\frac{\partial A_z}{\partial z}\vec{k}$$