## 2.11:

JoVE Core
Physik
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JoVE Core Physik

### Nächstes Video2.12: Divergence and Curl

The gradient of a scalar field represents the direction and magnitude of the maximum spatial rate of change of the field. The gradient is always normal to a surface of constant value.

To understand this, consider the scalar field of the partial pressure of carbon dioxide emitted in smoke.

At any point in space, the partial pressure can be represented as a function of three coordinate axes.

The partial derivative of this pressure along the axes, when added together, produces a vector quantity called the gradient of partial pressure of carbon dioxide.

Its magnitude indicates the maximum rate at which the pressure changes, whereas its direction shows the direction in which the pressure changes most.

Mathematically, the gradient of a scalar field can be written as a vector operating over a scalar. This vector is called the del operator.

In cylindrical and spherical coordinates, the gradient of a scalar field is expressed by the transformation relation, where the first term denotes the del operator in these coordinate systems.