it used in our practical life.. for ex. in hills r in mountains
the gradient of a scalar function of any quantity is defined as a vector field having magnitude equal to the maximum space rate of change of the quantity and having a direction identical with the direction of displacement along which the rate of change is maximum.
Because Electric field can be expressed as the gradient of a scalar. Curl of a gradient is always zero by rules of vector calculus.
It is the rate of change in the vector for a unit change in the direction under consideration. It may be calculated as the derivative of the vector in the relevant direction.
In the name of God; It must be mentioned that a vector has two important characteristics; 1- direction and 2- quantity. in other word for identification a vector these two characteristics must be defined. for example when we speak about displacement of a body it must has direction and quantity. but about gradient, it has a general mean: difference. Also a specified mean may be defined for it: "any increase or decrease in a vector or scalar field". it is a vector field.
say what
what do you mean by gradient of a scalar field? what do you mean by gradient of a scalar field?
No, the curl of a vector field is a vector field itself and is not required to be perpendicular to every vector field f. The curl is related to the local rotation of the vector field, not its orthogonality to other vector fields.
Any vector quantity does. Examples of vector quantities include but are not limited to . . . - Displacement - Velocity - Acceleration - Torque - Force - Electric field - Momentum - Poynting vector
The 'upside down' triangle symbol is the (greek?) letter Nabla. Nabla means the gradient. The gradient is the vector field whoose components are the partial derivatives of a function F given by (df/dx, df/dy).
Richmond Beckett McQuistan has written: 'Scalar and vector fields: a physical interpretation' -- subject(s): Scalar field theory, Vector analysis
Gradient= Change in field value/Distance
In general, it means a smooth blending. For graphics and optics, it is a smooth transition between colors. In things like meteorology, vector calculus and fluid dynamics it is a graph of vectors showing concentrations (of one form or another) between areas. In geometry, it means slope.