Gradient of a Scalar T (grad T) - Definition, Significance & Solved Examples.
- The gradient of a scalar field provides a vector field that states how the scalar value is changing throughout space – a change that has both a magnitude and direction. - A gradient is applied to a scalar quantity that is a function of a 3D vector field: position . The gradient measures the direction in which the scalar quantity changes the most, as well as the rate of change with respect to position. - The physical meaning of the gradient of a scalar is that it represents the steepness of the slope or line. For example, height is a scalar quantity; gradient of the height would be a vector pointing upwards. The length of the vector is proportional to the steepness of the slope. - A derivative is required that tells us how fast the function varies , if we move a little distance. - Consider a scalar function T which is a function of space coordinates x, y and z. - The projection or the component of ∇ T in the direction of a unit vector a l is ∇ T . a l and...