Scalar field and vector field pdf

What is the difference between a scalar and a vector field. Both the vector field and the scalar field can have the same domain, e. Scalar fields, vector fields and covector fields scalar. If we consider temperature within a solid then we have a scalar field since temperature is a scalar quantity and by a scalar field, we mean that there are a set of values of a scalar that must be assigned throughout a continuous region of space. A vector is a quantity which has both a magnitude and a direction in space. At an undergraduate multivariable vector calculus course it is taught an algorithm to find the scalar potential of a vector field, but such algorithm is ineffective.

We have seen that the temperature of the earths atmosphere at the surface is an example of a scalar field. A scalar field is a tensor field of order zero, and the term scalar field may be used to distinguish a function of this kind with a more general tensor field, density, or differential form. This potential is a modification of the two scalar potential functions introduced by e. The scalar complex potential of the electromagnetic field. A scalar field is a region in threedimensional space, in which there corresponds a scalar variable f to each point with coordinates x,y,z. A vector field on a domain in space or in the plane is a function that assigns a vector to each point in the space. The former two packages requires a bit of python programming. We know that many physical quantities like temperature, electric or gravitational field etc. For simplicity we will start with a scalar field instead of the vector. So the function, f x, y, z is called as the scalar field. A scalar field is a field for which there is a single number associated with every point in space. It has been shown that a longitudinal wave is a combination of a vector potential with a scalar potential. A scalar field is a fancy name for a function of space, i.

But, a scalar field has r as codomain whereas a vector field has rn with n1 as codomain. Ordered pair f is called a stationary scalar field, while function f is called the potential. Let f be a scalar function, such that any point x is attached a real number. Assume we have a field defined everywhere in space and time. Consider a cube or 3d space as shown in the following figure. Similarly, if f x,y,z is a scalar function of three variables, its gradient. Scalar field and vector field physics video in hindi. Every point of this cube can be represented as x, y, z. The of a vector field is the volume of fluid flowing through an element of surface area per unit time. The vector field maps points to vectors whereas the scalar field maps points to scalars.

How is the vector field different from the scalar field. Method to find a scalar potential of a conservative vector. Examples of vector quantities are displacement, velocity, magnetic field, etc. In this video we introduce the notion of a vector field, how it differs from a scalar field, and how to plot a basic 2d field by hand.