Section 1.2 Field
A physical quantity which has one or more definite values at each point of a region of space is said to be a point function in that region, and the region in which the physical quantity is defined is called a field. There are two types of point functions, the scalar point function and the vector point function. The physical quantities which are non - directional can be expressed at each point of a region of space by a scalar point function, \(\phi\text{.}\) For example, the density of a body and its temperature at any instant of time are scalar point functions, and the region is called a scalar field. If the physical quantities are directional then they can be expressed at each point of a region of space by a vector point function, \(\vec{V}\text{,}\) e.g., the velocity of a moving fluid at any instant, the distribution of electric or magnetic field intensity at a point of space are vector point functions, and the region of this space is called a vector field. If \(\phi (x,y,z)\) is a scalar function associated with every point \((x,y,z)\) of any region in space, then \(\phi\) is called a scalar point function and the region is defined as a scalar field. Again, if \(\vec{V}(x,y,z)\) is a vector associated with every point \((x,y,z)\) of any region in space, then \(\vec{V}\) is called a vector point function and the region is defined as a vector field. Remember, the gravitational field is a vector field which expresses the value of force, and Higg’s field is a scalar field which defines the mass or energy of a particle.
Level Surfaces: The portion of a scalar field upon which the scalar function has a fixed value is called a level surface. Isothermal surfaces and equipotential surfaces are examples of level surfaces for temperature and potential, respectively.
