Question

I have Studied Scalar field.It shows that .It could show a single function at a point of a space.
But I am confused that ,How It can take a three variable in a single function. (ie) T(x,y,z).
A scalar Quantity can be a only a 1 or 2 or three variable?

Answer 1

A scalar field shows the magnitude (as a single value) of the field at every point in space. That magnitude is defined in the form of a mathematical function. Now, a function can take as many variables as required - 1, 2, 3 or even 50.
For example, a polynomial function can be defined as :
2xy + 4z^2 + 5p + 7abc +.........(one can go on adding variables)
can you say that is not a function? No, right? This just means that 'we' need this many variables to depict the required condition.
Coming back to T(x,y,z), at different points in space, the values of x, y and z change; which when substituted in the function T, give us the magnitude of the field at the respective points.
So yes, a scalar quantity can be 'defined' using 1, 2, 3 or more variables. (Mind you, the variables themselves, are NOT independent scalar quantities)
Hope I helped!

Answer 2

A scalar field can have many variables to describe it. It is not the number of variables that make a field a scalar or a vector but whether or not there is direction associated with the number. For example if you think about the temperature in your house there are a number of different things that are going to affect it. Is the heater on? Is the a/c on? are there windows open? how warm is it outside? ect. All of these things affect the temperature of your house but the temperature still does not have a direction. Because the temperature does not have a direction it can not be a vector field. Therefore the temperature is a scalar field because it does not have a directional component.