How and where to use Static modifier in Java?

Question

How and where should we use a Static modifier for:

1. Field and
2. Method?

For example in java.lang.Math class, the fields

Answer 1

You can't instantiate an instance of java.lang.Math; there isn't a public constructor.

Try it:

public class MathTest
{
    public static void main(String [] args)
    {
        Math math = new Math();

        System.out.println("math.sqrt(2) = " + math.sqrt(2));
    }
}

Here's what you'll get:

C:\Documents and Settings\Michael\My Documents\MathTest.java:5: Math() has private access in java.lang.Math
        Math math = new Math();
                    ^
1 error

Tool completed with exit code 1