How can a sound of a different note be produced in a guitar without changing the length of wire?​

how tightly strung the wire is

-- Make the string tighter or looser.

-- Keep the same length, but make the string thicker or thinner.

-- Touch the string at a point exactly 1/2, 1/3, 1/4, or 1/5 of its length from one end.

electric field is a function of 1/r^2

yes, the force per unit charge for a point charge is inverse square law.