I wanted to ask if someone can clarify for me when one would use the Heaviside function instead of (or in combination with) the Dirac delta function.
Thanks in advance
Answers and Replies
If you were describing charge density, then the Heaviside step function would be used when you have a step in the charge density. For example if the charge density were zero for x<0 and p coulombs per unit volume for x >=0, then the charge density would be p * H(x) coulombs per unit volume. The Dirac delta function is used when you have a point charge, or maybe a line charge or maybe a plane charge. If you have a plane charge density that is p coulombs per unit area and the plane is the y-z plane then the charge density is p*delta(x) coulombs per unit volume. If its a line charge of p coulombs per unit length, and the line is the x axis, then the charge density is p * delta(y)*delta(z) coulombs per unit volume. If its a point charge with charge q, and the point is at the origin, then the charge density is q*delta(x)*delta(y)*delta(z) coulombs per unit volume.