Charge density and the Heaviside stepfunction

[khary23]

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

 

[Rap]

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.

 

[khary23]

Thank you for that very clear explanation.