Is the Dirac Delta Function Defined at Zero or Infinity?

In summary, the conversation discusses the concept of a delta function and how it cannot be determined solely based on the value of a function at a point. The divergence theorem is mentioned as a way to calculate the "charge" present on a sphere around the origin, with the 4*pi factor coming from the formula for the area of a sphere.
  • #1
yungman
5,718
240
I cannot get the answer as from the solution manuel.

2vl5jd0.jpg


Please tell me what am I assuming wrong.
Thanks
 
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  • #2
Just showing that the value of a function is '-infinity' at a point and zero otherwise doesn't tell you it's a delta function. Apply the divergence theorem to grad(1/r) on a sphere around the origin to figure out how much 'charge' is there.
 
  • #3
Dick said:
Just showing that the value of a function is '-infinity' at a point and zero otherwise doesn't tell you it's a delta function. Apply the divergence theorem to grad(1/r) on a sphere around the origin to figure out how much 'charge' is there.

I understand that and I showed in my own answer. What I don't get is where the 4[tex]\pi[/tex] come from!
Thanks
 
  • #4
No, all your answer said was the value at zero is '-infinity' (I'm putting that in quotes because I'm not even sure it makes sense). I said that DOESN'T mean it's a delta function. The 4*pi comes from checking the flux through a sphere around the origin. It comes from the 4*pi in the formula for the area of a sphere.
 

What is the Dirac Delta function?

The Dirac Delta function, denoted as δ(x), is a mathematical function that represents an infinitely narrow and infinitely tall spike at the origin (x=0) and zero elsewhere. It is commonly used in physics and engineering to model point sources and impulse signals.

What are the properties of the Dirac Delta function?

The Dirac Delta function has three main properties: it is infinitely tall, it is infinitely narrow, and it integrates to 1 over its support. This means that the integral of the Dirac Delta function from negative infinity to positive infinity is equal to 1.

What is the physical interpretation of the Dirac Delta function?

The Dirac Delta function can be thought of as a mathematical representation of an impulse or a point source. In physics and engineering, it is often used to describe the behavior of point masses, point charges, and point forces.

What are some applications of the Dirac Delta function?

The Dirac Delta function has many applications in physics and engineering. It is used to model point sources in electromagnetic fields, to describe the behavior of particles in quantum mechanics, and to solve differential equations in engineering problems.

How is the Dirac Delta function related to the Kronecker Delta function?

The Kronecker Delta function, denoted as δij, is a discrete version of the Dirac Delta function. It takes on the value of 1 when the two indices i and j are equal, and 0 otherwise. In other words, it is a discrete version of the Dirac Delta function with a finite number of possible values.

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