Is the Dirac Delta Function Defined at Zero or Infinity?

[yungman]

I cannot get the answer as from the solution manuel.

Please tell me what am I assuming wrong.
Thanks

 

[Dick]

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.

 

[yungman]

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$$\pi$$ come from!
Thanks

 

[Dick]

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.