What is the electric field of a point charge?

[Amin2014]

Assuming the point charge lies at the origin, what is the electric field at the origin? Zero or undefined?

 

[BvU]

undefined

 

[Amin2014]

undefined

I checked some books and you are right. However, I don't understand why we can't we just assign it a value of zero? After all, the charge cannot apply force on itself.

 

[BvU]

There is the issue of size. Equal to zero for a point. Zero E would mean constant potential over some region with size. Contradiction !

After all, the charge cannot apply force on itself

No, but it can apply force on a test charge, however close it comes...
No place where that force suddenly drops from near infinity to zero.

 

[Amin2014]

There is the issue of size. Equal to zero for a point. Zero E would mean constant potential over some region with size. Contradiction !

Ok I see. The field is zero at the center of a spherical charge distribution, no matter the size of sphere. So if our charge had dimensions (unlike a point charge), then the field would be zero at the origin.

 

[BvU]

Same difference: you refer to Gauss theorem: some charge density times zero volume. Doesn't fly when charge is within zero volume.

 

[Amin2014]

Same difference: you refer to Gauss theorem: some charge density times zero volume. Doesn't fly when charge is within zero volume.

I was validating your answer and completing it. The field would be zero only if the charge has dimensions.