# Q & A: Coulomb's law and Gauss' law

Q:
Sir; Is it true that the coulomb's law is much more powerful than the Gauss's law (in the differential or integral form). Even though one can be derived from the other at least for special cases. The Coulomb's law can be used to calculate electric field for ANY charge distribution. While Gauss's law cannot.
- Ajit Banerjee (age 18)
md, us
A:

Interesting question. Gauss' law gives the divergence of the static electric field in terms of the charge density. I guess you're right that it needs a bit of a supplement to give all the same results as Coulomb's law, which directly gives the field in terms of the charge distribution. The supplement would say two things:

1. The curl of the field is zero. (Obviously we're just talking about the static case here.)

2. The field goes to zero far away.

The second condition is needed since one could add a constant field everywhere without changing the divergence or curl. Of course, one needs some sort of boundary condition on distant charges for the Coulomb law too.

Mike W.

(published on 07/25/2013)