Does the Thermoelectric effect apply in sun?

Spinnor

Reading about the Thermocouple:

http://en.wikipedia.org/wiki/Thermocouple

I came upon:

"...

Principle of operation

Main article: Seebeck effect

In 1821, the German–Estonian physicist Thomas Johann Seebeck discovered that when any conductor is subjected to a thermal gradient, it will generate a voltage. ..."

Does this effect apply and produce a radial electric field in a star and in the Earth? There is a temperature gradiant in both, and both conduct?

Thanks for any help!