# Electricity, Gauss law concept question

1. Jan 20, 2010

### Larrytsai

A certain region bounded by an imaginary closed surface contains no charge. Is the electric field always zero everywhere on the surface? If not, under what circumstances is it zero on the surface.

I think it is zero everywhere because as the electric field is entering the closed surface, it is also leaving so, therefore the Net electric field is zero. Im not really sure though

2. Jan 21, 2010

### Staff: Mentor

Gauss' law talks about the electric flux, and if there are no charges inside the closed surface, there is no net flux in or out. But that's different from the electric field. Think about a closed surface that is suspended between the plates of a capacitor. What is the E field like?

3. Jan 22, 2010

### utkarsh1

I guess it depends on the the type of surface. But berkeman is right only net flux is zero. However, depending on surface you could conclude sometimes that E is zero. example, if the surface is sphere. than gauss law says Q = 1/epsilon(surface int.) of Edot ds. If it is a surface integral over sphere, you know that Edotds = E. and it is constant over sphere(keeping in mind you drew the gaussian surface properly) And alternatively: the surface int. turns into E*A = 0 --> E = 0.

However in capacitor the surface integral just yields: E*(top surface) - E*(bottom surface) = flux = 0

this u cannot conclude E = 0; because left most equation is inconclusive.