Question

lecuture 3, I don't understand the symmetry argument. exactly what it means by "uniformly distributed charge on a conductor" giving symmetry?

Answer 1

It is something that is explained later in the course. Walter Lewin asks you to accept as a given that charges in a circular/spherical conductor automatically distribute themselves uniformely around their surface, if there are no external forces.

So when this happens, if you think about it, the electric field E varies with distance, but its of the same magnitude for every given R around the center of your circular/spherical conductor.

Thats the symmetry arguement. Every circle around the conductor has an E of the same magnitude, no matter the angle you choose.

So later when you choose your Gauss surface, you choose one you can integrate over where |E| is constant.

Answer 2

by using the symmetry argument our problem gets easier.

Answer 3

Symmetry means we find the surface in which electric field will be tangent or normal to given surface i.e. we will get E.dA=0 or simply EdA or Constant.
So that we can easily use Gauss's law.