physics problem, please help

Question

Use Gauss' law to show that:

a) In electrostatic equilibrium, the net charge of a conductor must remain on the surface and the field must be normal to the surface, having modulus equal to σ/∈₀ where σ is a surface charge density.

b) A closed, hollow conductor shields its interior from external charges but does not shield its exterior from charges placed inside (inside the hole).

Answer 1

Hi Jessie!

a) Let's think about this conceptually. In physics when we talk about "equilibriums," we're typically talking about a state in which forces are balanced and (due to Newton's second law), there is no net acceleration of particles. As the electric field tells us how a test charge would accelerate when placed at a given location, we know the E field must be 0 inside a conductor in electrostatic equilibrium (so that nothing accelerates!). By Gauss' Law,   over an arbitrary "Gaussian surface." But because the E field is 0

 everywhere inside the conductor, 

any Gaussian surface we integrate over will give us 0 net charge enclosed! For this reason, all excess charge will remain on the surface on the conductor. Rearranging Gauss' Law, we can write Eout - Ein = Q/A/∈₀ , but this is just the modulus value σ/∈₀ !

2.Let's think about Gauss' Law again.   , where Q is the net charge enclosed. That's right- Gauss' Law doesn't care about anything outside of our Gaussian surface (i.e. external charges). Thus, a conductor "shields" its interior from outside charges (maintains 0 E field inside).

As for the second question, Let's draw a Gaussian surface that encapsulates the exterior of the conductor. By the Law, it again only cares about net charge enclosed. In this way, the E field will effectively disregard the conductor and reflect the total net charge contained within.