Applications of Gauss's Law — Prelims Questions

An infinitely long thin straight wire has uniform linear charge density $\lambda$. The electric field at a distance $r$ from the wire is given by:

A uniformly charged infinite plane sheet has a surface charge density $\sigma$. The electric field produced by the sheet is:

A hollow conducting sphere of radius $R$ is given a charge $Q$. The electric field inside the sphere (at a distance $r < R$ from the center) is:

A non-conducting solid sphere of radius $R$ has a total charge $Q$ uniformly distributed throughout its volume. The electric field at a distance $r < R$ from the center is proportional to:

Two large, thin metal plates are parallel and close to each other. They have surface charge densities of $+\sigma$ and $-\sigma$ respectively. The electric field in the region between the plates is:

A spherical charge distribution has a volume charge density $\rho(r) = ar$ for $r \le R$ and $\rho(r) = 0$ for $r > R$. What is the total charge $Q$ of the sphere?