Gauss's Law — Prelims Questions

A point charge $q$ is placed at the center of a cube of side $L$. What is the electric flux passing through one face of the cube?

An infinite line charge produces an electric field of $9 \times 10^4,\text{N/C}$ at a distance of $2,\text{cm}$. What is the linear charge density of the wire?

A uniformly charged spherical shell of radius $R$ has a total charge $Q$. What is the electric field at a distance $r < R$ from the center of the shell?

An isolated conductor of irregular shape is given a charge $Q$. Which of the following statements is true regarding the electric field inside the conductor?

A large non-conducting sheet has a uniform surface charge density $sigma$. What is the electric field just outside the sheet?

A solid non-conducting sphere of radius $R$ has a total charge $Q$ uniformly distributed throughout its volume. What is the electric field at a distance $r$ from the center, where $r < R$?