Electric Flux — Prelims Questions

A uniform electric field $\vec{E} = (2\hat{i} + 3\hat{j} - 4\hat{k})\,\text{N/C}$ exists in a region. Calculate the electric flux through a surface of area $10,\text{m}^2$ in the $yz$-plane.

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

An electric dipole is placed inside a closed surface. What is the total electric flux coming out of the surface?

A hollow conducting sphere of radius $R$ has a charge $Q$ on its surface. What is the electric flux through a concentric spherical Gaussian surface of radius $r < R$?

A uniform electric field of $100,\text{N/C}$ is directed along the positive $x$-axis. A circular loop of radius $0.1,\text{m}$ is placed such that its plane is parallel to the $yz$-plane. What is the electric flux through the loop?

A charge $Q$ is uniformly distributed over a large non-conducting sheet. If a cylindrical Gaussian surface of cross-sectional area $A$ and height $2h$ is placed such that its axis is perpendicular to the sheet, with the sheet passing through its center, what is the electric flux through the entire cylindrical surface?