Electrostatics — Prelims Questions

Two point charges, $q_1 = +4,mu\text{C}$ and $q_2 = -2,mu\text{C}$, are placed at a distance of $30,\text{cm}$ from each other in vacuum. What is the magnitude of the electrostatic force between them? (Given: $k = 9 \times 10^9,\text{N m}^2/\text{C}^2$)

An electric dipole consists of two charges, $+q$ and $-q$, separated by a distance $2a$. If this dipole is placed in a uniform electric field $vec{E}$, what is the maximum torque it can experience?

A hollow conducting sphere of radius $R$ is given a charge $Q$. Which of the following statements is true regarding the electric field ($E$) and electric potential ($V$) inside the sphere ($r < R$)?

An electric field in a region is given by $vec{E} = (300,\text{N/C}),hat{i}$. What is the potential difference between point A $(0, 0, 0)$ and point B $(2,\text{m}, 0, 0)$?

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?

The electric potential $V$ in a region is given by $V(x) = (5x^2 - 3x + 10),\text{V}$. What is the magnitude of the electric field at $x = 1,\text{m}$?