Potential Energy in External Field — Prelims Questions

A point charge of $+3\,\text{nC}$ is placed at a point P in an external electric field where the electric potential is $V = 200\,\text{V}$. What is the potential energy of the charge at point P?

Two point charges, $q_1 = +2,\mu\text{C}$ and $q_2 = -4,\mu\text{C}$, are placed $0.2\,\text{m}$ apart. They are in a region where a uniform external electric potential exists, such that the potential at $q_1$'s location is $V_1 = 100\,\text{V}$ and at $q_2$'s location is $V_2 = -50\,\text{V}$. Calculate the total potential energy of the system. (Given: $k = \frac{1}{4piepsilon_0} = 9 \times 10^9\,\text{Nm}^2/\text{C}^2$)

An electric dipole with dipole moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$. The potential energy of the dipole is minimum when the angle $\theta$ between $\vec{p}$ and $\vec{E}$ is:

An electric dipole of moment $p = 2 \times 10^{-8},\text{C}\cdot\text{m}$ is initially aligned parallel to a uniform electric field $E = 3 \times 10^5\,\text{N/C}$. How much work is required to rotate the dipole to an anti-parallel orientation?

A square of side 'a' has charges $+q$, $-q$, $+q$, and $-q$ placed at its corners A, B, C, and D respectively, in a cyclic order. If this square is placed in a uniform external electric potential $V_0$ at each corner, what is the total potential energy of the system?

An electric dipole is placed in a non-uniform electric field. Which of the following statements is true regarding its behavior?

The work done by an external agent to bring a charge $q$ from point A to point B in an electric field, without changing its kinetic energy, is $W_{AB}$. Which of the following statements is correct?