Electric Potential — Prelims Questions

The electric potential at a point $(x,y,z)$ is given by $V = 4x^2$ Volts. The electric field at point $(1\,\text{m}, 0, 2\,\text{m})$ is:

Two point charges $q_1 = +4\,\text{nC}$ and $q_2 = -2\,\text{nC}$ are placed at $(0,0)$ and $(3\,\text{m},0)$ respectively. What is the electric potential at the midpoint of the line joining the two charges?

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

If the electric potential $V$ is constant throughout a given region of space, what can be inferred about the electric field $\vec{E}$ in that region?

How much work is required to carry a $3\,\mu\text{C}$ charge from a point at $100\,\text{V}$ to a point at $200\,\text{V}$?

Three point charges, each of charge $+q$, are placed at the vertices of an equilateral triangle of side $a$. What is the electric potential energy of this system?