Find the potential $V$ of an electrostatic field $\vec{E} = a(y\hat{i} + x\hat{j})$,where $a$ is a constant.

The potential (in volts) of a charge distribution is given by $V(z) = 30 - 5z^2$ for $|z| \le 1 \ m$ and $V(z) = 35 - 10|z|$ for $|z| \ge 1 \ m$. $V(z)$ does not depend on $x$ and $y$. If this potential is generated by a constant charge per unit volume $\rho_0$ (in units of $\varepsilon_0$) which is spread over a certain region,then choose the correct statement.

The potential of the electric field produced by a point charge at any point $(x, y, z)$ is given by $V = 3x^2 + 5$,where $x, y$ are in metres and $V$ is in volts. The intensity of the electric field at $(-2, 1, 0)$ is

In a certain region,the electric potential is given by $V = 6x - 8xy^2 - 8y + 6yz - 4z^2 \, V$. The magnitude of the force on a charge of $2 \, C$ at the origin is ........ $N$.

The potential difference between two parallel plates is $10^4 \,V$. If the plates are separated by $0.5 \,cm$, the force on an electron between the plates is

The electric potential at a point in free space due to charge $Q$ coulomb is $V = Q \times 10^{11} \, V$. The electric field at that point is: