A uniform electric field of $30 {\mathrm{NC}}^{-1}$ exists along the $X$-axis. Calculate the potential difference $V_B-V_A$ between the points $A\left(4 \mathrm{m}, 2 \mathrm{m}\right)$ and $B\left(10 \mathrm{m}, 5 \mathrm{m}\right)$.

An electric field $\overrightarrow{E}=20\hat{i}+30\hat{j} {\mathrm{NC}}^{-1}$ exists in free space. If the potential at the origin is taken zero, determine the potential at point $(2\mathrm{m},2\mathrm{m}).$

The electric field in a region is given by $\overrightarrow{E}=\frac{A}{x^3}\hat{i}.$ Write the SI unit for $\mathrm{A}$. Write an expression for the potential in the region, assuming the potential at infinity to be zero.

Shows the figure some equipotential surfaces. What can you say about the magnitude and the direction of the electric field?

Two-point charges $+10 \mu C$ and $-10 \mu C$ are separated by a distance of $2.0 \mathrm{cm}$in air. (i) Calculate the potential energy of the system, assuming the zero of the potential energy to be at infinity. (ii) Draw an equipotential surface of the system.

Two-point charges $A$ and $B$ of values $+15 \mu C$ and $+9 \mu C$ are kept $18 \mathrm{cm}$ apart in the air. Calculate the work done when the charge $B$ is moved by $3 \mathrm{cm}$towards $A$.

Two point charges $20\times {10}^{-6}\mathrm{C}$ and $-4\times {10}^{-6}\mathrm{C}$ are separated by a distance of $50 \mathrm{cm}$ in air. (i)Find the point on the line joining the charges, where the electric potential is zero. (ii) Also, find the electrostatic potential energy of the system.

Two charges, of magnitude $5 nC$and $-2\mathrm{ }\mathrm{nC},$ are placed at points $(2 \mathrm{cm},0,0)$ and $(x \mathrm{cm},0,0)$in a region of space, where there is no other external field. If the electrostatic potential energy of the system is $-0.5 \mu \mathrm{J}$, what is the value of  $x$?

Three-point charges are arranged, as shown in Figure. What is their mutual potential energy? Take $q=1.0\times {10}^{-4}C$ and $a=10 \mathrm{cm}.$