Two equal charges, $2.0\times {10}^{-7}\mathrm{ }\mathrm{C}$ each are held fixed at a separation of $20 \mathrm{cm}$. A third charge of equal magnitude is placed midway between the two charges. It is now moved to a point $20 \mathrm{cm}$ from both the charges. How much work is done by the electric field during the process?

$ABC$ is a right-angled triangle, where $AB$ and $BC$ are $25 \mathrm{cm}$ and $60 \mathrm{cm}$ respectively; a metal sphere of $2 \mathrm{cm}$ radius charged to a potential of $9\times {10}^5 \mathrm{V}$ is placed at $B$. Find the amount of work done in carrying a positive charge of $1 C$ from $C$ to $A$.

A uniform electric field of $20 {\mathrm{NC}}^{-1}$ exists in the vertically downward direction, Determine the increase in the electric potential as one goes up through a height of $50 \mathrm{cm}$.

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 $A$.