Calculate the potential at the centre of a square $ABCD$ of each side $\sqrt{2} \mathrm{m}$ due to charges $2,-2,-3$ and $6 \mu C$ at four corners of it.

Charges of $+1.0\times {10}^{-11}\mathrm{C},-2.0\times {10}^{-11}\mathrm{ }\mathrm{C},+1.0\times {10}^{-11}\mathrm{ }\mathrm{C}$ are placed respectively at the corners $B, C$ and $D$ of a rectangle $ABCD$. Determine the potential at the corner $A$. Given $AB=4 \mathrm{cm}$ and $BC=3 \mathrm{cm}$.

Positive charges of $6,12$ and $24 \mathrm{nC}$ are placed at the three vertices of a square. What charge must be placed at the fourth vertex so that total potential at the centre of the square is zero?

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 $(2\mathrm{m},2\mathrm{m}).$