A charge $q=+1 \mu C$ is held at $O$ between the points $A$ and $B$ such that $AO=2 \mathrm{m}$ and $BO=1 \mathrm{m}$, as shown in Fig. (a). Calculate the potential difference  $\left(V_A-V_B\right)$. What will be the value of the potential difference $\left(V_A-V_B\right)$ if the position of $B$ is changed, as shown in Fig (b)

 

Two small spheres of radius $\text{'}a\text{'}$ each carrying charges $+q$ and $-q$ are placed at points $A$ and $B, d$ distance apart. Calculate the potential difference between points $A$ and $B$.

The sides of rectangle $ABCD$ are $15 \mathrm{cm}$ and $5 \mathrm{cm}$, as shown in Fig. Point charges of $-5 \mu C$ and $+2 \mu C$ are placed at the vertices $B$ and $D$ respectively. Calculate electric potentials at the vertices $A$ and $C$. Also calculate the work done in carrying a charge of $3 \mu C$ from $A$ to $C$.

Charges of $2.0\times {10}^{-6}\mathrm{ }\mathrm{C}$  and $1.0\times {10}^{-6}\mathrm{ }\mathrm{C}$ are placed at the corners $A$ and $B$ of a square of side $5.0 \mathrm{cm}$, as shown in Fig. How much work will be done in moving a charge of $1.0\times {10}^{-6}\mathrm{ }\mathrm{C}$ from $C$ to $D$ against the electric field?

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?