Two-point charges $q$ and $-2 q$ are kept $\text{'}d\text{'}$ distance apart. Find the location of the point relative to charge $\text{'}q\text{'}$ at which potential due to this system of charges is zero.

Two-point charges, one of +100 µC and another of -400 µC, are kept 30 cm apart. Find the points of zero potential on the line joining the two charges (assume the potential at infinity to be zero).

[3 Marks]

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 $BC=3 \mathrm{cm}$.